TSTP Solution File: PHI003^2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : PHI003^2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 16:47:18 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 56
% Syntax : Number of formulae : 98 ( 42 unt; 30 typ; 23 def)
% Number of atoms : 289 ( 88 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 522 ( 146 ~; 61 |; 4 &; 308 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 223 ( 223 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 3 con; 0-4 aty)
% Number of variables : 172 ( 59 ^ 109 !; 4 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
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_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_positive,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(tp_rel,type,
rel: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY6,type,
sK2_SY6: ( mu > $i > $o ) > $i > $i ).
thf(tp_sK3_SY13,type,
sK3_SY13: $i > ( mu > $i > $o ) > mu ).
thf(tp_sK4_SY14,type,
sK4_SY14: mu > $i > mu > $i > $o ).
thf(god,definition,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',god) ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
& ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mbox_generic) ).
thf(mdia,definition,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mdia_generic) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_ind) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
<=> ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( ^ [W: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Psi @ W )
=> ( Phi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
mvalid @ ( positive @ god ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA3) ).
thf(2,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( positive @ Phi )
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT1) ).
thf(3,conjecture,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corC) ).
thf(4,negated_conjecture,
( ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( positive @ Phi )
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( Phi @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(7,plain,
( ( mvalid @ ( positive @ god ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(8,plain,
( ( ~ ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
( ~ ( positive @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( rel @ SX0 @ SX2 )
| ~ ~ ! [SX3: mu] :
~ ( SX1 @ SX3 @ SX2 ) ) ) )
= $true ),
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,mtrue,mvalid,mxor]) ).
thf(10,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)],[8,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,mtrue,mvalid,mxor]) ).
thf(11,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX2 )
| ( SX3 @ SX1 @ SX2 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[7,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,mtrue,mvalid,mxor]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY0: mu > $i > $o] :
( ~ ( positive @ SY0 @ SV1 )
| ~ ! [SY1: $i] :
~ ~ ( ~ ( rel @ SV1 @ SY1 )
| ~ ~ ! [SX3: mu] :
~ ( SY0 @ SX3 @ SY1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( rel @ SX0 @ SX1 )
| ~ ~ ! [SX2: mu] :
~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX1 )
| ( SX3 @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV2: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX2 )
| ( SX3 @ SX1 @ SX2 ) )
@ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ~ ( positive @ SV3 @ SV1 )
| ~ ! [SY6: $i] :
~ ~ ( ~ ( rel @ SV1 @ SY6 )
| ~ ~ ! [SY7: mu] :
~ ( SV3 @ SY7 @ SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ~ ! [SY8: $i] :
~ ~ ( ~ ( rel @ sK1_SX0 @ SY8 )
| ~ ~ ! [SX2: mu] :
~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SY8 )
| ( SX3 @ SX2 @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(17,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ( positive @ SV3 @ SV1 ) )
= $true )
| ( ( ~ ! [SY6: $i] :
~ ~ ( ~ ( rel @ SV1 @ SY6 )
| ~ ~ ! [SY7: mu] :
~ ( SV3 @ SY7 @ SY6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY8: $i] :
~ ~ ( ~ ( rel @ sK1_SX0 @ SY8 )
| ~ ~ ! [SX2: mu] :
~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SY8 )
| ( SX3 @ SX2 @ SY8 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( ~ ! [SY6: $i] :
~ ~ ( ~ ( rel @ SV1 @ SY6 )
| ~ ~ ! [SY7: mu] :
~ ( SV3 @ SY7 @ SY6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( rel @ sK1_SX0 @ SV4 )
| ~ ~ ! [SY11: mu] :
~ ! [SY12: mu > $i > $o] :
( ~ ( positive @ SY12 @ SV4 )
| ( SY12 @ SY11 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV3: mu > $i > $o,SV1: $i] :
