TSTP Solution File: SYN044^4 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN044^4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 08:22:51 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 56
% Syntax : Number of formulae : 190 ( 45 unt; 31 typ; 19 def)
% Number of atoms : 1347 ( 347 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 1770 ( 311 ~; 429 |; 2 &;1026 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 102 ( 102 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 6 con; 0-3 aty)
% Number of variables : 356 ( 31 ^ 323 !; 2 ?; 356 :)
% 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_p,type,
p: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(tp_r,type,
r: $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY2,type,
sK2_SY2: $i > $i ).
thf(tp_sK3_SY6,type,
sK3_SY6: $i > $i ).
thf(tp_sK4_SY8,type,
sK4_SY8: $i > $i ).
thf(tp_sK5_SY12,type,
sK5_SY12: $i ).
thf(tp_sK6_SY14,type,
sK6_SY14: $i ).
thf(tp_sK7_SY14,type,
sK7_SY14: $i ).
thf(tp_sK8_SY14,type,
sK8_SY14: $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 @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10_3) ).
thf(2,axiom,
ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10_2) ).
thf(3,axiom,
ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10_1) ).
thf(4,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(5,axiom,
! [X: $i] : ( irel @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).
thf(6,conjecture,
ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10) ).
thf(7,negated_conjecture,
( ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ~ ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( irel @ X @ Y )
| ~ ( irel @ Y @ Z )
| ( irel @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( irel @ X @ Y )
| ~ ( irel @ Y @ Z )
| ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(13,plain,
( ( ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(14,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(15,plain,
( ( ~ ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(16,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( r @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(17,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( p @ SX1 )
| ~ ( q @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(18,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) ) ) ) )
= $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,
! [SV1: $i] :
( ( irel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ( irel @ SV2 @ SY0 )
| ~ ( irel @ SY0 @ SY1 )
| ( irel @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(22,plain,
! [SV3: $i] :
( ( ~ ! [SY2: $i] :
( ~ ( irel @ SV3 @ SY2 )
| ( p @ SY2 ) )
| ! [SY3: $i] :
( ~ ( irel @ SV3 @ SY3 )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( r @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV4: $i] :
( ( ~ ! [SY6: $i] :
( ~ ( irel @ SV4 @ SY6 )
| ( r @ SY6 ) )
| ! [SY7: $i] :
( ~ ( irel @ SV4 @ SY7 )
| ~ ( ~ ( p @ SY7 )
| ~ ( q @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV5: $i] :
( ( ~ ! [SY8: $i] :
( ~ ( irel @ SV5 @ SY8 )
| ( q @ SY8 ) )
| ! [SY9: $i] :
( ~ ( irel @ SV5 @ SY9 )
| ( r @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY10: $i] :
( ~ ( irel @ SV2 @ SV6 )
| ~ ( irel @ SV6 @ SY10 )
| ( irel @ SV2 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV3: $i] :
( ( ( ~ ! [SY2: $i] :
( ~ ( irel @ SV3 @ SY2 )
| ( p @ SY2 ) ) )
= $true )
| ( ( ! [SY3: $i] :
( ~ ( irel @ SV3 @ SY3 )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( r @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( ~ ! [SY6: $i] :
( ~ ( irel @ SV4 @ SY6 )
| ( r @ SY6 ) ) )
= $true )
| ( ( ! [SY7: $i] :
( ~ ( irel @ SV4 @ SY7 )
| ~ ( ~ ( p @ SY7 )
| ~ ( q @ SY7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV5: $i] :
( ( ( ~ ! [SY8: $i] :
( ~ ( irel @ SV5 @ SY8 )
| ( q @ SY8 ) ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( irel @ SV5 @ SY9 )
| ( r @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK1_SX0 @ SY11 )
| ( p @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK1_SX0 @ SY12 )
| ( q @ SY12 ) ) )
| ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(31,plain,
! [SV7: $i,SV6: $i,SV2: $i] :
( ( ~ ( irel @ SV2 @ SV6 )
| ~ ( irel @ SV6 @ SV7 )
| ( irel @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: $i] :
( ( ( ! [SY2: $i] :
( ~ ( irel @ SV3 @ SY2 )
| ( p @ SY2 ) ) )
= $false )
| ( ( ! [SY3: $i] :
( ~ ( irel @ SV3 @ SY3 )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( r @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i] :
( ( ( ! [SY6: $i] :
( ~ ( irel @ SV4 @ SY6 )
| ( r @ SY6 ) ) )
= $false )
| ( ( ! [SY7: $i] :
( ~ ( irel @ SV4 @ SY7 )
| ~ ( ~ ( p @ SY7 )
| ~ ( q @ SY7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV5: $i] :
