%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN045^4 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 11:02:45 AM UTC 2026
% Result : Theorem 0.49s 0.29s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 188 ( 80 unt; 0 typ; 19 def)
% Number of atoms : 1568 ( 353 equ; 0 cnn)
% Maximal formula atoms : 21 ( 8 avg)
% Number of connectives : 2391 ( 420 ~; 523 |; 27 &;1336 @)
% ( 0 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 17 con; 0-3 aty)
% Number of variables : 434 ( 31 ^; 401 !; 2 ?; 434 :)
% 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_sK10_SY211,type,
sK10_SY211: $i ).
thf(tp_sK11_SY210,type,
sK11_SY210: $i ).
thf(tp_sK12_SY211,type,
sK12_SY211: $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i ).
thf(tp_sK14_SY217,type,
sK14_SY217: $i ).
thf(tp_sK15_SY218,type,
sK15_SY218: $i ).
thf(tp_sK1_SY151,type,
sK1_SY151: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY208,type,
sK3_SY208: $i ).
thf(tp_sK4_SY209,type,
sK4_SY209: $i ).
thf(tp_sK5_SY210,type,
sK5_SY210: $i ).
thf(tp_sK6_SY211,type,
sK6_SY211: $i ).
thf(tp_sK7_SY210,type,
sK7_SY210: $i ).
thf(tp_sK8_SY211,type,
sK8_SY211: $i ).
thf(tp_sK9_SY210,type,
sK9_SY210: $i ).
thf(iand,definition,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iand) ).
thf(iatom,definition,
( iatom
= ( ^ [P: $i > $o] : P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iatom) ).
thf(icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icountersatisfiable) ).
thf(iequiv,definition,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iequiv) ).
thf(ifalse,definition,
( ifalse
= ( inot @ itrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifalse) ).
thf(iimplied,definition,
( iimplied
= ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplied) ).
thf(iimplies,definition,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies) ).
thf(iinvalid,definition,
( iinvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iinvalid) ).
thf(inot,definition,
( inot
= ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inot) ).
thf(ior,definition,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ior) ).
thf(isatisfiable,definition,
( isatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isatisfiable) ).
thf(itrue,definition,
( itrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',itrue) ).
thf(ivalid,definition,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ivalid) ).
thf(ixor,definition,
( ixor
= ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ixor) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mimplies,definition,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).
thf(2,axiom,
! [X: $i] : ( irel @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).
thf(3,conjecture,
ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel13) ).
thf(4,negated_conjecture,
( ( ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [SY151: $i] :
( ( ~ ! [SY152: $i] :
( ( irel @ SY151 @ SY152 )
=> ( ! [SY23: $i] :
( ( irel @ SY152 @ SY23 )
=> ( p @ SY23 ) )
| ! [SY24: $i] :
( ( irel @ SY152 @ SY24 )
=> ( ( q @ SY24 )
& ( r @ SY24 ) ) ) ) )
| ! [SY155: $i] :
( ( irel @ SY151 @ SY155 )
=> ( ( ! [SY139: $i] :
( ( irel @ SY155 @ SY139 )
=> ( p @ SY139 ) )
| ! [SY140: $i] :
( ( irel @ SY155 @ SY140 )
