%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PHI002^1 : 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 10:36:09 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of formulae : 106 ( 71 unt; 0 typ; 25 def)
% Number of atoms : 535 ( 146 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1211 ( 192 ~; 131 |; 18 &; 852 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 247 ( 247 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 3 con; 0-3 aty)
% Number of variables : 338 ( 122 ^; 200 !; 16 ?; 338 :)
% 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_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_SY22,type,
sK1_SY22: $i ).
thf(tp_sK2_SY224,type,
sK2_SY224: mu > $i > $o ).
thf(tp_sK3_SY193,type,
sK3_SY193: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > $i ).
thf(tp_sK4_SY229,type,
sK4_SY229: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > mu ).
thf(essence,definition,
( essence
= ( ^ [Phi: mu > $i > $o,X: mu] :
( mand @ ( Phi @ X )
@ ( mforall_indset
@ ^ [Psi: mu > $i > $o] :
( mimplies @ ( Psi @ X )
@ ( mbox
@ ( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( Phi @ Y ) @ ( Psi @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD2) ).
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(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,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( mbox @ ( positive @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA4) ).
thf(3,axiom,
mvalid @ ( positive @ god ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA3) ).
thf(4,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mforall_indset
@ ^ [Psi: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ Phi )
@ ( mbox
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( Phi @ X ) @ ( Psi @ X ) ) ) ) )
@ ( positive @ Psi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA2) ).
thf(5,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) )
@ ( mnot @ ( positive @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1) ).
thf(6,conjecture,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( positive @ Phi )
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT1) ).
thf(7,negated_conjecture,
( ( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( positive @ Phi )
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( Phi @ X ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [SY22: $i,SY23: mu > $i > $o] :
( ( positive @ SY23 @ SY22 )
=> ? [SY24: $i] :
( ( rel @ SY22 @ SY24 )
& ? [SY17: mu] : ( SY23 @ SY17 @ SY24 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7,essence,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,necessary_existence]) ).
thf(9,plain,
( ( ! [SY31: $i] :
( positive
@ ^ [SY32: mu,SY83: $i] :
! [SY84: mu > $i > $o] :
( ( ( SY84 @ SY32 @ SY83 )
& ! [SY99: mu > $i > $o] :
( ( SY99 @ SY32 @ SY83 )
=> ! [SY100: $i] :
( ~ ( rel @ SY83 @ SY100 )
| ! [SY88: mu] :
( ( SY84 @ SY88 @ SY100 )
=> ( SY99 @ SY88 @ SY100 ) ) ) ) )
=> ! [SY102: $i] :
( ~ ( rel @ SY83 @ SY102 )
| ? [SY96: mu] : ( SY84 @ SY96 @ SY102 ) ) )
@ SY31 ) )
= $true ),
inference(unfold_def,[status(thm)],[1,essence,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,necessary_existence]) ).
thf(10,plain,
( ( ! [SY127: $i,SY128: mu > $i > $o] :
( ( positive @ SY128 @ SY127 )
=> ! [SY129: $i] :
( ~ ( rel @ SY127 @ SY129 )
| ( positive @ SY128 @ SY129 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,essence,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,necessary_existence]) ).
thf(11,plain,
( ( ! [SY134: $i] :
( positive
@ ^ [SY135: mu,SY140: $i] :
! [SY141: mu > $i > $o] :
( ( positive @ SY141 @ SY140 )
=> ( SY141 @ SY135 @ SY140 ) )
@ SY134 ) )
= $true ),
inference(unfold_def,[status(thm)],[3,essence,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,necessary_existence]) ).
thf(12,plain,
( ( ! [SY190: $i,SY191: mu > $i > $o,SY192: mu > $i > $o] :
( ( ( positive @ SY191 @ SY190 )
& ! [SY193: $i] :
( ~ ( rel @ SY190 @ SY193 )
| ! [SY186: mu] :
( ( SY191 @ SY186 @ SY193 )
=> ( SY192 @ SY186 @ SY193 ) ) ) )
=> ( positive @ SY192 @ SY190 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,essence,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,necessary_existence]) ).
