%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PHI002^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.10s 0.28s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 84 ( 55 unt; 0 typ; 22 def)
% Number of atoms : 409 ( 118 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 804 ( 175 ~; 99 |; 12 &; 506 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 171 ( 171 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 3 con; 0-3 aty)
% Number of variables : 261 ( 94 ^; 151 !; 16 ?; 261 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
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_SY22,type,
sK1_SY22: $i ).
thf(tp_sK2_SY107,type,
sK2_SY107: mu > $i > $o ).
thf(tp_sK3_SY128,type,
sK3_SY128: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > $i ).
thf(tp_sK4_SY131,type,
sK4_SY131: $i > ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
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
@ ( 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/sandbox2/benchmark/theBenchmark.p',axA2) ).
thf(2,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) )
@ ( mnot @ ( positive @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA1) ).
thf(3,conjecture,
( 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(4,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)],[3]) ).
thf(5,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)],[4,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(6,plain,
( ( ! [SY73: $i,SY74: mu > $i > $o,SY75: mu > $i > $o] :
( ( ( positive @ SY74 @ SY73 )
& ! [SY76: $i] :
( ~ ( rel @ SY73 @ SY76 )
| ! [SY69: mu] :
( ( SY74 @ SY69 @ SY76 )
=> ( SY75 @ SY69 @ SY76 ) ) ) )
=> ( positive @ SY75 @ SY73 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,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(7,plain,
( ( ! [SY99: $i,SY100: mu > $i > $o] :
( ( positive
@ ^ [SY95: mu,SY96: $i] :
~ ( SY100 @ SY95 @ SY96 )
@ SY99 )
<=> ~ ( positive @ SY100 @ SY99 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,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(8,plain,
( ( ! [SY107: mu > $i > $o] :
( ( positive @ SY107 @ sK1_SY22 )
=> ? [SY108: $i] :
( ( rel @ sK1_SY22 @ SY108 )
& ? [SY17: mu] : ( SY107 @ SY17 @ SY108 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ( positive @ sK2_SY107 @ sK1_SY22 )
=> ? [SY110: $i] :
( ( rel @ sK1_SY22 @ SY110 )
& ? [SY111: mu] : ( sK2_SY107 @ SY111 @ SY110 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( positive @ sK2_SY107 @ sK1_SY22 )
= $true ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(11,plain,
( ( ? [SY110: $i] :
( ( rel @ sK1_SY22 @ SY110 )
& ? [SY111: mu] : ( sK2_SY107 @ SY111 @ SY110 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ? [SY110: $i] :
( ( rel @ sK1_SY22 @ SY110 )
& ? [SY111: mu] : ( sK2_SY107 @ SY111 @ SY110 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY99: $i,SY100: mu > $i > $o] :
( ( positive
@ ^ [SY95: mu,SY96: $i] :
~ ( SY100 @ SY95 @ SY96 )
@ SY99 )
<=> ~ ( positive @ SY100 @ SY99 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ! [SY73: $i,SY74: mu > $i > $o,SY75: mu > $i > $o] :
( ( ( positive @ SY74 @ SY73 )
& ! [SY76: $i] :
( ~ ( rel @ SY73 @ SY76 )
| ! [SY69: mu] :
( ( SY74 @ SY69 @ SY76 )
=> ( SY75 @ SY69 @ SY76 ) ) ) )
=> ( positive @ SY75 @ SY73 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( positive @ sK2_SY107 @ sK1_SY22 )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ~ ? [SY110: $i] :
( ( rel @ sK1_SY22 @ SY110 )
& ? [SY111: mu] : ( sK2_SY107 @ SY111 @ SY110 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o,SX2: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SX1 @ SX0 )
| ~ ! [SX3: $i] :
( ~ ( rel @ SX0 @ SX3 )
| ! [SX4: mu] :
( ~ ( SX1 @ SX4 @ SX3 )
| ( SX2 @ SX4 @ SX3 ) ) ) )
| ( positive @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,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(18,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( rel @ sK1_SY22 @ SX0 )
| ~ ~ ! [SX1: mu] :
~ ( sK2_SY107 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,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(19,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
~ ( ~ ( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 )
| ~ ( positive @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( positive @ SX1 @ SX0 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,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(20,plain,
