%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO068^4.001 : TPTP v9.3.1. Released v4.0.0.
% 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 : n020.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 11:07:33 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of formulae : 90 ( 44 unt; 0 typ; 19 def)
% Number of atoms : 699 ( 189 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 939 ( 130 ~; 202 |; 4 &; 591 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 3 con; 0-3 aty)
% Number of variables : 229 ( 31 ^; 196 !; 2 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_iand,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_iatom,type,
iatom: ( $i > $o ) > $i > $o ).
thf(tp_icountersatisfiable,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(tp_iequiv,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_ifalse,type,
ifalse: $i > $o ).
thf(tp_iimplied,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_iimplies,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_iinvalid,type,
iinvalid: ( $i > $o ) > $o ).
thf(tp_inot,type,
inot: ( $i > $o ) > $i > $o ).
thf(tp_ior,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_irel,type,
irel: $i > $i > $o ).
thf(tp_isatisfiable,type,
isatisfiable: ( $i > $o ) > $o ).
thf(tp_itrue,type,
itrue: $i > $o ).
thf(tp_ivalid,type,
ivalid: ( $i > $o ) > $o ).
thf(tp_ixor,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_p0,type,
p0: $i > $o ).
thf(tp_p1,type,
p1: $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY60,type,
sK2_SY60: $i > $i ).
thf(tp_sK3_SY65,type,
sK3_SY65: $i > $i > $i ).
thf(tp_sK4_SY67,type,
sK4_SY67: $i > $i > $i ).
thf(iand,definition,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iand) ).
thf(iatom,definition,
( iatom
= ( ^ [P: $i > $o] : P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iatom) ).
thf(icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',icountersatisfiable) ).
thf(iequiv,definition,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iequiv) ).
thf(ifalse,definition,
( ifalse
= ( inot @ itrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifalse) ).
thf(iimplied,definition,
( iimplied
= ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplied) ).
thf(iimplies,definition,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplies) ).
thf(iinvalid,definition,
( iinvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iinvalid) ).
thf(inot,definition,
( inot
= ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inot) ).
thf(ior,definition,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ior) ).
thf(isatisfiable,definition,
( isatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isatisfiable) ).
thf(itrue,definition,
( itrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',itrue) ).
thf(ivalid,definition,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ivalid) ).
thf(ixor,definition,
( ixor
= ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ixor) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mimplies,definition,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(2,axiom,
ivalid @ ( iatom @ p1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom) ).
thf(4,axiom,
! [X: $i] : ( irel @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).
thf(5,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(6,negated_conjecture,
( ( ivalid @ ( iatom @ p0 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [SY0: $i] : ( p0 @ SY0 ) )
= $false ),
inference(unfold_def,[status(thm)],[6,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(8,plain,
( ( ! [SY42: $i] :
( ~ ! [SY43: $i] :
( ( irel @ SY42 @ SY43 )
=> ( p1 @ SY43 ) )
| ! [SY44: $i] :
( ( irel @ SY42 @ SY44 )
=> ( ~ ! [SY40: $i] :
( ( irel @ SY44 @ SY40 )
=> ( p1 @ SY40 ) )
| ! [SY41: $i] :
( ( irel @ SY44 @ SY41 )
=> ( p0 @ SY41 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(9,plain,
( ( ! [SY52: $i] : ( p1 @ SY52 ) )
= $true ),
inference(unfold_def,[status(thm)],[2,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(11,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[4,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(12,plain,
( ( p0 @ sK1_SY0 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ~ ( p0 @ sK1_SY0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [SY52: $i] : ( p1 @ SY52 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [SY42: $i] :
( ~ ! [SY43: $i] :
( ( irel @ SY42 @ SY43 )
=> ( p1 @ SY43 ) )
| ! [SY44: $i] :