=> ( q @ SY140 ) ) )
& ( ! [SY141: $i] :
( ( irel @ SY155 @ SY141 )
=> ( p @ SY141 ) )
| ! [SY142: $i] :
( ( irel @ SY155 @ SY142 )
=> ( r @ SY142 ) ) ) ) ) )
& ( ~ ! [SY160: $i] :
( ( irel @ SY151 @ SY160 )
=> ( ( ! [SY144: $i] :
( ( irel @ SY160 @ SY144 )
=> ( p @ SY144 ) )
| ! [SY145: $i] :
( ( irel @ SY160 @ SY145 )
=> ( q @ SY145 ) ) )
& ( ! [SY146: $i] :
( ( irel @ SY160 @ SY146 )
=> ( p @ SY146 ) )
| ! [SY147: $i] :
( ( irel @ SY160 @ SY147 )
=> ( r @ SY147 ) ) ) ) )
| ! [SY165: $i] :
( ( irel @ SY151 @ SY165 )
=> ( ! [SY82: $i] :
( ( irel @ SY165 @ SY82 )
=> ( p @ SY82 ) )
| ! [SY83: $i] :
( ( irel @ SY165 @ SY83 )
=> ( ( q @ SY83 )
& ( r @ SY83 ) ) ) ) ) ) ) )
= $false ),
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(6,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $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(7,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $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(8,plain,
( ( ( ~ ! [SY189: $i] :
( ( irel @ sK1_SY151 @ SY189 )
=> ( ! [SY23: $i] :
( ( irel @ SY189 @ SY23 )
=> ( p @ SY23 ) )
| ! [SY24: $i] :
( ( irel @ SY189 @ SY24 )
=> ( ( q @ SY24 )
& ( r @ SY24 ) ) ) ) )
| ! [SY192: $i] :
( ( irel @ sK1_SY151 @ SY192 )
=> ( ( ! [SY139: $i] :
( ( irel @ SY192 @ SY139 )
=> ( p @ SY139 ) )
| ! [SY140: $i] :
( ( irel @ SY192 @ SY140 )
=> ( q @ SY140 ) ) )
& ( ! [SY141: $i] :
( ( irel @ SY192 @ SY141 )
=> ( p @ SY141 ) )
| ! [SY142: $i] :
( ( irel @ SY192 @ SY142 )
=> ( r @ SY142 ) ) ) ) ) )
& ( ~ ! [SY197: $i] :
( ( irel @ sK1_SY151 @ SY197 )
=> ( ( ! [SY144: $i] :
( ( irel @ SY197 @ SY144 )
=> ( p @ SY144 ) )
| ! [SY145: $i] :
( ( irel @ SY197 @ SY145 )
=> ( q @ SY145 ) ) )
& ( ! [SY146: $i] :
( ( irel @ SY197 @ SY146 )
=> ( p @ SY146 ) )
| ! [SY147: $i] :
( ( irel @ SY197 @ SY147 )
=> ( r @ SY147 ) ) ) ) )
| ! [SY202: $i] :
( ( irel @ sK1_SY151 @ SY202 )
=> ( ! [SY82: $i] :
( ( irel @ SY202 @ SY82 )
=> ( p @ SY82 ) )
| ! [SY83: $i] :
( ( irel @ SY202 @ SY83 )
=> ( ( q @ SY83 )
& ( r @ SY83 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ~ ! [SY189: $i] :
( ( irel @ sK1_SY151 @ SY189 )
=> ( ! [SY23: $i] :
( ( irel @ SY189 @ SY23 )
=> ( p @ SY23 ) )
| ! [SY24: $i] :
( ( irel @ SY189 @ SY24 )
=> ( ( q @ SY24 )
& ( r @ SY24 ) ) ) ) )
| ! [SY192: $i] :
( ( irel @ sK1_SY151 @ SY192 )
=> ( ( ! [SY139: $i] :
( ( irel @ SY192 @ SY139 )
=> ( p @ SY139 ) )
| ! [SY140: $i] :
( ( irel @ SY192 @ SY140 )
=> ( q @ SY140 ) ) )
& ( ! [SY141: $i] :
( ( irel @ SY192 @ SY141 )
=> ( p @ SY141 ) )
| ! [SY142: $i] :
( ( irel @ SY192 @ SY142 )
=> ( r @ SY142 ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[8]) ).
thf(10,plain,
( ( ~ ! [SY197: $i] :
( ( irel @ sK1_SY151 @ SY197 )
=> ( ( ! [SY144: $i] :
( ( irel @ SY197 @ SY144 )
=> ( p @ SY144 ) )
| ! [SY145: $i] :
( ( irel @ SY197 @ SY145 )
=> ( q @ SY145 ) ) )
& ( ! [SY146: $i] :
( ( irel @ SY197 @ SY146 )
=> ( p @ SY146 ) )
| ! [SY147: $i] :
( ( irel @ SY197 @ SY147 )
=> ( r @ SY147 ) ) ) ) )
| ! [SY202: $i] :
( ( irel @ sK1_SY151 @ SY202 )
=> ( ! [SY82: $i] :
( ( irel @ SY202 @ SY82 )
=> ( p @ SY82 ) )
| ! [SY83: $i] :
( ( irel @ SY202 @ SY83 )
=> ( ( q @ SY83 )
& ( r @ SY83 ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[8]) ).