! [SV1: $i] :
( ( ! [SY112: mu > $i > $o,SY113: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SY112 @ SV1 )
| ~ ! [SY114: $i] :
( ~ ( rel @ SV1 @ SY114 )
| ! [SX4: mu] :
( ~ ( SY112 @ SX4 @ SY114 )
| ( SY113 @ SX4 @ SY114 ) ) ) )
| ( positive @ SY113 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( rel @ sK1_SY22 @ SX0 )
| ~ ~ ! [SX1: mu] :
~ ( sK2_SY107 @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i] :
( ( ! [SY116: mu > $i > $o] :
~ ( ~ ( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY116 @ SX2 @ SX3 )
@ SV2 )
| ~ ( positive @ SY116 @ SV2 ) )
| ~ ( ~ ~ ( positive @ SY116 @ SV2 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY116 @ SX2 @ SX3 )
@ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i,SV3: mu > $i > $o] :
( ( ! [SY121: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SV3 @ SV1 )
| ~ ! [SY122: $i] :
( ~ ( rel @ SV1 @ SY122 )
| ! [SY123: mu] :
( ~ ( SV3 @ SY123 @ SY122 )
| ( SY121 @ SY123 @ SY122 ) ) ) )
| ( positive @ SY121 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( rel @ sK1_SY22 @ SX0 )
| ~ ~ ! [SX1: mu] :
~ ( sK2_SY107 @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ~ ( ~ ( ~ ( positive
@ ^ [SY124: mu,SY125: $i] :
~ ( SV4 @ SY124 @ SY125 )
@ SV2 )
| ~ ( positive @ SV4 @ SV2 ) )
| ~ ( ~ ~ ( positive @ SV4 @ SV2 )
| ( positive
@ ^ [SY126: mu,SY127: $i] :
~ ( SV4 @ SY126 @ SY127 )
@ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ~ ~ ( ~ ( positive @ SV3 @ SV1 )
| ~ ! [SY128: $i] :
( ~ ( rel @ SV1 @ SY128 )
| ! [SY129: mu] :
( ~ ( SV3 @ SY129 @ SY128 )
| ( SV5 @ SY129 @ SY128 ) ) ) )
| ( positive @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( rel @ sK1_SY22 @ SV6 )
| ~ ~ ! [SY130: mu] :
~ ( sK2_SY107 @ SY130 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ~ ( ~ ( positive
@ ^ [SY124: mu,SY125: $i] :
~ ( SV4 @ SY124 @ SY125 )
@ SV2 )
| ~ ( positive @ SV4 @ SV2 ) )
| ~ ( ~ ~ ( positive @ SV4 @ SV2 )
| ( positive
@ ^ [SY126: mu,SY127: $i] :
~ ( SV4 @ SY126 @ SY127 )
@ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ~ ( ~ ( positive @ SV3 @ SV1 )
| ~ ! [SY128: $i] :
( ~ ( rel @ SV1 @ SY128 )
| ! [SY129: mu] :
( ~ ( SV3 @ SY129 @ SY128 )
| ( SV5 @ SY129 @ SY128 ) ) ) ) )
= $true )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV6: $i] :
( ( ~ ( ~ ( rel @ sK1_SY22 @ SV6 )
| ~ ~ ! [SY130: mu] :
~ ( sK2_SY107 @ SY130 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ~ ( ~ ( positive
@ ^ [SY124: mu,SY125: $i] :
~ ( SV4 @ SY124 @ SY125 )
@ SV2 )
| ~ ( positive @ SV4 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ~ ( ~ ~ ( positive @ SV4 @ SV2 )
| ( positive
@ ^ [SY126: mu,SY127: $i] :
~ ( SV4 @ SY126 @ SY127 )
@ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ( ~ ( positive @ SV3 @ SV1 )
| ~ ! [SY128: $i] :
( ~ ( rel @ SV1 @ SY128 )
| ! [SY129: mu] :
( ~ ( SV3 @ SY129 @ SY128 )
| ( SV5 @ SY129 @ SY128 ) ) ) ) )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV6: $i] :
( ( ~ ( rel @ sK1_SY22 @ SV6 )
| ~ ~ ! [SY130: mu] :
~ ( sK2_SY107 @ SY130 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ~ ( positive
@ ^ [SY124: mu,SY125: $i] :
~ ( SV4 @ SY124 @ SY125 )
@ SV2 )
| ~ ( positive @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ~ ~ ( positive @ SV4 @ SV2 )
| ( positive
@ ^ [SY126: mu,SY127: $i] :
~ ( SV4 @ SY126 @ SY127 )
@ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ( positive @ SV3 @ SV1 )
| ~ ! [SY128: $i] :
( ~ ( rel @ SV1 @ SY128 )
| ! [SY129: mu] :
( ~ ( SV3 @ SY129 @ SY128 )
| ( SV5 @ SY129 @ SY128 ) ) ) )
= $true )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV6: $i] :
( ( ( ~ ( rel @ sK1_SY22 @ SV6 ) )
= $true )
| ( ( ~ ~ ! [SY130: mu] :
~ ( sK2_SY107 @ SY130 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SY124: mu,SY125: $i] :
~ ( SV4 @ SY124 @ SY125 )
@ SV2 ) )
= $true )
| ( ( ~ ( positive @ SV4 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ( ~ ~ ( positive @ SV4 @ SV2 ) )
= $true )
| ( ( positive
@ ^ [SY126: mu,SY127: $i] :
~ ( SV4 @ SY126 @ SY127 )
@ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ( positive @ SV3 @ SV1 ) )
= $true )
| ( ( ~ ! [SY128: $i] :
( ~ ( rel @ SV1 @ SY128 )
| ! [SY129: mu] :
( ~ ( SV3 @ SY129 @ SY128 )
| ( SV5 @ SY129 @ SY128 ) ) ) )
= $true )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV6: $i] :
( ( ( rel @ sK1_SY22 @ SV6 )
