%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PHI006^5 : TPTP v9.3.1. Released v6.4.0.
% 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 : n026.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 10:36:11 AM UTC 2026
% Result : Theorem 90.02s 15.39s
% Output : CNFRefutation 90.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 26
% Syntax : Number of formulae : 91 ( 45 unt; 0 typ; 22 def)
% Number of atoms : 506 ( 156 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1081 ( 153 ~; 113 |; 6 &; 796 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 235 ( 235 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 2 con; 0-3 aty)
% Number of variables : 398 ( 217 ^; 175 !; 6 ?; 398 :)
% 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_mdia,type,
mdia: ( $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_sK1_SY106,type,
sK1_SY106: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > $i ).
thf(tp_sK2_SY167,type,
sK2_SY167: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > mu ).
thf(essence,definition,
( essence
= ( ^ [Phi: mu > $i > $o,X: mu] :
( 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(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
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] : ( Phi @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: $i > $o,W: $i] :
? [V: $i] : ( Phi @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
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] :
( 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(3,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( mnot @ ( positive @ Phi ) )
@ ( positive
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1b) ).
thf(4,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies
@ ( positive
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) )
@ ( mnot @ ( positive @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1a) ).
thf(8,plain,
( ( ! [SY1: $i] :
( positive
@ ^ [SY2: mu,SY49: $i] :
! [SY50: mu > $i > $o] :
( ! [SY57: mu > $i > $o] :
( ( SY57 @ SY2 @ SY49 )
=> ! [SY53: $i,SY54: mu] :
( ( SY50 @ SY54 @ SY53 )
=> ( SY57 @ SY54 @ SY53 ) ) )
=> ! [SY55: $i] :
? [SY56: mu] : ( SY50 @ SY56 @ SY55 ) )
@ SY1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1,essence,mand,mbox,mdia,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,
( ( ! [SY111: $i,SY112: mu > $i > $o,SY113: mu > $i > $o] :
( ( ( positive @ SY112 @ SY111 )
& ! [SY106: $i,SY107: mu] :
( ( SY112 @ SY107 @ SY106 )
=> ( SY113 @ SY107 @ SY106 ) ) )
=> ( positive @ SY113 @ SY111 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,essence,mand,mbox,mdia,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,
( ( ! [SY135: $i,SY136: mu > $i > $o] :
( ~ ( positive @ SY136 @ SY135 )
=> ( positive
@ ^ [SY131: mu,SY132: $i] :
~ ( SY136 @ SY131 @ SY132 )
@ SY135 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,essence,mand,mbox,mdia,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,
( ( ! [SY159: $i,SY160: mu > $i > $o] :
( ( positive
@ ^ [SY155: mu,SY156: $i] :
~ ( SY160 @ SY155 @ SY156 )
@ SY159 )
=> ~ ( positive @ SY160 @ SY159 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,essence,mand,mbox,mdia,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,
( ( ! [SY111: $i,SY112: mu > $i > $o,SY113: mu > $i > $o] :
( ( ( SY112 @ ( sK2_SY167 @ SY113 @ SY112 @ SY111 ) @ ( sK1_SY106 @ SY113 @ SY112 @ SY111 ) )
& ~ ( SY113 @ ( sK2_SY167 @ SY113 @ SY112 @ SY111 ) @ ( sK1_SY106 @ SY113 @ SY112 @ SY111 ) ) )
| ~ ( positive @ SY112 @ SY111 )
| ( positive @ SY113 @ SY111 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(14,plain,
( ( ! [SY135: $i,SY136: mu > $i > $o] :
( ( positive @ SY136 @ SY135 )
| ( positive
@ ^ [SY131: mu,SY132: $i] :
~ ( SY136 @ SY131 @ SY132 )
@ SY135 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(15,plain,
( ( ! [SY159: $i,SY160: mu > $i > $o] :
( ~ ( positive
@ ^ [SY155: mu,SY156: $i] :
~ ( SY160 @ SY155 @ SY156 )
@ SY159 )
| ~ ( positive @ SY160 @ SY159 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(16,plain,
( ( ! [SY159: $i,SY160: mu > $i > $o] :
( ~ ( positive
@ ^ [SY155: mu,SY156: $i] :
~ ( SY160 @ SY155 @ SY156 )
@ SY159 )
| ~ ( positive @ SY160 @ SY159 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [SY135: $i,SY136: mu > $i > $o] :
( ( positive @ SY136 @ SY135 )
| ( positive
@ ^ [SY131: mu,SY132: $i] :
~ ( SY136 @ SY131 @ SY132 )
@ SY135 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [SY111: $i,SY112: mu > $i > $o,SY113: mu > $i > $o] :
( ( ( SY112 @ ( sK2_SY167 @ SY113 @ SY112 @ SY111 ) @ ( sK1_SY106 @ SY113 @ SY112 @ SY111 ) )
& ~ ( SY113 @ ( sK2_SY167 @ SY113 @ SY112 @ SY111 ) @ ( sK1_SY106 @ SY113 @ SY112 @ SY111 ) ) )
| ~ ( positive @ SY112 @ SY111 )
| ( positive @ SY113 @ SY111 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SY1: $i] :
( positive
@ ^ [SY2: mu,SY49: $i] :
! [SY50: mu > $i > $o] :
( ! [SY57: mu > $i > $o] :
( ( SY57 @ SY2 @ SY49 )
=> ! [SY53: $i,SY54: mu] :