thf(11,plain,
( ( ~ ( ~ ! [SY189: $i] :
( ( irel @ sK1_SY151 @ SY189 )
=> ( ! [SY23: $i] :
( ( irel @ SY189 @ SY23 )
=> ( p @ SY23 ) )
| ! [SY24: $i] :
( ( irel @ SY189 @ SY24 )
=> ( ( q @ SY24 )
& ( r @ SY24 ) ) ) ) )
| ! [SY192: $i] :
( ( irel @ sK1_SY151 @ SY192 )
=> ( ( ! [SY139: $i] :
( ( irel @ SY192 @ SY139 )
=> ( p @ SY139 ) )
| ! [SY140: $i] :
( ( irel @ SY192 @ SY140 )
=> ( q @ SY140 ) ) )
& ( ! [SY141: $i] :
( ( irel @ SY192 @ SY141 )
=> ( p @ SY141 ) )
| ! [SY142: $i] :
( ( irel @ SY192 @ SY142 )
=> ( r @ SY142 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ! [SY197: $i] :
( ( irel @ sK1_SY151 @ SY197 )
=> ( ( ! [SY144: $i] :
( ( irel @ SY197 @ SY144 )
=> ( p @ SY144 ) )
| ! [SY145: $i] :
( ( irel @ SY197 @ SY145 )
=> ( q @ SY145 ) ) )
& ( ! [SY146: $i] :
( ( irel @ SY197 @ SY146 )
=> ( p @ SY146 ) )
| ! [SY147: $i] :
( ( irel @ SY197 @ SY147 )
=> ( r @ SY147 ) ) ) ) )
| ! [SY202: $i] :
( ( irel @ sK1_SY151 @ SY202 )
=> ( ! [SY82: $i] :
( ( irel @ SY202 @ SY82 )
=> ( p @ SY82 ) )
| ! [SY83: $i] :
( ( irel @ SY202 @ SY83 )
=> ( ( q @ SY83 )
& ( r @ SY83 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( ~ ( ~ ! [SY189: $i] :
( ( irel @ sK1_SY151 @ SY189 )
=> ( ! [SY23: $i] :
( ( irel @ SY189 @ SY23 )
=> ( p @ SY23 ) )
| ! [SY24: $i] :
( ( irel @ SY189 @ SY24 )
=> ( ( q @ SY24 )
& ( r @ SY24 ) ) ) ) )
| ! [SY192: $i] :
( ( irel @ sK1_SY151 @ SY192 )
=> ( ( ! [SY139: $i] :
( ( irel @ SY192 @ SY139 )
=> ( p @ SY139 ) )
| ! [SY140: $i] :
( ( irel @ SY192 @ SY140 )
=> ( q @ SY140 ) ) )
& ( ! [SY141: $i] :
( ( irel @ SY192 @ SY141 )
=> ( p @ SY141 ) )
| ! [SY142: $i] :
( ( irel @ SY192 @ SY142 )
=> ( r @ SY142 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( irel @ SX0 @ SX1 )
| ~ ( irel @ SX1 @ SX2 ) )
| ( irel @ SX0 @ 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] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( q @ SX1 )
| ~ ( r @ SX1 ) ) ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ~ ( ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ 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(18,plain,
! [SV1: $i] :
( ( irel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ~ ( ~ ( irel @ SV2 @ SY205 )
| ~ ( irel @ SY205 @ SY206 ) )
| ( irel @ SV2 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( q @ SX1 )
| ~ ( r @ SX1 ) ) ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ~ ( ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV3: $i,SV2: $i] :
( ( ! [SY207: $i] :
( ~ ~ ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SY207 ) )
| ( irel @ SV2 @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( q @ SX1 )
| ~ ( r @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ~ ( ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ~ ~ ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 ) )
| ( irel @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( q @ SX1 )
| ~ ( r @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( irel @ sK1_SY151 @ sK2_SX0 )
| ~ ( ~ ( ! [SY208: $i] :
( ~ ( irel @ sK2_SX0 @ SY208 )
| ( p @ SY208 ) )
| ! [SY209: $i] :
( ~ ( irel @ sK2_SX0 @ SY209 )
| ( q @ SY209 ) ) )
| ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(27,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 ) ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV5: $i] :
( ( ~ ( irel @ sK1_SY151 @ SV5 )
| ! [SY212: $i] :
( ~ ( irel @ SV5 @ SY212 )
| ( p @ SY212 ) )
| ! [SY213: $i] :
( ~ ( irel @ SV5 @ SY213 )
| ~ ( ~ ( q @ SY213 )
| ~ ( r @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ( irel @ sK1_SY151 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ( ~ ( ! [SY208: $i] :
( ~ ( irel @ sK2_SX0 @ SY208 )
| ( p @ SY208 ) )
| ! [SY209: $i] :
( ~ ( irel @ sK2_SX0 @ SY209 )
| ( q @ SY209 ) ) )
| ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 ) ) )
= $false )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV5: $i] :
( ( ( ~ ( irel @ sK1_SY151 @ SV5 ) )
= $true )
| ( ( ! [SY212: $i] :
( ~ ( irel @ SV5 @ SY212 )
| ( p @ SY212 ) )
| ! [SY213: $i] :
( ~ ( irel @ SV5 @ SY213 )
| ~ ( ~ ( q @ SY213 )
| ~ ( r @ SY213 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( irel @ sK1_SY151 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( ! [SY208: $i] :
( ~ ( irel @ sK2_SX0 @ SY208 )
| ( p @ SY208 ) )
| ! [SY209: $i] :
( ~ ( irel @ sK2_SX0 @ SY209 )
| ( q @ SY209 ) ) )
| ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV5: $i] :
( ( ( irel @ sK1_SY151 @ SV5 )
= $false )
