%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO064^4.003 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:07:31 AM UTC 2026
% Result : Theorem 3.12s 0.82s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 201 ( 86 unt; 0 typ; 19 def)
% Number of atoms : 2494 ( 610 equ; 0 cnn)
% Maximal formula atoms : 21 ( 12 avg)
% Number of connectives : 3567 ( 518 ~; 926 |; 16 &;2047 @)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 9 con; 0-3 aty)
% Number of variables : 773 ( 31 ^; 740 !; 2 ?; 773 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i > $o ).
thf(tp_a1,type,
a1: $i > $o ).
thf(tp_a2,type,
a2: $i > $o ).
thf(tp_a3,type,
a3: $i > $o ).
thf(tp_b,type,
b: $i > $o ).
thf(tp_b1,type,
b1: $i > $o ).
thf(tp_b2,type,
b2: $i > $o ).
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_sK1_SY63,type,
sK1_SY63: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY281,type,
sK4_SY281: $i > $i ).
thf(tp_sK5_SY293,type,
sK5_SY293: $i > $i ).
thf(tp_sK6_SY300,type,
sK6_SY300: $i ).
thf(tp_sK7_SY301,type,
sK7_SY301: $i ).
thf(tp_sK8_SY310,type,
sK8_SY310: $i ).
thf(tp_sK9_SY311,type,
sK9_SY311: $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,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(2,axiom,
ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(3,axiom,
ivalid @ ( iimplies @ ( iatom @ b1 ) @ ( ior @ ( ior @ ( iatom @ b2 ) @ ( iatom @ a2 ) ) @ ( iatom @ b2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(4,axiom,
ivalid @ ( iatom @ a3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(5,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(6,axiom,
! [X: $i] : ( irel @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).
thf(7,conjecture,
ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( ior @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iand @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(8,negated_conjecture,
( ( ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( ior @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iand @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [SY63: $i] :
( ! [SY64: $i] :
( ( irel @ SY63 @ SY64 )
=> ( a @ SY64 ) )
| ! [SY65: $i] :
( ( irel @ SY63 @ SY65 )
=> ( ! [SY59: $i] :
( ( irel @ SY65 @ SY59 )
=> ( ( b @ SY59 )
& ( a1 @ SY59 ) ) )
| ! [SY60: $i] :
( ( irel @ SY65 @ SY60 )
=> ( ! [SY54: $i] :
( ( irel @ SY60 @ SY54 )
=> ( ( b1 @ SY54 )
& ( a2 @ SY54 ) ) )
| ! [SY55: $i] :
( ( irel @ SY60 @ SY55 )
=> ( ( b2 @ SY55 )
& ( a3 @ SY55 ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(10,plain,
( ( ! [SY113: $i] :
( ! [SY114: $i] :
( ( irel @ SY113 @ SY114 )
=> ( ! [SY94: $i] :
( ( irel @ SY114 @ SY94 )
=> ( b @ SY94 ) )
| ! [SY95: $i] :
( ( irel @ SY114 @ SY95 )
=> ( a @ SY95 ) ) ) )
| ! [SY117: $i] :
( ( irel @ SY113 @ SY117 )
=> ( b @ SY117 ) ) ) )
= $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(11,plain,
( ( ! [SY182: $i] :
( ~ ! [SY183: $i] :
( ( irel @ SY182 @ SY183 )
=> ( b @ SY183 ) )
| ! [SY184: $i] :
( ( irel @ SY182 @ SY184 )
=> ( ! [SY178: $i] :
( ( irel @ SY184 @ SY178 )
=> ( ! [SY156: $i] :
( ( irel @ SY178 @ SY156 )
=> ( b1 @ SY156 ) )
| ! [SY157: $i] :
( ( irel @ SY178 @ SY157 )
=> ( a1 @ SY157 ) ) ) )
| ! [SY181: $i] :
( ( irel @ SY184 @ SY181 )
=> ( b1 @ SY181 ) ) ) ) ) )
= $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(12,plain,
( ( ! [SY255: $i] :
( ~ ! [SY256: $i] :
( ( irel @ SY255 @ SY256 )
=> ( b1 @ SY256 ) )
| ! [SY257: $i] :
( ( irel @ SY255 @ SY257 )
=> ( ! [SY251: $i] :
( ( irel @ SY257 @ SY251 )
=> ( ! [SY229: $i] :
( ( irel @ SY251 @ SY229 )
=> ( b2 @ SY229 ) )
| ! [SY230: $i] :
( ( irel @ SY251 @ SY230 )
=> ( a2 @ SY230 ) ) ) )
| ! [SY254: $i] :
( ( irel @ SY257 @ SY254 )
=> ( b2 @ SY254 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(13,plain,