( ( SY50 @ SY54 @ SY53 )
=> ( SY57 @ SY54 @ SY53 ) ) )
=> ! [SY55: $i] :
? [SY56: mu] : ( SY50 @ SY56 @ SY55 ) )
@ SY1 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i,SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) )
| ! [SX4: $i] :
~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[19,essence,mand,mbox,mdia,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(22,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o,SX2: mu > $i > $o] :
( ~ ( ~ ( SX1 @ ( sK2_SY167 @ SX2 @ SX1 @ SX0 ) @ ( sK1_SY106 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( SX2 @ ( sK2_SY167 @ SX2 @ SX1 @ SX0 ) @ ( sK1_SY106 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( positive @ SX1 @ SX0 )
| ( positive @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,essence,mand,mbox,mdia,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(23,plain,
! [SV1: $i] :
( ( ! [SY168: mu > $i > $o] :
( ~ ( positive
@ ^ [SY155: mu,SY156: $i] :
~ ( SY168 @ SY155 @ SY156 )
@ SV1 )
| ~ ( positive @ SY168 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV2: $i] :
( ( ! [SY171: mu > $i > $o] :
( ( positive @ SY171 @ SV2 )
| ( positive
@ ^ [SY131: mu,SY132: $i] :
~ ( SY171 @ SY131 @ SY132 )
@ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(26,plain,
! [SV3: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i,SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) )
| ! [SX4: $i] :
~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) )
@ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV4: $i] :
( ( ! [SY182: mu > $i > $o,SY183: mu > $i > $o] :
( ~ ( ~ ( SY182 @ ( sK2_SY167 @ SY183 @ SY182 @ SV4 ) @ ( sK1_SY106 @ SY183 @ SY182 @ SV4 ) )
| ~ ~ ( SY183 @ ( sK2_SY167 @ SY183 @ SY182 @ SV4 ) @ ( sK1_SY106 @ SY183 @ SY182 @ SV4 ) ) )
| ~ ( positive @ SY182 @ SV4 )
| ( positive @ SY183 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ~ ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
| ~ ( positive @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( positive @ SV6 @ SV2 )
| ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ! [SY188: mu > $i > $o] :
( ~ ( ~ ( SV7 @ ( sK2_SY167 @ SY188 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SY188 @ SV7 @ SV4 ) )
| ~ ~ ( SY188 @ ( sK2_SY167 @ SY188 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SY188 @ SV7 @ SV4 ) ) )
| ~ ( positive @ SV7 @ SV4 )
| ( positive @ SY188 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) )
= $true )
| ( ( ~ ( positive @ SV5 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( positive @ SV6 @ SV2 )
= $true )
| ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: $i,SV8: mu > $i > $o,SV7: mu > $i > $o] :
( ( ~ ( ~ ( SV7 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
| ~ ~ ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) ) )
| ~ ( positive @ SV7 @ SV4 )
| ( positive @ SV8 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false )
| ( ( ~ ( positive @ SV5 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV4: $i,SV8: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ( ~ ( SV7 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
| ~ ~ ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) ) )
| ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( positive @ SV5 @ SV1 )
= $false )
| ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV4: $i,SV8: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ( ~ ( SV7 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
| ~ ~ ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV4: $i,SV8: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ( SV7 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
| ~ ~ ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV4: $i,SV8: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( ~ ( SV7 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(40,plain,
! [SV4: $i,SV7: mu > $i > $o,SV8: mu > $i > $o] :
( ( ( ~ ~ ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV4: $i,SV8: mu > $i > $o,SV7: mu > $i > $o] :
( ( ( SV7 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
! [SV4: $i,SV7: mu > $i > $o,SV8: mu > $i > $o] :
( ( ( ~ ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) ) )
= $true )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV8: mu > $i > $o,SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( SV7 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV4: $i,SV7: mu > $i > $o,SV8: mu > $i > $o] :
( ( ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
= $false )
| ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV8: mu > $i > $o,SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( SV8 @ ( sK2_SY167 @ SV8 @ SV7 @ SV4 ) @ ( sK1_SY106 @ SV8 @ SV7 @ SV4 ) )
= $false )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( SV7
@ ( sK2_SY167
@ ^ [SX0: mu,SX1: $i] : $true
@ SV7
@ SV4 )
@ ( sK1_SY106
@ ^ [SX0: mu,SX1: $i] : $true
@ SV7
@ SV4 ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV8,$thf( ^ [SV14: mu] : ^ [SV15: $i] : $true ))]]) ).