| ( ( ! [SY212: $i] :
( ~ ( irel @ SV5 @ SY212 )
| ( p @ SY212 ) )
| ! [SY213: $i] :
( ~ ( irel @ SV5 @ SY213 )
| ~ ( ~ ( q @ SY213 )
| ~ ( r @ SY213 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
( ( ( ~ ( ! [SY208: $i] :
( ~ ( irel @ sK2_SX0 @ SY208 )
| ( p @ SY208 ) )
| ! [SY209: $i] :
( ~ ( irel @ sK2_SX0 @ SY209 )
| ( q @ SY209 ) ) ) )
= $true )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( irel @ SV3 @ SV4 ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( ! [SY212: $i] :
( ~ ( irel @ SV5 @ SY212 )
| ( p @ SY212 ) ) )
= $true )
| ( ( ! [SY213: $i] :
( ~ ( irel @ SV5 @ SY213 )
| ~ ( ~ ( q @ SY213 )
| ~ ( r @ SY213 ) ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
( ( ( ! [SY208: $i] :
( ~ ( irel @ sK2_SX0 @ SY208 )
| ( p @ SY208 ) )
| ! [SY209: $i] :
( ~ ( irel @ sK2_SX0 @ SY209 )
| ( q @ SY209 ) ) )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( irel @ SV2 @ SV3 )
= $false )
| ( ( ~ ( irel @ SV3 @ SV4 ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV6: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV6 )
| ( p @ SV6 ) )
= $true )
| ( ( ! [SY213: $i] :
( ~ ( irel @ SV5 @ SY213 )
| ~ ( ~ ( q @ SY213 )
| ~ ( r @ SY213 ) ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( ( ! [SY208: $i] :
( ~ ( irel @ sK2_SX0 @ SY208 )
| ( p @ SY208 ) ) )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ( ! [SY209: $i] :
( ~ ( irel @ sK2_SX0 @ SY209 )
| ( q @ SY209 ) ) )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: $i,SV4: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV4 )
= $false )
| ( ( irel @ SV2 @ SV3 )
= $false )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV6: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV6 ) )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( ! [SY213: $i] :
( ~ ( irel @ SV5 @ SY213 )
| ~ ( ~ ( q @ SY213 )
| ~ ( r @ SY213 ) ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK3_SY208 )
| ( p @ sK3_SY208 ) )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(48,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK4_SY209 )
| ( q @ sK4_SY209 ) )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(49,plain,
! [SV6: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( ! [SY213: $i] :
( ~ ( irel @ SV5 @ SY213 )
| ~ ( ~ ( q @ SY213 )
| ~ ( r @ SY213 ) ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK3_SY208 ) )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
( ( ( p @ sK3_SY208 )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(52,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK4_SY209 ) )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( ( q @ sK4_SY209 )
= $false )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV6: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV7 )
| ~ ( ~ ( q @ SV7 )
| ~ ( r @ SV7 ) ) )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
( ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
( ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true )
| ( ( ~ ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(58,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV6: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( q @ SV7 )
| ~ ( r @ SV7 ) ) )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(60,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) ) )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
( ( ( ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(63,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) )
| ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) ) )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
( ( ( ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
! [SV6: $i,SV7: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( ~ ( ~ ( q @ SV7 )
| ~ ( r @ SV7 ) ) )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(67,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(68,plain,
( ( ( ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(69,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK5_SY210 )
| ( p @ sK5_SY210 ) )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(70,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK6_SY211 )
| ( r @ sK6_SY211 ) )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(71,plain,
( ( ( ! [SY210: $i] :
( ~ ( irel @ sK2_SX0 @ SY210 )
| ( p @ SY210 ) ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(72,plain,
( ( ( ! [SY211: $i] :
( ~ ( irel @ sK2_SX0 @ SY211 )