( ( ! [SY269: $i] : ( a3 @ SY269 ) )
= $true ),
inference(unfold_def,[status(thm)],[4,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(15,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[6,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(16,plain,
( ( ! [SY275: $i] :
( ( irel @ sK1_SY63 @ SY275 )
=> ( a @ SY275 ) )
| ! [SY276: $i] :
( ( irel @ sK1_SY63 @ SY276 )
=> ( ! [SY59: $i] :
( ( irel @ SY276 @ SY59 )
=> ( ( b @ SY59 )
& ( a1 @ SY59 ) ) )
| ! [SY60: $i] :
( ( irel @ SY276 @ SY60 )
=> ( ! [SY54: $i] :
( ( irel @ SY60 @ SY54 )
=> ( ( b1 @ SY54 )
& ( a2 @ SY54 ) ) )
| ! [SY55: $i] :
( ( irel @ SY60 @ SY55 )
=> ( ( b2 @ SY55 )
& ( a3 @ SY55 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( ~ ( ! [SY275: $i] :
( ( irel @ sK1_SY63 @ SY275 )
=> ( a @ SY275 ) )
| ! [SY276: $i] :
( ( irel @ sK1_SY63 @ SY276 )
=> ( ! [SY59: $i] :
( ( irel @ SY276 @ SY59 )
=> ( ( b @ SY59 )
& ( a1 @ SY59 ) ) )
| ! [SY60: $i] :
( ( irel @ SY276 @ SY60 )
=> ( ! [SY54: $i] :
( ( irel @ SY60 @ SY54 )
=> ( ( b1 @ SY54 )
& ( a2 @ SY54 ) ) )
| ! [SY55: $i] :
( ( irel @ SY60 @ SY55 )
=> ( ( b2 @ SY55 )
& ( a3 @ SY55 ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [SY269: $i] : ( a3 @ SY269 ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [SY255: $i] :
( ~ ! [SY256: $i] :
( ( irel @ SY255 @ SY256 )
=> ( b1 @ SY256 ) )
| ! [SY257: $i] :
( ( irel @ SY255 @ SY257 )
=> ( ! [SY251: $i] :
( ( irel @ SY257 @ SY251 )
=> ( ! [SY229: $i] :
( ( irel @ SY251 @ SY229 )
=> ( b2 @ SY229 ) )
| ! [SY230: $i] :
( ( irel @ SY251 @ SY230 )
=> ( a2 @ SY230 ) ) ) )
| ! [SY254: $i] :
( ( irel @ SY257 @ SY254 )
=> ( b2 @ SY254 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [SY182: $i] :
( ~ ! [SY183: $i] :
( ( irel @ SY182 @ SY183 )
=> ( b @ SY183 ) )
| ! [SY184: $i] :
( ( irel @ SY182 @ SY184 )
=> ( ! [SY178: $i] :
( ( irel @ SY184 @ SY178 )
=> ( ! [SY156: $i] :
( ( irel @ SY178 @ SY156 )
=> ( b1 @ SY156 ) )
| ! [SY157: $i] :
( ( irel @ SY178 @ SY157 )
=> ( a1 @ SY157 ) ) ) )
| ! [SY181: $i] :
( ( irel @ SY184 @ SY181 )
=> ( b1 @ SY181 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [SY113: $i] :
( ! [SY114: $i] :
( ( irel @ SY113 @ SY114 )
=> ( ! [SY94: $i] :
( ( irel @ SY114 @ SY94 )
=> ( b @ SY94 ) )
| ! [SY95: $i] :
( ( irel @ SY114 @ SY95 )
=> ( a @ SY95 ) ) ) )
| ! [SY117: $i] :
( ( irel @ SY113 @ SY117 )
=> ( b @ SY117 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ ( ! [SY275: $i] :
( ( irel @ sK1_SY63 @ SY275 )
=> ( a @ SY275 ) )
| ! [SY276: $i] :
( ( irel @ sK1_SY63 @ SY276 )
=> ( ! [SY59: $i] :
( ( irel @ SY276 @ SY59 )
=> ( ( b @ SY59 )
& ( a1 @ SY59 ) ) )
| ! [SY60: $i] :
( ( irel @ SY276 @ SY60 )
=> ( ! [SY54: $i] :
( ( irel @ SY60 @ SY54 )
=> ( ( b1 @ SY54 )
& ( a2 @ SY54 ) ) )
| ! [SY55: $i] :
( ( irel @ SY60 @ SY55 )
=> ( ( b2 @ SY55 )
& ( a3 @ SY55 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( b1 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( b2 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(26,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY63 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY63 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( b @ SX1 )
| ~ ( a1 @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( b1 @ SX2 )
| ~ ( a2 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( b2 @ SX2 )
| ~ ( a3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(27,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( b @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( a @ SX2 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( b @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( irel @ SX0 @ SX1 )
| ~ ( irel @ SX1 @ SX2 ) )
| ( irel @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(29,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( b @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( b1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(30,plain,