( ( ( ! [SY8: $i] :
( ~ ( irel @ SV5 @ SY8 )
| ( q @ SY8 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( irel @ SV5 @ SY9 )
| ( r @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK1_SX0 @ SY11 )
| ( p @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK1_SX0 @ SY12 )
| ( q @ SY12 ) ) )
| ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(36,plain,
! [SV7: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV6 )
| ~ ( irel @ SV6 @ SV7 ) )
= $true )
| ( ( irel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV3: $i] :
( ( ( ~ ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
| ( p @ ( sK2_SY2 @ SV3 ) ) )
= $false )
| ( ( ! [SY3: $i] :
( ~ ( irel @ SV3 @ SY3 )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( r @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(38,plain,
! [SV4: $i] :
( ( ( ~ ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
| ( r @ ( sK3_SY6 @ SV4 ) ) )
= $false )
| ( ( ! [SY7: $i] :
( ~ ( irel @ SV4 @ SY7 )
| ~ ( ~ ( p @ SY7 )
| ~ ( q @ SY7 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( ~ ( irel @ SV5 @ ( sK4_SY8 @ SV5 ) )
| ( q @ ( sK4_SY8 @ SV5 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( irel @ SV5 @ SY9 )
| ( r @ SY9 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(40,plain,
( ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK1_SX0 @ SY11 )
| ( p @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK1_SX0 @ SY12 )
| ( q @ SY12 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV7: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( irel @ SV6 @ SV7 ) )
= $true )
| ( ( irel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV3: $i] :
( ( ( ~ ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) ) )
= $false )
| ( ( ! [SY3: $i] :
( ~ ( irel @ SV3 @ SY3 )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( r @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false )
| ( ( ! [SY3: $i] :
( ~ ( irel @ SV3 @ SY3 )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( r @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(44,plain,
! [SV4: $i] :
( ( ( ~ ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) ) )
= $false )
| ( ( ! [SY7: $i] :
( ~ ( irel @ SV4 @ SY7 )
| ~ ( ~ ( p @ SY7 )
| ~ ( q @ SY7 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(45,plain,
! [SV4: $i] :
( ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false )
| ( ( ! [SY7: $i] :
( ~ ( irel @ SV4 @ SY7 )
| ~ ( ~ ( p @ SY7 )
| ~ ( q @ SY7 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( ~ ( irel @ SV5 @ ( sK4_SY8 @ SV5 ) ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( irel @ SV5 @ SY9 )
| ( r @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(47,plain,
! [SV5: $i] :
( ( ( q @ ( sK4_SY8 @ SV5 ) )
= $false )
| ( ( ! [SY9: $i] :
( ~ ( irel @ SV5 @ SY9 )
| ( r @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(48,plain,
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK1_SX0 @ SY11 )
| ( p @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK1_SX0 @ SY12 )
| ( q @ SY12 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV7: $i,SV6: $i,SV2: $i] :
( ( ( irel @ SV2 @ SV6 )
= $false )
| ( ( ~ ( irel @ SV6 @ SV7 ) )
= $true )
| ( ( irel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV3: $i] :
( ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true )
| ( ( ! [SY3: $i] :
( ~ ( irel @ SV3 @ SY3 )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( q @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY3 @ SX2 )
| ( r @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(51,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV8 )
| ! [SY15: $i] :
( ~ ( irel @ SV8 @ SY15 )
| ( q @ SY15 ) )
| ! [SY16: $i] :
( ~ ( irel @ SV8 @ SY16 )
| ( r @ SY16 ) ) )
= $true )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true )
| ( ( ! [SY7: $i] :
( ~ ( irel @ SV4 @ SY7 )
| ~ ( ~ ( p @ SY7 )
| ~ ( q @ SY7 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(53,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV9 )
| ~ ( ~ ( p @ SV9 )
| ~ ( q @ SV9 ) ) )
= $true )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV5: $i] :
( ( ( irel @ SV5 @ ( sK4_SY8 @ SV5 ) )
= $true )
| ( ( ! [SY9: $i] :
( ~ ( irel @ SV5 @ SY9 )
| ( r @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(55,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV10 )
| ( r @ SV10 ) )
= $true )
| ( ( q @ ( sK4_SY8 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(56,plain,
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK1_SX0 @ SY11 )
| ( p @ SY11 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(57,plain,
( ( ( ! [SY12: $i] :
( ~ ( irel @ sK1_SX0 @ SY12 )
| ( q @ SY12 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(58,plain,
! [SV2: $i,SV7: $i,SV6: $i] :
( ( ( irel @ SV6 @ SV7 )