thf(13,plain,
( ( ! [SY216: $i,SY217: mu > $i > $o] :
( ( positive
@ ^ [SY212: mu,SY213: $i] :
~ ( SY217 @ SY212 @ SY213 )
@ SY216 )
<=> ~ ( positive @ SY217 @ SY216 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,essence,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,necessary_existence]) ).
thf(14,plain,
( ( ! [SY224: mu > $i > $o] :
( ( positive @ SY224 @ sK1_SY22 )
=> ? [SY225: $i] :
( ( rel @ sK1_SY22 @ SY225 )
& ? [SY17: mu] : ( SY224 @ SY17 @ SY225 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ( positive @ sK2_SY224 @ sK1_SY22 )
=> ? [SY227: $i] :
( ( rel @ sK1_SY22 @ SY227 )
& ? [SY228: mu] : ( sK2_SY224 @ SY228 @ SY227 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( positive @ sK2_SY224 @ sK1_SY22 )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(17,plain,
( ( ? [SY227: $i] :
( ( rel @ sK1_SY22 @ SY227 )
& ? [SY228: mu] : ( sK2_SY224 @ SY228 @ SY227 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ? [SY227: $i] :
( ( rel @ sK1_SY22 @ SY227 )
& ? [SY228: mu] : ( sK2_SY224 @ SY228 @ SY227 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [SY227: $i] :
( ! [SY228: mu] :
~ ( sK2_SY224 @ SY228 @ SY227 )
| ~ ( rel @ sK1_SY22 @ SY227 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(20,plain,
( ( ! [SY127: $i,SY128: mu > $i > $o] :
( ~ ( positive @ SY128 @ SY127 )
| ! [SY129: $i] :
( ~ ( rel @ SY127 @ SY129 )
| ( positive @ SY128 @ SY129 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(21,plain,
( ( ! [SY190: $i,SY191: mu > $i > $o,SY192: mu > $i > $o] :
( ( ( rel @ SY190 @ ( sK3_SY193 @ SY192 @ SY191 @ SY190 ) )
& ( SY191 @ ( sK4_SY229 @ SY192 @ SY191 @ SY190 ) @ ( sK3_SY193 @ SY192 @ SY191 @ SY190 ) )
& ~ ( SY192 @ ( sK4_SY229 @ SY192 @ SY191 @ SY190 ) @ ( sK3_SY193 @ SY192 @ SY191 @ SY190 ) ) )
| ~ ( positive @ SY191 @ SY190 )
| ( positive @ SY192 @ SY190 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(22,plain,
( ( ! [SY216: $i,SY217: mu > $i > $o] :
( ~ ( positive
@ ^ [SY212: mu,SY213: $i] :
~ ( SY217 @ SY212 @ SY213 )
@ SY216 )
| ~ ( positive @ SY217 @ SY216 ) )
& ! [SY216: $i,SY217: mu > $i > $o] :
( ( positive @ SY217 @ SY216 )
| ( positive
@ ^ [SY212: mu,SY213: $i] :
~ ( SY217 @ SY212 @ SY213 )
@ SY216 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(23,plain,
( ( ! [SY216: $i,SY217: mu > $i > $o] :
( ~ ( positive
@ ^ [SY212: mu,SY213: $i] :
~ ( SY217 @ SY212 @ SY213 )
@ SY216 )
| ~ ( positive @ SY217 @ SY216 ) )
& ! [SY216: $i,SY217: mu > $i > $o] :
( ( positive @ SY217 @ SY216 )
| ( positive
@ ^ [SY212: mu,SY213: $i] :
~ ( SY217 @ SY212 @ SY213 )
@ SY216 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [SY190: $i,SY191: mu > $i > $o,SY192: mu > $i > $o] :
( ( ( rel @ SY190 @ ( sK3_SY193 @ SY192 @ SY191 @ SY190 ) )
& ( SY191 @ ( sK4_SY229 @ SY192 @ SY191 @ SY190 ) @ ( sK3_SY193 @ SY192 @ SY191 @ SY190 ) )