| ( r @ SY211 ) ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(73,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK7_SY210 )
| ( p @ sK7_SY210 ) )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(74,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK8_SY211 )
| ( r @ sK8_SY211 ) )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(75,plain,
! [SV6: $i,SV5: $i,SV7: $i] :
( ( ( ~ ( q @ SV7 )
| ~ ( r @ SV7 ) )
= $false )
| ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(76,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK9_SY210 )
| ( p @ sK9_SY210 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(77,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK10_SY211 )
| ( r @ sK10_SY211 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(78,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK5_SY210 ) )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(79,plain,
( ( ( p @ sK5_SY210 )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(80,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK6_SY211 ) )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(81,plain,
( ( ( r @ sK6_SY211 )
= $false )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(82,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK11_SY210 )
| ( p @ sK11_SY210 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(83,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK12_SY211 )
| ( r @ sK12_SY211 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(84,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK7_SY210 ) )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(85,plain,
( ( ( p @ sK7_SY210 )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(86,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK8_SY211 ) )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(87,plain,
( ( ( r @ sK8_SY211 )
= $false )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(88,plain,
! [SV6: $i,SV5: $i,SV7: $i] :
( ( ( ~ ( q @ SV7 ) )
= $false )
| ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(89,plain,
! [SV6: $i,SV5: $i,SV7: $i] :
( ( ( ~ ( r @ SV7 ) )
= $false )
| ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(90,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK9_SY210 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(91,plain,
( ( ( p @ sK9_SY210 )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(92,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK10_SY211 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(93,plain,
( ( ( r @ sK10_SY211 )
= $false )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(94,plain,
( ( ( irel @ sK2_SX0 @ sK5_SY210 )
= $true )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(95,plain,
( ( ( irel @ sK2_SX0 @ sK6_SY211 )
= $true )
| ( ( p @ sK3_SY208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(96,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK11_SY210 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(97,plain,
( ( ( p @ sK11_SY210 )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(98,plain,
( ( ( ~ ( irel @ sK2_SX0 @ sK12_SY211 ) )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(99,plain,
( ( ( r @ sK12_SY211 )
= $false )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(100,plain,
( ( ( irel @ sK2_SX0 @ sK7_SY210 )
= $true )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(101,plain,
( ( ( irel @ sK2_SX0 @ sK8_SY211 )
= $true )
| ( ( q @ sK4_SY209 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(102,plain,
! [SV6: $i,SV5: $i,SV7: $i] :
( ( ( q @ SV7 )
= $true )
| ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(103,plain,
! [SV6: $i,SV5: $i,SV7: $i] :
( ( ( r @ SV7 )
= $true )
| ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( irel @ SV5 @ SV6 )
= $false )
| ( ( irel @ sK1_SY151 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(104,plain,
( ( ( irel @ sK2_SX0 @ sK9_SY210 )
= $true )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(105,plain,
( ( ( irel @ sK2_SX0 @ sK10_SY211 )
= $true )
| ( ( irel @ sK2_SX0 @ sK3_SY208 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(106,plain,
( ( ( irel @ sK2_SX0 @ sK11_SY210 )
= $true )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(107,plain,
( ( ( irel @ sK2_SX0 @ sK12_SY211 )
= $true )
| ( ( irel @ sK2_SX0 @ sK4_SY209 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(108,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,107,106,105,104,103,102,101,100,99,97,95,94,93,91,87,85,81,79,45,33]) ).