( ( irel @ SY42 @ SY44 )
=> ( ~ ! [SY40: $i] :
( ( irel @ SY44 @ SY40 )
=> ( p1 @ SY40 ) )
| ! [SY41: $i] :
( ( irel @ SY44 @ SY41 )
=> ( p0 @ SY41 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(18,plain,
( ( ~ ( p0 @ sK1_SY0 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( irel @ SX0 @ SX1 )
| ~ ( irel @ SX1 @ SX2 ) )
| ( irel @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(20,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p1 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( p0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(21,plain,
! [SV1: $i] :
( ( irel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(22,plain,
! [SV2: $i] :
( ( p1 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
( ( p0 @ sK1_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ~ ( ~ ( irel @ SV3 @ SY58 )
| ~ ( irel @ SY58 @ SY59 ) )
| ( irel @ SV3 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV4: $i] :
( ( ~ ! [SY60: $i] :
( ~ ( irel @ SV4 @ SY60 )
| ( p1 @ SY60 ) )
| ! [SY61: $i] :
( ~ ( irel @ SV4 @ SY61 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ( irel @ SV3 @ SV5 )
| ~ ( irel @ SV5 @ SY64 ) )
| ( irel @ SV3 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV4: $i] :
( ( ( ~ ! [SY60: $i] :
( ~ ( irel @ SV4 @ SY60 )
| ( p1 @ SY60 ) ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( irel @ SV4 @ SY61 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ~ ~ ( ~ ( irel @ SV3 @ SV5 )
| ~ ( irel @ SV5 @ SV6 ) )
| ( irel @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( ! [SY60: $i] :
( ~ ( irel @ SV4 @ SY60 )
| ( p1 @ SY60 ) ) )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( irel @ SV4 @ SY61 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( irel @ SV3 @ SV5 )
| ~ ( irel @ SV5 @ SV6 ) ) )
= $true )
| ( ( irel @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV4: $i] :
( ( ( ~ ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
| ( p1 @ ( sK2_SY60 @ SV4 ) ) )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( irel @ SV4 @ SY61 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(32,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( ~ ( irel @ SV3 @ SV5 )
| ~ ( irel @ SV5 @ SV6 ) ) )
= $false )
| ( ( irel @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV4: $i] :
( ( ( ~ ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) ) )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( irel @ SV4 @ SY61 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: $i] :
( ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( irel @ SV4 @ SY61 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV5 )
| ~ ( irel @ SV5 @ SV6 ) )
= $true )
| ( ( irel @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( irel @ SV4 @ SY61 )
| ~ ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY61 @ SX2 )
| ( p0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV7 )
| ~ ! [SY65: $i] :
( ~ ( irel @ SV7 @ SY65 )
| ( p1 @ SY65 ) )
| ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( irel @ SV5 @ SV6 ) )
= $true )
| ( ( irel @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV8 )
| ~ ! [SY67: $i] :
( ~ ( irel @ SV8 @ SY67 )
| ( p1 @ SY67 ) )
| ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV7 ) )
= $true )
| ( ( ~ ! [SY65: $i] :
( ~ ( irel @ SV7 @ SY65 )
| ( p1 @ SY65 ) )
| ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV5 )
= $false )
| ( ( ~ ( irel @ SV5 @ SV6 ) )
= $true )
| ( ( irel @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV8 ) )
= $true )
| ( ( ~ ! [SY67: $i] :
( ~ ( irel @ SV8 @ SY67 )
| ( p1 @ SY67 ) )
| ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV7: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( ~ ! [SY65: $i] :
( ~ ( irel @ SV7 @ SY65 )
| ( p1 @ SY65 ) )
| ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV3: $i,SV6: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ SV3 @ SV5 )
= $false )
| ( ( irel @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV8: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ~ ! [SY67: $i] :
( ~ ( irel @ SV8 @ SY67 )
| ( p1 @ SY67 ) )
| ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ! [SY65: $i] :
( ~ ( irel @ SV7 @ SY65 )
| ( p1 @ SY65 ) ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ! [SY67: $i] :
( ~ ( irel @ SV8 @ SY67 )
| ( p1 @ SY67 ) ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV4: $i,SV7: $i] :
( ( ( ! [SY65: $i] :
( ~ ( irel @ SV7 @ SY65 )
| ( p1 @ SY65 ) ) )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV4: $i,SV8: $i] :