( ( ( ! [SY6: $i] :
~ ~ ( ~ ( rel @ SV1 @ SY6 )
| ~ ~ ! [SY7: mu] :
~ ( SV3 @ SY7 @ SY6 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV4: $i] :
( ( ~ ( ~ ( rel @ sK1_SX0 @ SV4 )
| ~ ~ ! [SY11: mu] :
~ ! [SY12: mu > $i > $o] :
( ~ ( positive @ SY12 @ SV4 )
| ( SY12 @ SY11 @ SV4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV3: mu > $i > $o,SV1: $i] :
( ( ( ~ ~ ( ~ ( rel @ SV1 @ ( sK2_SY6 @ SV3 @ SV1 ) )
| ~ ~ ! [SY13: mu] :
~ ( SV3 @ SY13 @ ( sK2_SY6 @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(24,plain,
! [SV4: $i] :
( ( ~ ( rel @ sK1_SX0 @ SV4 )
| ~ ~ ! [SY11: mu] :
~ ! [SY12: mu > $i > $o] :
( ~ ( positive @ SY12 @ SV4 )
| ( SY12 @ SY11 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
! [SV3: mu > $i > $o,SV1: $i] :
( ( ( ~ ( ~ ( rel @ SV1 @ ( sK2_SY6 @ SV3 @ SV1 ) )
| ~ ~ ! [SY13: mu] :
~ ( SV3 @ SY13 @ ( sK2_SY6 @ SV3 @ SV1 ) ) ) )
= $true )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV4: $i] :
( ( ( ~ ( rel @ sK1_SX0 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY11: mu] :
~ ! [SY12: mu > $i > $o] :
( ~ ( positive @ SY12 @ SV4 )
| ( SY12 @ SY11 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV3: mu > $i > $o,SV1: $i] :
( ( ( ~ ( rel @ SV1 @ ( sK2_SY6 @ SV3 @ SV1 ) )
| ~ ~ ! [SY13: mu] :
~ ( SV3 @ SY13 @ ( sK2_SY6 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( rel @ sK1_SX0 @ SV4 )
= $false )
| ( ( ~ ~ ! [SY11: mu] :
~ ! [SY12: mu > $i > $o] :
( ~ ( positive @ SY12 @ SV4 )
| ( SY12 @ SY11 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: mu > $i > $o,SV1: $i] :
( ( ( ~ ( rel @ SV1 @ ( sK2_SY6 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ~ ! [SY13: mu] :
~ ( SV3 @ SY13 @ ( sK2_SY6 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: $i] :
( ( ( ~ ! [SY11: mu] :
~ ! [SY12: mu > $i > $o] :
( ~ ( positive @ SY12 @ SV4 )
| ( SY12 @ SY11 @ SV4 ) ) )
= $false )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV3: mu > $i > $o,SV1: $i] :
( ( ( rel @ SV1 @ ( sK2_SY6 @ SV3 @ SV1 ) )
= $true )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ! [SY13: mu] :
~ ( SV3 @ SY13 @ ( sK2_SY6 @ SV3 @ SV1 ) ) )
= $true )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV4: $i] :
( ( ( ! [SY11: mu] :
~ ! [SY12: mu > $i > $o] :
( ~ ( positive @ SY12 @ SV4 )
| ( SY12 @ SY11 @ SV4 ) ) )
= $true )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ( ! [SY13: mu] :
~ ( SV3 @ SY13 @ ( sK2_SY6 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV5: mu,SV4: $i] :
( ( ( ~ ! [SY14: mu > $i > $o] :
( ~ ( positive @ SY14 @ SV4 )
| ( SY14 @ SV5 @ SV4 ) ) )
= $true )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ( SV3 @ ( sK3_SY13 @ SV1 @ SV3 ) @ ( sK2_SY6 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(38,plain,
! [SV5: mu,SV4: $i] :
( ( ( ! [SY14: mu > $i > $o] :
( ~ ( positive @ SY14 @ SV4 )
| ( SY14 @ SV5 @ SV4 ) ) )
= $false )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ( SV3 @ ( sK3_SY13 @ SV1 @ SV3 ) @ ( sK2_SY6 @ SV3 @ SV1 ) )
= $true )
| ( ( positive @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(40,plain,
! [SV4: $i,SV5: mu] :
( ( ( ~ ( positive @ ( sK4_SY14 @ SV5 @ SV4 ) @ SV4 )
| ( sK4_SY14 @ SV5 @ SV4 @ SV5 @ SV4 ) )
= $false )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(41,plain,
! [SV4: $i,SV5: mu] :
( ( ( ~ ( positive @ ( sK4_SY14 @ SV5 @ SV4 ) @ SV4 ) )
= $false )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(42,plain,
! [SV4: $i,SV5: mu] :
( ( ( sK4_SY14 @ SV5 @ SV4 @ SV5 @ SV4 )
= $false )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV4: $i,SV5: mu] :
( ( ( positive @ ( sK4_SY14 @ SV5 @ SV4 ) @ SV4 )
= $true )
| ( ( rel @ sK1_SX0 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,43,42,39,32]) ).
thf(45,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PHI003^2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 02:04:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 2
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 3646
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.19/0.40
% 0.19/0.40 ********************************
% 0.19/0.40 * All subproblems solved! *
% 0.19/0.40 ********************************
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40
% 0.19/0.40 %**** Beginning of derivation protocol ****
% 0.19/0.40 % SZS output start CNFRefutation
% See solution above
% 0.19/0.40
% 0.19/0.40 %**** End of derivation protocol ****
% 0.19/0.40 %**** no. of clauses in derivation: 45 ****
% 0.19/0.40 %**** clause counter: 44 ****
% 0.19/0.40
% 0.19/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------