thf(109,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(111,plain,
( ( ~ ( ~ ! [SY197: $i] :
( ( irel @ sK1_SY151 @ SY197 )
=> ( ( ! [SY144: $i] :
( ( irel @ SY197 @ SY144 )
=> ( p @ SY144 ) )
| ! [SY145: $i] :
( ( irel @ SY197 @ SY145 )
=> ( q @ SY145 ) ) )
& ( ! [SY146: $i] :
( ( irel @ SY197 @ SY146 )
=> ( p @ SY146 ) )
| ! [SY147: $i] :
( ( irel @ SY197 @ SY147 )
=> ( r @ SY147 ) ) ) ) )
| ! [SY202: $i] :
( ( irel @ sK1_SY151 @ SY202 )
=> ( ! [SY82: $i] :
( ( irel @ SY202 @ SY82 )
=> ( p @ SY82 ) )
| ! [SY83: $i] :
( ( irel @ SY202 @ SY83 )
=> ( ( q @ SY83 )
& ( r @ SY83 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( irel @ SX0 @ SX1 )
| ~ ( irel @ SX1 @ SX2 ) )
| ( irel @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(113,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ~ ( ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( q @ SX1 )
| ~ ( r @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(114,plain,
! [SV8: $i] :
( ( irel @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV9: $i] :
( ( ! [SY214: $i,SY215: $i] :
( ~ ~ ( ~ ( irel @ SV9 @ SY214 )
| ~ ( irel @ SY214 @ SY215 ) )
| ( irel @ SV9 @ SY215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(116,plain,
( ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ~ ( ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( q @ SX1 )
| ~ ( r @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV10: $i,SV9: $i] :
( ( ! [SY216: $i] :
( ~ ~ ( ~ ( irel @ SV9 @ SV10 )
| ~ ( irel @ SV10 @ SY216 ) )
| ( irel @ SV9 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(118,plain,
( ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ~ ( ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( q @ SX1 )
| ~ ( r @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(120,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ~ ~ ( ~ ( irel @ SV9 @ SV10 )
| ~ ( irel @ SV10 @ SV11 ) )
| ( irel @ SV9 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(121,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY151 @ SX0 )
| ~ ( ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ~ ( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( r @ SX1 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(122,plain,
( ( ~ ( irel @ sK1_SY151 @ sK13_SX0 )
| ! [SY217: $i] :
( ~ ( irel @ sK13_SX0 @ SY217 )
| ( p @ SY217 ) )
| ! [SY218: $i] :
( ~ ( irel @ sK13_SX0 @ SY218 )
| ~ ( ~ ( q @ SY218 )
| ~ ( r @ SY218 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(123,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( irel @ SV9 @ SV10 )
| ~ ( irel @ SV10 @ SV11 ) ) )
= $true )
| ( ( irel @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(124,plain,
! [SV12: $i] :
( ( ~ ( irel @ sK1_SY151 @ SV12 )
| ~ ( ~ ( ! [SY219: $i] :
( ~ ( irel @ SV12 @ SY219 )
| ( p @ SY219 ) )
| ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
| ~ ( ! [SY221: $i] :
( ~ ( irel @ SV12 @ SY221 )
| ( p @ SY221 ) )
| ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(125,plain,
( ( ~ ( irel @ sK1_SY151 @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(126,plain,
( ( ! [SY217: $i] :
( ~ ( irel @ sK13_SX0 @ SY217 )
| ( p @ SY217 ) )
| ! [SY218: $i] :
( ~ ( irel @ sK13_SX0 @ SY218 )
| ~ ( ~ ( q @ SY218 )
| ~ ( r @ SY218 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( ~ ( irel @ SV9 @ SV10 )
| ~ ( irel @ SV10 @ SV11 ) ) )
= $false )
| ( ( irel @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV12: $i] :
( ( ( ~ ( irel @ sK1_SY151 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY219: $i] :
( ~ ( irel @ SV12 @ SY219 )
| ( p @ SY219 ) )
| ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
| ~ ( ! [SY221: $i] :
( ~ ( irel @ SV12 @ SY221 )
| ( p @ SY221 ) )
| ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(129,plain,
( ( irel @ sK1_SY151 @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(130,plain,