& ~ ( SY192 @ ( sK4_SY229 @ SY192 @ SY191 @ SY190 ) @ ( sK3_SY193 @ SY192 @ SY191 @ SY190 ) ) )
| ~ ( positive @ SY191 @ SY190 )
| ( positive @ SY192 @ SY190 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SY134: $i] :
( positive
@ ^ [SY135: mu,SY140: $i] :
! [SY141: mu > $i > $o] :
( ( positive @ SY141 @ SY140 )
=> ( SY141 @ SY135 @ SY140 ) )
@ SY134 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [SY127: $i,SY128: mu > $i > $o] :
( ~ ( positive @ SY128 @ SY127 )
| ! [SY129: $i] :
( ~ ( rel @ SY127 @ SY129 )
| ( positive @ SY128 @ SY129 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ! [SY31: $i] :
( positive
@ ^ [SY32: mu,SY83: $i] :
! [SY84: mu > $i > $o] :
( ( ( SY84 @ SY32 @ SY83 )
& ! [SY99: mu > $i > $o] :
( ( SY99 @ SY32 @ SY83 )
=> ! [SY100: $i] :
( ~ ( rel @ SY83 @ SY100 )
| ! [SY88: mu] :
( ( SY84 @ SY88 @ SY100 )
=> ( SY99 @ SY88 @ SY100 ) ) ) ) )
=> ! [SY102: $i] :
( ~ ( rel @ SY83 @ SY102 )
| ? [SY96: mu] : ( SY84 @ SY96 @ SY102 ) ) )
@ SY31 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(28,plain,
( ( positive @ sK2_SY224 @ sK1_SY22 )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( ! [SY227: $i] :
( ! [SY228: mu] :
~ ( sK2_SY224 @ SY228 @ SY227 )
| ~ ( rel @ sK1_SY22 @ SY227 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ~ ( ~ ( SX3 @ SX1 @ SX2 )
| ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i] :
( ~ ( rel @ SX2 @ SX5 )
| ! [SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) ) ) )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[27,essence,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,necessary_existence]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o,SX2: mu > $i > $o] :
( ~ ( ~ ( rel @ SX0 @ ( sK3_SY193 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( SX1 @ ( sK4_SY229 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY193 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( SX2 @ ( sK4_SY229 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY193 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( positive @ SX1 @ SX0 )
| ( positive @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,essence,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,necessary_existence]) ).
thf(32,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)],[25,essence,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,necessary_existence]) ).
thf(33,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: mu > $i > $o] :
( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 )
| ~ ( positive @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: mu > $i > $o] :
( ( positive @ SX1 @ SX0 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,essence,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,necessary_existence]) ).