= $false )
| ( ( irel @ SV2 @ SV6 )
= $false )
| ( ( irel @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV11 )
| ! [SY17: $i] :
( ~ ( irel @ SV11 @ SY17 )
| ( q @ SY17 ) )
| ! [SY18: $i] :
( ~ ( irel @ SV11 @ SY18 )
| ( r @ SY18 ) ) )
= $true )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV8 ) )
= $true )
| ( ( ! [SY15: $i] :
( ~ ( irel @ SV8 @ SY15 )
| ( q @ SY15 ) )
| ! [SY16: $i] :
( ~ ( irel @ SV8 @ SY16 )
| ( r @ SY16 ) ) )
= $true )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV12 )
| ~ ( ~ ( p @ SV12 )
| ~ ( q @ SV12 ) ) )
= $true )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( p @ SV9 )
| ~ ( q @ SV9 ) ) )
= $true )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV13 )
| ( r @ SV13 ) )
= $true )
| ( ( irel @ SV5 @ ( sK4_SY8 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV10 ) )
= $true )
| ( ( r @ SV10 )
= $true )
| ( ( q @ ( sK4_SY8 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(65,plain,
( ( ( ! [SY11: $i] :
( ~ ( irel @ sK1_SX0 @ SY11 )
| ( p @ SY11 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(66,plain,
( ( ( ~ ( irel @ sK1_SX0 @ sK5_SY12 )
| ( q @ sK5_SY12 ) )
= $false )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(67,plain,
! [SV11: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV11 ) )
= $true )
| ( ( ! [SY17: $i] :
( ~ ( irel @ SV11 @ SY17 )
| ( q @ SY17 ) )
| ! [SY18: $i] :
( ~ ( irel @ SV11 @ SY18 )
| ( r @ SY18 ) ) )
= $true )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV8: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( ! [SY15: $i] :
( ~ ( irel @ SV8 @ SY15 )
| ( q @ SY15 ) )
| ! [SY16: $i] :
( ~ ( irel @ SV8 @ SY16 )
| ( r @ SY16 ) ) )
= $true )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( p @ SV12 )
| ~ ( q @ SV12 ) ) )
= $true )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV9: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV9 )
= $false )
| ( ( ~ ( ~ ( p @ SV9 )
| ~ ( q @ SV9 ) ) )
= $true )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV13 ) )
= $true )
| ( ( r @ SV13 )
= $true )
| ( ( irel @ SV5 @ ( sK4_SY8 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV10: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV10 )
= $false )
| ( ( r @ SV10 )
= $true )
| ( ( q @ ( sK4_SY8 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV14: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV14 )
| ( p @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
( ( ( ~ ( irel @ sK1_SX0 @ sK5_SY12 ) )
= $false )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(75,plain,
( ( ( q @ sK5_SY12 )
= $false )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(76,plain,
! [SV11: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( ! [SY17: $i] :
( ~ ( irel @ SV11 @ SY17 )
| ( q @ SY17 ) )
| ! [SY18: $i] :
( ~ ( irel @ SV11 @ SY18 )
| ( r @ SY18 ) ) )
= $true )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV3: $i,SV8: $i] :
( ( ( ! [SY15: $i] :
( ~ ( irel @ SV8 @ SY15 )
| ( q @ SY15 ) ) )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( irel @ SV8 @ SY16 )
| ( r @ SY16 ) ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV12: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV12 )
= $false )
| ( ( ~ ( ~ ( p @ SV12 )
| ~ ( q @ SV12 ) ) )
= $true )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV4: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( q @ SV9 ) )
= $false )
| ( ( irel @ SV4 @ SV9 )
= $false )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV13: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV13 )
= $false )
| ( ( r @ SV13 )
= $true )
| ( ( irel @ SV5 @ ( sK4_SY8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV14: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV14 ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(82,plain,
( ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(83,plain,
( ( ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) )
= $false )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV3: $i,SV11: $i] :
( ( ( ! [SY17: $i] :
( ~ ( irel @ SV11 @ SY17 )
| ( q @ SY17 ) ) )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( irel @ SV11 @ SY18 )
| ( r @ SY18 ) ) )
= $true )
| ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV3: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV15 )
| ( q @ SV15 ) )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( irel @ SV8 @ SY16 )
| ( r @ SY16 ) ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 )
| ~ ( q @ SV12 ) )
= $false )
| ( ( irel @ SV4 @ SV12 )
= $false )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV4: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 ) )
= $false )
| ( ( irel @ SV4 @ SV9 )
= $false )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(88,plain,
! [SV4: $i,SV9: $i] :
( ( ( ~ ( q @ SV9 ) )