( ( ( ! [SY67: $i] :
( ~ ( irel @ SV8 @ SY67 )
| ( p1 @ SY67 ) ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( irel @ SV7 @ ( sK3_SY65 @ SV4 @ SV7 ) )
| ( p1 @ ( sK3_SY65 @ SV4 @ SV7 ) ) )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(51,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ ( sK4_SY67 @ SV4 @ SV8 ) )
| ( p1 @ ( sK4_SY67 @ SV4 @ SV8 ) ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(52,plain,
! [SV4: $i,SV7: $i] :
( ( ( ~ ( irel @ SV7 @ ( sK3_SY65 @ SV4 @ SV7 ) ) )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(53,plain,
! [SV7: $i,SV4: $i] :
( ( ( p1 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ ( sK4_SY67 @ SV4 @ SV8 ) ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV8: $i,SV4: $i] :
( ( ( p1 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV4: $i,SV7: $i] :
( ( ( irel @ SV7 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( irel @ SV7 @ SY66 )
| ( p0 @ SY66 ) ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( irel @ SV7 @ SV9 )
| ( p0 @ SV9 ) )
= $true )
| ( ( p1 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $false )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV4: $i,SV8: $i] :
( ( ( irel @ SV8 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( irel @ SV8 @ SY68 )
| ( p0 @ SY68 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV10 )
| ( p0 @ SV10 ) )
= $true )
| ( ( p1 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $false )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV4: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( irel @ SV7 @ SV11 )
| ( p0 @ SV11 ) )
= $true )
| ( ( irel @ SV7 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( irel @ SV7 @ SV9 ) )
= $true )
| ( ( p0 @ SV9 )
= $true )
| ( ( p1 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $false )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV12 )
| ( p0 @ SV12 ) )
= $true )
| ( ( irel @ SV8 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV4: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV10 ) )
= $true )
| ( ( p0 @ SV10 )
= $true )
| ( ( p1 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $false )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV4: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( irel @ SV7 @ SV11 ) )
= $true )
| ( ( p0 @ SV11 )
= $true )
| ( ( irel @ SV7 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( irel @ SV7 @ SV9 )
= $false )
| ( ( p0 @ SV9 )
= $true )
| ( ( p1 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $false )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV12 ) )
= $true )
| ( ( p0 @ SV12 )
= $true )
| ( ( irel @ SV8 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV4: $i,SV10: $i,SV8: $i] :
( ( ( irel @ SV8 @ SV10 )
= $false )
| ( ( p0 @ SV10 )
= $true )
| ( ( p1 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $false )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV4: $i,SV11: $i,SV7: $i] :
( ( ( irel @ SV7 @ SV11 )
= $false )
| ( ( p0 @ SV11 )
= $true )
| ( ( irel @ SV7 @ ( sK3_SY65 @ SV4 @ SV7 ) )
= $true )
| ( ( irel @ SV4 @ SV7 )
= $false )
| ( ( p1 @ ( sK2_SY60 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( irel @ SV8 @ SV12 )
= $false )
| ( ( p0 @ SV12 )
= $true )
| ( ( irel @ SV8 @ ( sK4_SY67 @ SV4 @ SV8 ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV4 @ ( sK2_SY60 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(70,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,69,68,67,65,44,23,22]) ).
thf(71,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO068^4.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 17:32:21 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.26
% 0.07/0.26 No.of.Axioms: 4
% 0.07/0.26
% 0.07/0.26 Length.of.Defs: 2753
% 0.07/0.26
% 0.07/0.26 Contains.Choice.Funs: false
% 0.07/0.26 ..
% 0.07/0.26
% 0.07/0.26 ********************************
% 0.07/0.26 * All subproblems solved! *
% 0.07/0.26 ********************************
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:70,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.26
% 0.07/0.26 %**** Beginning of derivation protocol ****
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26
% 0.07/0.26 %**** End of derivation protocol ****
% 0.07/0.26 %**** no. of clauses in derivation: 71 ****
% 0.07/0.26 %**** clause counter: 70 ****
% 0.07/0.26
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:70,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------