thf(34,plain,
! [SV1: $i] :
( ( ! [SY230: mu > $i > $o] :
( ~ ( positive @ SY230 @ SV1 )
| ! [SY231: $i] :
( ~ ( rel @ SV1 @ SY231 )
| ( positive @ SY230 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV2: $i] :
( ( ! [SY232: mu] :
~ ( sK2_SY224 @ SY232 @ SV2 )
| ~ ( rel @ sK1_SY22 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV3: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ~ ( ~ ( SX3 @ SX1 @ SX2 )
| ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i] :
( ~ ( rel @ SX2 @ SX5 )
| ! [SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) ) ) )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV4: $i] :
( ( ! [SY241: mu > $i > $o,SY242: mu > $i > $o] :
( ~ ( ~ ( rel @ SV4 @ ( sK3_SY193 @ SY242 @ SY241 @ SV4 ) )
| ~ ~ ( ~ ( SY241 @ ( sK4_SY229 @ SY242 @ SY241 @ SV4 ) @ ( sK3_SY193 @ SY242 @ SY241 @ SV4 ) )
| ~ ~ ( SY242 @ ( sK4_SY229 @ SY242 @ SY241 @ SV4 ) @ ( sK3_SY193 @ SY242 @ SY241 @ SV4 ) ) ) )
| ~ ( positive @ SY241 @ SV4 )
| ( positive @ SY242 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV5: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX2 )
| ( SX3 @ SX1 @ SX2 ) )
@ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ~ ! [SX0: $i,SX1: mu > $i > $o] :
( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 )
| ~ ( positive @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: mu > $i > $o] :
( ( positive @ SX1 @ SX0 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV1: $i,SV6: mu > $i > $o] :
( ( ~ ( positive @ SV6 @ SV1 )
| ! [SY246: $i] :
( ~ ( rel @ SV1 @ SY246 )
| ( positive @ SV6 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV2: $i] :
( ( ( ! [SY232: mu] :
~ ( sK2_SY224 @ SY232 @ SV2 ) )
= $true )
| ( ( ~ ( rel @ sK1_SY22 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV7: mu > $i > $o,SV4: $i] :
( ( ! [SY247: mu > $i > $o] :
( ~ ( ~ ( rel @ SV4 @ ( sK3_SY193 @ SY247 @ SV7 @ SV4 ) )
| ~ ~ ( ~ ( SV7 @ ( sK4_SY229 @ SY247 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SY247 @ SV7 @ SV4 ) )
| ~ ~ ( SY247 @ ( sK4_SY229 @ SY247 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SY247 @ SV7 @ SV4 ) ) ) )
| ~ ( positive @ SV7 @ SV4 )
| ( positive @ SY247 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
( ( ~ ! [SX0: $i,SX1: mu > $i > $o] :
( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 )
| ~ ( positive @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ! [SX0: $i,SX1: mu > $i > $o] :
( ( positive @ SX1 @ SX0 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV1: $i,SV6: mu > $i > $o] :
( ( ( ~ ( positive @ SV6 @ SV1 ) )
= $true )
| ( ( ! [SY246: $i] :
( ~ ( rel @ SV1 @ SY246 )
| ( positive @ SV6 @ SY246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV2: $i,SV8: mu] :
( ( ( ~ ( sK2_SY224 @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ( rel @ sK1_SY22 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV7: mu > $i > $o,SV9: mu > $i > $o,SV4: $i] :
( ( ~ ( ~ ( rel @ SV4 @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) ) )
| ~ ( positive @ SV7 @ SV4 )
| ( positive @ SV9 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 )
| ~ ( positive @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
( ( positive @ SX1 @ SX0 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV1: $i,SV6: mu > $i > $o] :
( ( ( positive @ SV6 @ SV1 )
= $false )
| ( ( ! [SY246: $i] :
( ~ ( rel @ SV1 @ SY246 )
| ( positive @ SV6 @ SY246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: $i,SV8: mu] :
( ( ( sK2_SY224 @ SV8 @ SV2 )
= $false )
| ( ( ~ ( rel @ sK1_SY22 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV7: mu > $i > $o,SV9: mu > $i > $o,SV4: $i] :
( ( ( ~ ( ~ ( rel @ SV4 @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) ) )
| ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV10: $i] :
( ( ! [SY248: mu > $i > $o] :
( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY248 @ SX2 @ SX3 )
@ SV10 )
| ~ ( positive @ SY248 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV11: $i] :
( ( ! [SY251: mu > $i > $o] :
( ( positive @ SY251 @ SV11 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY251 @ SX2 @ SX3 )
@ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV6: mu > $i > $o,SV12: $i,SV1: $i] :
( ( ( ~ ( rel @ SV1 @ SV12 )
| ( positive @ SV6 @ SV12 ) )
= $true )
| ( ( positive @ SV6 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV8: mu,SV2: $i] :