( ( ! [SY217: $i] :
( ~ ( irel @ sK13_SX0 @ SY217 )
| ( p @ SY217 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(131,plain,
( ( ! [SY218: $i] :
( ~ ( irel @ sK13_SX0 @ SY218 )
| ~ ( ~ ( q @ SY218 )
| ~ ( r @ SY218 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(132,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( irel @ SV9 @ SV10 )
| ~ ( irel @ SV10 @ SV11 ) )
= $true )
| ( ( irel @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV12: $i] :
( ( ( irel @ sK1_SY151 @ SV12 )
= $false )
| ( ( ~ ( ~ ( ! [SY219: $i] :
( ~ ( irel @ SV12 @ SY219 )
| ( p @ SY219 ) )
| ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
| ~ ( ! [SY221: $i] :
( ~ ( irel @ SV12 @ SY221 )
| ( p @ SY221 ) )
| ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(134,plain,
( ( ~ ( irel @ sK13_SX0 @ sK14_SY217 )
| ( p @ sK14_SY217 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(135,plain,
( ( ~ ( irel @ sK13_SX0 @ sK15_SY218 )
| ~ ( ~ ( q @ sK15_SY218 )
| ~ ( r @ sK15_SY218 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[131]) ).
thf(136,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( ~ ( irel @ SV9 @ SV10 ) )
= $true )
| ( ( ~ ( irel @ SV10 @ SV11 ) )
= $true )
| ( ( irel @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV12: $i] :
( ( ( ~ ( ! [SY219: $i] :
( ~ ( irel @ SV12 @ SY219 )
| ( p @ SY219 ) )
| ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
| ~ ( ! [SY221: $i] :
( ~ ( irel @ SV12 @ SY221 )
| ( p @ SY221 ) )
| ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) ) )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
( ( ~ ( irel @ sK13_SX0 @ sK14_SY217 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(139,plain,
( ( p @ sK14_SY217 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(140,plain,
( ( ~ ( irel @ sK13_SX0 @ sK15_SY218 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(141,plain,
( ( ~ ( ~ ( q @ sK15_SY218 )
| ~ ( r @ sK15_SY218 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(142,plain,
! [SV11: $i,SV10: $i,SV9: $i] :
( ( ( irel @ SV9 @ SV10 )
= $false )
| ( ( ~ ( irel @ SV10 @ SV11 ) )
= $true )
| ( ( irel @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV12: $i] :
( ( ( ~ ( ! [SY219: $i] :
( ~ ( irel @ SV12 @ SY219 )
| ( p @ SY219 ) )
| ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) ) )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(144,plain,
! [SV12: $i] :
( ( ( ~ ( ! [SY221: $i] :
( ~ ( irel @ SV12 @ SY221 )
| ( p @ SY221 ) )
| ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) ) )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(145,plain,
( ( irel @ sK13_SX0 @ sK14_SY217 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(146,plain,
( ( irel @ sK13_SX0 @ sK15_SY218 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(147,plain,
( ( ~ ( q @ sK15_SY218 )
| ~ ( r @ sK15_SY218 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(148,plain,
! [SV9: $i,SV11: $i,SV10: $i] :
( ( ( irel @ SV10 @ SV11 )
= $false )
| ( ( irel @ SV9 @ SV10 )
= $false )
| ( ( irel @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV12: $i] :
( ( ( ! [SY219: $i] :
( ~ ( irel @ SV12 @ SY219 )
| ( p @ SY219 ) )
| ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(150,plain,
! [SV12: $i] :
( ( ( ! [SY221: $i] :
( ~ ( irel @ SV12 @ SY221 )
| ( p @ SY221 ) )
| ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(151,plain,
( ( ( ~ ( q @ sK15_SY218 ) )
= $true )
| ( ( ~ ( r @ sK15_SY218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(152,plain,
! [SV12: $i] :
( ( ( ! [SY219: $i] :
( ~ ( irel @ SV12 @ SY219 )
| ( p @ SY219 ) ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(153,plain,
! [SV12: $i] :
( ( ( ! [SY221: $i] :
( ~ ( irel @ SV12 @ SY221 )
| ( p @ SY221 ) ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(154,plain,