= $false )
| ( ( ~ ~ ! [SY130: mu] :
~ ( sK2_SY107 @ SY130 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ( positive
@ ^ [SY124: mu,SY125: $i] :
~ ( SV4 @ SY124 @ SY125 )
@ SV2 )
= $false )
| ( ( ~ ( positive @ SV4 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ( ~ ( positive @ SV4 @ SV2 ) )
= $false )
| ( ( positive
@ ^ [SY126: mu,SY127: $i] :
~ ( SV4 @ SY126 @ SY127 )
@ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( ~ ! [SY128: $i] :
( ~ ( rel @ SV1 @ SY128 )
| ! [SY129: mu] :
( ~ ( SV3 @ SY129 @ SY128 )
| ( SV5 @ SY129 @ SY128 ) ) ) )
= $true )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV6: $i] :
( ( ( ~ ! [SY130: mu] :
~ ( sK2_SY107 @ SY130 @ SV6 ) )
= $false )
| ( ( rel @ sK1_SY22 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ( positive @ SV4 @ SV2 )
= $false )
| ( ( positive
@ ^ [SY124: mu,SY125: $i] :
~ ( SV4 @ SY124 @ SY125 )
@ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV2: $i,SV4: mu > $i > $o] :
( ( ( positive @ SV4 @ SV2 )
= $true )
| ( ( positive
@ ^ [SY126: mu,SY127: $i] :
~ ( SV4 @ SY126 @ SY127 )
@ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: mu > $i > $o,SV3: mu > $i > $o,SV1: $i] :
( ( ( ! [SY128: $i] :
( ~ ( rel @ SV1 @ SY128 )
| ! [SY129: mu] :
( ~ ( SV3 @ SY129 @ SY128 )
| ( SV5 @ SY129 @ SY128 ) ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( ! [SY130: mu] :
~ ( sK2_SY107 @ SY130 @ SV6 ) )
= $true )
| ( ( rel @ sK1_SY22 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV3: mu > $i > $o,SV5: mu > $i > $o,SV1: $i] :
( ( ( ~ ( rel @ SV1 @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) )
| ! [SY131: mu] :
( ~ ( SV3 @ SY131 @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) )
| ( SV5 @ SY131 @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(52,plain,
! [SV6: $i,SV7: mu] :
( ( ( ~ ( sK2_SY107 @ SV7 @ SV6 ) )
= $true )
| ( ( rel @ sK1_SY22 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV3: mu > $i > $o,SV5: mu > $i > $o,SV1: $i] :
( ( ( ~ ( rel @ SV1 @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV1: $i,SV5: mu > $i > $o,SV3: mu > $i > $o] :
( ( ( ! [SY131: mu] :
( ~ ( SV3 @ SY131 @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) )
| ( SV5 @ SY131 @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV6: $i,SV7: mu] :
( ( ( sK2_SY107 @ SV7 @ SV6 )
= $false )
| ( ( rel @ sK1_SY22 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV3: mu > $i > $o,SV5: mu > $i > $o,SV1: $i] :
( ( ( rel @ SV1 @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ( SV3 @ ( sK4_SY131 @ SV1 @ SV5 @ SV3 ) @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) )
| ( SV5 @ ( sK4_SY131 @ SV1 @ SV5 @ SV3 ) @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(58,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( ~ ( SV3 @ ( sK4_SY131 @ SV1 @ SV5 @ SV3 ) @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(59,plain,
! [SV3: mu > $i > $o,SV1: $i,SV5: mu > $i > $o] :
( ( ( SV5 @ ( sK4_SY131 @ SV1 @ SV5 @ SV3 ) @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) )
= $false )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(60,plain,
! [SV5: mu > $i > $o,SV1: $i,SV3: mu > $i > $o] :
( ( ( SV3 @ ( sK4_SY131 @ SV1 @ SV5 @ SV3 ) @ ( sK3_SY128 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( positive @ SV3 @ SV1 )
= $false )
| ( ( positive @ SV5 @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,60,59,56,55,48,47]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI002^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.20 % Computer : n010.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Oct 6 13:49:55 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.28
% 0.10/0.28 No.of.Axioms: 2
% 0.10/0.28
% 0.10/0.28 Length.of.Defs: 3466
% 0.10/0.28
% 0.10/0.28 Contains.Choice.Funs: false
% 0.10/0.28 ..
% 0.10/0.28
% 0.10/0.28 ********************************
% 0.10/0.28 * All subproblems solved! *
% 0.10/0.28 ********************************
% 0.10/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.28
% 0.10/0.28 %**** Beginning of derivation protocol ****
% 0.10/0.28 % SZS output start CNFRefutation
% See solution above
% 0.10/0.28
% 0.10/0.28 %**** End of derivation protocol ****
% 0.10/0.28 %**** no. of clauses in derivation: 62 ****
% 0.10/0.28 %**** clause counter: 61 ****
% 0.10/0.28
% 0.10/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------