thf(47,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( SV7
@ ( sK2_SY167
@ ^ [SX0: mu,SX1: $i] : $false
@ SV7
@ SV4 )
@ ( sK1_SY106
@ ^ [SX0: mu,SX1: $i] : $false
@ SV7
@ SV4 ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV8,$thf( ^ [SV12: mu] : ^ [SV13: $i] : $false ))]]) ).
thf(48,plain,
! [SV11: mu > $i > $o,SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( SV7
@ ( sK2_SY167
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV7
@ SV4 )
@ ( sK1_SY106
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV7
@ SV4 ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV8,$thf( ^ [SV9: mu] : ^ [SV10: $i] : ~ ( SV11 @ SV9 @ SV10 ) ))]]) ).
thf(50,plain,
! [SV8: mu > $i > $o,SV4: $i] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV4 )
= $false )
| ( $false = $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV7,$thf( ^ [SV19: mu] : ^ [SV20: $i] : $false ))]]) ).
thf(51,plain,
! [SV8: mu > $i > $o,SV4: $i,SV18: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 )
= $false )
| ( ( ~ ( SV18
@ ( sK2_SY167 @ SV8
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 )
@ ( sK1_SY106 @ SV8
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 ) ) )
= $true )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[43:[bind(SV7,$thf( ^ [SV16: mu] : ^ [SV17: $i] : ~ ( SV18 @ SV16 @ SV17 ) ))]]) ).
thf(52,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( $true = $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[45:[bind(SV8,$thf( ^ [SV14: mu] : ^ [SV15: $i] : $true ))]]) ).
thf(54,plain,
! [SV11: mu > $i > $o,SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( ~ ( SV11
@ ( sK2_SY167
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV7
@ SV4 )
@ ( sK1_SY106
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV7
@ SV4 ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[45:[bind(SV8,$thf( ^ [SV9: mu] : ^ [SV10: $i] : ~ ( SV11 @ SV9 @ SV10 ) ))]]) ).
thf(55,plain,
! [SV8: mu > $i > $o,SV4: $i] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV4 )
= $false )
| ( ( SV8
@ ( sK2_SY167 @ SV8
@ ^ [SX0: mu,SX1: $i] : $true
@ SV4 )
@ ( sK1_SY106 @ SV8
@ ^ [SX0: mu,SX1: $i] : $true
@ SV4 ) )
= $false )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[45:[bind(SV7,$thf( ^ [SV21: mu] : ^ [SV22: $i] : $true ))]]) ).
thf(56,plain,
! [SV8: mu > $i > $o,SV4: $i] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV4 )
= $false )
| ( ( SV8
@ ( sK2_SY167 @ SV8
@ ^ [SX0: mu,SX1: $i] : $false
@ SV4 )
@ ( sK1_SY106 @ SV8
@ ^ [SX0: mu,SX1: $i] : $false
@ SV4 ) )
= $false )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[45:[bind(SV7,$thf( ^ [SV19: mu] : ^ [SV20: $i] : $false ))]]) ).
thf(57,plain,
! [SV8: mu > $i > $o,SV4: $i,SV18: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 )
= $false )
| ( ( SV8
@ ( sK2_SY167 @ SV8
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 )
@ ( sK1_SY106 @ SV8
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 ) )
= $false )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(prim_subst,[status(thm)],[45:[bind(SV7,$thf( ^ [SV16: mu] : ^ [SV17: $i] : ~ ( SV18 @ SV16 @ SV17 ) ))]]) ).