( ( ( rel @ sK1_SY22 @ SV2 )
= $false )
| ( ( sK2_SY224 @ SV8 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV7: mu > $i > $o,SV9: mu > $i > $o,SV4: $i] :
( ( ( ~ ( ~ ( rel @ SV4 @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV10: $i,SV13: mu > $i > $o] :
( ( ~ ( positive
@ ^ [SY254: mu,SY255: $i] :
~ ( SV13 @ SY254 @ SY255 )
@ SV10 )
| ~ ( positive @ SV13 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV11: $i,SV14: mu > $i > $o] :
( ( ( positive @ SV14 @ SV11 )
| ( positive
@ ^ [SY256: mu,SY257: $i] :
~ ( SV14 @ SY256 @ SY257 )
@ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV6: mu > $i > $o,SV12: $i,SV1: $i] :
( ( ( ~ ( rel @ SV1 @ SV12 ) )
= $true )
| ( ( positive @ SV6 @ SV12 )
= $true )
| ( ( positive @ SV6 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV7: mu > $i > $o,SV9: mu > $i > $o,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV10: $i,SV13: mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SY254: mu,SY255: $i] :
~ ( SV13 @ SY254 @ SY255 )
@ SV10 ) )
= $true )
| ( ( ~ ( positive @ SV13 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV11: $i,SV14: mu > $i > $o] :
( ( ( positive @ SV14 @ SV11 )
= $true )
| ( ( positive
@ ^ [SY256: mu,SY257: $i] :
~ ( SV14 @ SY256 @ SY257 )
@ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: mu > $i > $o,SV12: $i,SV1: $i] :
( ( ( rel @ SV1 @ SV12 )
= $false )
| ( ( positive @ SV6 @ SV12 )
= $true )
| ( ( positive @ SV6 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV7: mu > $i > $o,SV9: mu > $i > $o,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV4: $i,SV9: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ~ ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(67,plain,
! [SV10: $i,SV13: mu > $i > $o] :
( ( ( positive
@ ^ [SY254: mu,SY255: $i] :
~ ( SV13 @ SY254 @ SY255 )
@ SV10 )
= $false )
| ( ( ~ ( positive @ SV13 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV7: mu > $i > $o,SV9: mu > $i > $o,SV4: $i] :
( ( ( rel @ SV4 @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV4: $i,SV9: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(70,plain,
! [SV10: $i,SV13: mu > $i > $o] :
( ( ( positive @ SV13 @ SV10 )
= $false )
| ( ( positive
@ ^ [SY254: mu,SY255: $i] :
~ ( SV13 @ SY254 @ SY255 )
@ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV9: mu > $i > $o,SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( rel @ SV4 @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV4: $i,SV9: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV4: $i,SV9: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(74,plain,
! [SV4: $i,SV7: mu > $i > $o,SV9: mu > $i > $o] :
( ( ( ~ ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(75,plain,
! [SV4: $i,SV9: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(76,plain,
! [SV4: $i,SV7: mu > $i > $o,SV9: mu > $i > $o] :
( ( ( ~ ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(77,plain,
! [SV9: mu > $i > $o,SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( SV7 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(78,plain,
! [SV4: $i,SV7: mu > $i > $o,SV9: mu > $i > $o] :
( ( ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(79,plain,
! [SV9: mu > $i > $o,SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( SV9 @ ( sK4_SY229 @ SV9 @ SV7 @ SV4 ) @ ( sK3_SY193 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( positive @ SV9 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(80,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,79,77,71,70,64,63,56,38,36]) ).
thf(81,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI002^1 : 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
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 13:51:24 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 5
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 4142
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .....
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:80,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24
% 0.08/0.24 %**** End of derivation protocol ****
% 0.08/0.24 %**** no. of clauses in derivation: 81 ****
% 0.08/0.24 %**** clause counter: 80 ****
% 0.08/0.24
% 0.08/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:80,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------