= $false )
| ( ( irel @ SV4 @ SV9 )
= $false )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(89,plain,
! [SV14: $i] :
( ( ( irel @ sK1_SX0 @ SV14 )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( ~ ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(90,plain,
( ( ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) )
= $false )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(91,plain,
( ( ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) ) )
= $false )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(92,plain,
( ( ( ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) )
= $false )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(93,plain,
! [SV3: $i,SV16: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV16 )
| ( q @ SV16 ) )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( irel @ SV11 @ SY18 )
| ( r @ SY18 ) ) )
= $true )
| ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV3: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV15 ) )
= $true )
| ( ( q @ SV15 )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( irel @ SV8 @ SY16 )
| ( r @ SY16 ) ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 ) )
= $false )
| ( ( irel @ SV4 @ SV12 )
= $false )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(96,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( q @ SV12 ) )
= $false )
| ( ( irel @ SV4 @ SV12 )
= $false )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(97,plain,
! [SV4: $i,SV9: $i] :
( ( ( p @ SV9 )
= $true )
| ( ( irel @ SV4 @ SV9 )
= $false )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(98,plain,
! [SV4: $i,SV9: $i] :
( ( ( q @ SV9 )
= $true )
| ( ( irel @ SV4 @ SV9 )
= $false )
| ( ( r @ ( sK3_SY6 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(99,plain,
! [SV14: $i] :
( ( ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) )
| ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(100,plain,
( ( ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) ) )
= $false )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(101,plain,
( ( ( ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) )
= $false )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(102,plain,
( ( ( ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) ) )
= $true )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(103,plain,
( ( ( ~ ( irel @ sK1_SX0 @ sK6_SY14 )
| ( p @ sK6_SY14 ) )
= $false )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(104,plain,
! [SV3: $i,SV16: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV16 ) )
= $true )
| ( ( q @ SV16 )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( irel @ SV11 @ SY18 )
| ( r @ SY18 ) ) )
= $true )
| ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV3: $i,SV15: $i,SV8: $i] :
( ( ( irel @ SV8 @ SV15 )
= $false )
| ( ( q @ SV15 )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( irel @ SV8 @ SY16 )
| ( r @ SY16 ) ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV4: $i,SV12: $i] :
( ( ( p @ SV12 )
= $true )
| ( ( irel @ SV4 @ SV12 )
= $false )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(107,plain,
! [SV4: $i,SV12: $i] :
( ( ( q @ SV12 )
= $true )
| ( ( irel @ SV4 @ SV12 )
= $false )
| ( ( irel @ SV4 @ ( sK3_SY6 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(108,plain,
! [SV14: $i] :
( ( ( ~ ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) ) )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(109,plain,
! [SV14: $i] :
( ( ( ! [SY14: $i] :
( ~ ( irel @ sK1_SX0 @ SY14 )
| ( p @ SY14 ) ) )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(110,plain,
( ( ( ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) ) )
= $true )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(111,plain,
( ( ( ~ ( irel @ sK1_SX0 @ sK7_SY14 )
| ( p @ sK7_SY14 ) )
= $false )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(112,plain,
! [SV17: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV17 )
| ( q @ SV17 ) )
= $true )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(113,plain,
( ( ( ~ ( irel @ sK1_SX0 @ sK6_SY14 ) )
= $false )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(114,plain,
( ( ( p @ sK6_SY14 )
= $false )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(115,plain,
! [SV3: $i,SV16: $i,SV11: $i] :
( ( ( irel @ SV11 @ SV16 )
= $false )
| ( ( q @ SV16 )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( irel @ SV11 @ SY18 )
| ( r @ SY18 ) ) )
= $true )
| ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV3: $i,SV15: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV18 )
| ( r @ SV18 ) )
= $true )
| ( ( q @ SV15 )
= $true )
| ( ( irel @ SV8 @ SV15 )
= $false )
| ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV14: $i] :
( ( ( ! [SY13: $i] :
( ~ ( irel @ sK1_SX0 @ SY13 )