( ( ( q @ sK15_SY218 )
= $false )
| ( ( ~ ( r @ sK15_SY218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(155,plain,
! [SV13: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV13 )
| ( p @ SV13 ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(156,plain,
! [SV14: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV14 )
| ( p @ SV14 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(157,plain,
( ( ( r @ sK15_SY218 )
= $false )
| ( ( q @ sK15_SY218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV13: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV13 ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV14: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV14 ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(160,plain,
! [SV13: $i,SV12: $i] :
( ( ( irel @ SV12 @ SV13 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( irel @ SV12 @ SY220 )
| ( q @ SY220 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(161,plain,
! [SV14: $i,SV12: $i] :
( ( ( irel @ SV12 @ SV14 )
= $false )
| ( ( p @ SV14 )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( irel @ SV12 @ SY222 )
| ( r @ SY222 ) ) )
= $true )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(162,plain,
! [SV13: $i,SV15: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV15 )
| ( q @ SV15 ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( irel @ SV12 @ SV13 )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(163,plain,
! [SV14: $i,SV16: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV16 )
| ( r @ SV16 ) )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ SV12 @ SV14 )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(164,plain,
! [SV13: $i,SV15: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV15 ) )
= $true )
| ( ( q @ SV15 )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( irel @ SV12 @ SV13 )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(165,plain,
! [SV14: $i,SV16: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV16 ) )
= $true )
| ( ( r @ SV16 )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ SV12 @ SV14 )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(166,plain,
! [SV13: $i,SV15: $i,SV12: $i] :
( ( ( irel @ SV12 @ SV15 )
= $false )
| ( ( q @ SV15 )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( irel @ SV12 @ SV13 )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(167,plain,
! [SV14: $i,SV16: $i,SV12: $i] :
( ( ( irel @ SV12 @ SV16 )
= $false )
| ( ( r @ SV16 )
= $true )
| ( ( p @ SV14 )
= $true )
| ( ( irel @ SV12 @ SV14 )
= $false )
| ( ( irel @ sK1_SY151 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(168,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[114,167,166,157,148,146,145,139,129]) ).
thf(169,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[168,108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN045^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 17:21:54 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.29
% 0.49/0.29 No.of.Axioms: 2
% 0.49/0.29
% 0.49/0.29 Length.of.Defs: 2734
% 0.49/0.29
% 0.49/0.29 Contains.Choice.Funs: false
% 0.49/0.29 ......
% 0.49/0.29
% 0.49/0.29 ********************************
% 0.49/0.29 * All subproblems solved! *
% 0.49/0.29 ********************************
% 0.49/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:168,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.49/0.29
% 0.49/0.29 %**** Beginning of derivation protocol ****
% 0.49/0.29 % SZS output start CNFRefutation
% See solution above
% 0.49/0.29
% 0.49/0.29 %**** End of derivation protocol ****
% 0.49/0.29 %**** no. of clauses in derivation: 169 ****
% 0.49/0.29 %**** clause counter: 168 ****
% 0.49/0.29
% 0.49/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:168,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------