thf(58,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true )
| ( ( ( positive @ SV6 @ SV2 )
= ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[32]) ).
thf(59,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false )
| ( ( ( positive @ SV5 @ SV1 )
= ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[36]) ).
thf(60,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( ~ ( ( positive @ SV6 @ SV2 )
| ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 ) )
| ~ ( ~ ( positive @ SV6 @ SV2 )
| ~ ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 ) ) )
= $false )
| ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( ~ ( ( positive @ SV5 @ SV1 )
| ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) )
| ~ ( ~ ( positive @ SV5 @ SV1 )
| ~ ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) ) )
= $false )
| ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[59]) ).
thf(64,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( ~ ( ( positive @ SV6 @ SV2 )
| ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 ) ) )
= $false )
| ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( ~ ( ~ ( positive @ SV5 @ SV1 )
| ~ ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) ) )
= $false )
| ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( ( positive @ SV6 @ SV2 )
| ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 ) )
= $true )
| ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( ~ ( positive @ SV5 @ SV1 )
| ~ ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) )
= $true )
| ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( positive @ SV6 @ SV2 )
= $true )
| ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true )
| ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( ~ ( positive @ SV5 @ SV1 ) )
= $true )
| ( ( ~ ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) )
= $true )
| ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( positive @ SV5 @ SV1 )
= $false )
| ( ( ~ ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 ) )
= $true )
| ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $false )
| ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(80,plain,
! [SV4: $i,SV8: mu > $i > $o,SV18: mu > $i > $o] :
( ( ( SV18
@ ( sK2_SY167 @ SV8
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 )
@ ( sK1_SY106 @ SV8
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 )
@ SV4 )
= $false )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(81,plain,
! [SV4: $i,SV7: mu > $i > $o,SV11: mu > $i > $o] :
( ( ( SV11
@ ( sK2_SY167
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV7
@ SV4 )
@ ( sK1_SY106
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV7
@ SV4 ) )
= $true )
| ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV11 @ SX0 @ SX1 )
@ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(82,plain,
! [SV2: $i,SV6: mu > $i > $o] :
( ( ( positive @ SV6 @ SV2 )
= $true )
| ( ( positive
@ ^ [SY186: mu,SY187: $i] :
~ ( SV6 @ SY186 @ SY187 )
@ SV2 )
= $true ) ),
inference(sim,[status(thm)],[72]) ).
thf(83,plain,
! [SV1: $i,SV5: mu > $i > $o] :
( ( ( positive
@ ^ [SY184: mu,SY185: $i] :
~ ( SV5 @ SY184 @ SY185 )
@ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $false ) ),
inference(sim,[status(thm)],[79]) ).
thf(84,plain,
! [SV8: mu > $i > $o,SV4: $i] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV4 )
= $false )
| ( ( positive @ SV8 @ SV4 )
= $true ) ),
inference(sim,[status(thm)],[50]) ).
thf(85,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV4 )
= $true ) ),
inference(sim,[status(thm)],[52]) ).
thf(86,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,85,84,83,82,81,80,57,56,55,48,47,46,45,43,36,32]) ).
thf(87,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI006^5 : TPTP v9.3.1. Released v6.4.0.
% 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
% 0.06/0.19 % Computer : n026.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 13:53:01 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 90.02/15.39
% 90.02/15.39 No.of.Axioms: 4
% 90.02/15.39
% 90.02/15.39 Length.of.Defs: 3606
% 90.02/15.39
% 90.02/15.39 Contains.Choice.Funs: false
% 90.02/15.39 ....eprover: CPU time limit exceeded, terminating
% 90.02/15.39
% 90.02/15.39
% 90.02/15.39 ********************************
% 90.02/15.39 * All subproblems solved! *
% 90.02/15.39 ********************************
% 90.02/15.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:86,loop_count:0,foatp_calls:2,translation:fof_full)
% 90.02/15.39
% 90.02/15.39 %**** Beginning of derivation protocol ****
% 90.02/15.39 % SZS output start CNFRefutation
% See solution above
% 90.02/15.39
% 90.02/15.39 %**** End of derivation protocol ****
% 90.02/15.39 %**** no. of clauses in derivation: 69 ****
% 90.02/15.40 %**** clause counter: 86 ****
% 90.02/15.40
% 90.02/15.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:86,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------