| ( q @ SY13 ) ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(118,plain,
! [SV14: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ ( sK8_SY14 @ SV14 ) )
| ( p @ ( sK8_SY14 @ SV14 ) ) )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(119,plain,
! [SV19: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV19 )
| ( q @ SV19 ) )
= $true )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(120,plain,
( ( ( ~ ( irel @ sK1_SX0 @ sK7_SY14 ) )
= $false )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(121,plain,
( ( ( p @ sK7_SY14 )
= $false )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV17: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV17 ) )
= $true )
| ( ( q @ SV17 )
= $true )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(123,plain,
( ( ( irel @ sK1_SX0 @ sK6_SY14 )
= $true )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(124,plain,
! [SV3: $i,SV16: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV20 )
| ( r @ SV20 ) )
= $true )
| ( ( q @ SV16 )
= $true )
| ( ( irel @ SV11 @ SV16 )
= $false )
| ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(125,plain,
! [SV3: $i,SV15: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV18 ) )
= $true )
| ( ( r @ SV18 )
= $true )
| ( ( q @ SV15 )
= $true )
| ( ( irel @ SV8 @ SV15 )
= $false )
| ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV14: $i,SV21: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV21 )
| ( q @ SV21 ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(127,plain,
! [SV14: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ ( sK8_SY14 @ SV14 ) ) )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(128,plain,
! [SV14: $i] :
( ( ( p @ ( sK8_SY14 @ SV14 ) )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(129,plain,
! [SV19: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV19 ) )
= $true )
| ( ( q @ SV19 )
= $true )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
( ( ( irel @ sK1_SX0 @ sK7_SY14 )
= $true )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(131,plain,
! [SV17: $i] :
( ( ( irel @ sK1_SX0 @ SV17 )
= $false )
| ( ( q @ SV17 )
= $true )
| ( ( q @ sK5_SY12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(132,plain,
! [SV3: $i,SV16: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV20 ) )
= $true )
| ( ( r @ SV20 )
= $true )
| ( ( q @ SV16 )
= $true )
| ( ( irel @ SV11 @ SV16 )
= $false )
| ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV3: $i,SV15: $i,SV18: $i,SV8: $i] :
( ( ( irel @ SV8 @ SV18 )
= $false )
| ( ( r @ SV18 )
= $true )
| ( ( q @ SV15 )
= $true )
| ( ( irel @ SV8 @ SV15 )
= $false )
| ( ( irel @ SV3 @ SV8 )
= $false )
| ( ( p @ ( sK2_SY2 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV14: $i,SV21: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV21 ) )
= $true )
| ( ( q @ SV21 )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV14: $i] :
( ( ( irel @ sK1_SX0 @ ( sK8_SY14 @ SV14 ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(136,plain,
! [SV19: $i] :
( ( ( irel @ sK1_SX0 @ SV19 )
= $false )
| ( ( q @ SV19 )
= $true )
| ( ( irel @ sK1_SX0 @ sK5_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV3: $i,SV16: $i,SV20: $i,SV11: $i] :
( ( ( irel @ SV11 @ SV20 )
= $false )
| ( ( r @ SV20 )
= $true )
| ( ( q @ SV16 )
= $true )
| ( ( irel @ SV11 @ SV16 )
= $false )
| ( ( irel @ SV3 @ SV11 )
= $false )
| ( ( irel @ SV3 @ ( sK2_SY2 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(138,plain,
! [SV14: $i,SV21: $i] :
( ( ( irel @ sK1_SX0 @ SV21 )
= $false )
| ( ( q @ SV21 )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ sK1_SX0 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,138,137,136,135,133,131,130,128,123,121,114,107,106,98,97,80,72,58]) ).
thf(140,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN044^4 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 20:30:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 5
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 2753
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:5,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.19/0.52
% 0.19/0.52 ********************************
% 0.19/0.52 * All subproblems solved! *
% 0.19/0.52 ********************************
% 0.19/0.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:139,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.53
% 0.19/0.53 %**** Beginning of derivation protocol ****
% 0.19/0.53 % SZS output start CNFRefutation
% See solution above
% 0.19/0.53
% 0.19/0.53 %**** End of derivation protocol ****
% 0.19/0.53 %**** no. of clauses in derivation: 140 ****
% 0.19/0.53 %**** clause counter: 139 ****
% 0.19/0.53
% 0.19/0.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:139,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------