! [SV1: $i] :
( ( irel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(31,plain,
! [SV2: $i] :
( ( a3 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(32,plain,
! [SV3: $i] :
( ( ~ ! [SY281: $i] :
( ~ ( irel @ SV3 @ SY281 )
| ( b1 @ SY281 ) )
| ! [SY282: $i] :
( ~ ( irel @ SV3 @ SY282 )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ( b2 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY63 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY63 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( b @ SX1 )
| ~ ( a1 @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( b1 @ SX2 )
| ~ ( a2 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( b2 @ SX2 )
| ~ ( a3 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV4: $i] :
( ( ! [SY287: $i] :
( ~ ( irel @ SV4 @ SY287 )
| ! [SX2: $i] :
( ~ ( irel @ SY287 @ SX2 )
| ( b @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY287 @ SX2 )
| ( a @ SX2 ) ) )
| ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV5: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ~ ~ ( ~ ( irel @ SV5 @ SY291 )
| ~ ( irel @ SY291 @ SY292 ) )
| ( irel @ SV5 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV6: $i] :
( ( ~ ! [SY293: $i] :
( ~ ( irel @ SV6 @ SY293 )
| ( b @ SY293 ) )
| ! [SY294: $i] :
( ~ ( irel @ SV6 @ SY294 )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ( b1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV3: $i] :
( ( ( ~ ! [SY281: $i] :
( ~ ( irel @ SV3 @ SY281 )
| ( b1 @ SY281 ) ) )
= $true )
| ( ( ! [SY282: $i] :
( ~ ( irel @ SV3 @ SY282 )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ( b2 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY63 @ SX0 )
| ( a @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(39,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY63 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( b @ SX1 )
| ~ ( a1 @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( b1 @ SX2 )
| ~ ( a2 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( b2 @ SX2 )
| ~ ( a3 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(40,plain,
! [SV4: $i] :
( ( ( ! [SY287: $i] :
( ~ ( irel @ SV4 @ SY287 )
| ! [SX2: $i] :
( ~ ( irel @ SY287 @ SX2 )
| ( b @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY287 @ SX2 )
| ( a @ SX2 ) ) ) )
= $true )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV7: $i,SV5: $i] :
( ( ! [SY299: $i] :
( ~ ~ ( ~ ( irel @ SV5 @ SV7 )
| ~ ( irel @ SV7 @ SY299 ) )
| ( irel @ SV5 @ SY299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV6: $i] :
( ( ( ~ ! [SY293: $i] :
( ~ ( irel @ SV6 @ SY293 )
| ( b @ SY293 ) ) )
= $true )
| ( ( ! [SY294: $i] :
( ~ ( irel @ SV6 @ SY294 )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ( b1 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( ! [SY281: $i] :
( ~ ( irel @ SV3 @ SY281 )
| ( b1 @ SY281 ) ) )
= $false )
| ( ( ! [SY282: $i] :
( ~ ( irel @ SV3 @ SY282 )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ( b2 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(44,plain,
( ( ~ ( irel @ sK1_SY63 @ sK2_SX0 )
| ( a @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(45,plain,
( ( ~ ( irel @ sK1_SY63 @ sK3_SX0 )
| ! [SY300: $i] :
( ~ ( irel @ sK3_SX0 @ SY300 )
| ~ ( ~ ( b @ SY300 )
| ~ ( a1 @ SY300 ) ) )
| ! [SY301: $i] :
( ~ ( irel @ sK3_SX0 @ SY301 )
| ! [SX2: $i] :
( ~ ( irel @ SY301 @ SX2 )
| ~ ( ~ ( b1 @ SX2 )
| ~ ( a2 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY301 @ SX2 )
| ~ ( ~ ( b2 @ SX2 )
| ~ ( a3 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(46,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV8 )
| ! [SY304: $i] :
( ~ ( irel @ SV8 @ SY304 )
| ( b @ SY304 ) )
| ! [SY305: $i] :
( ~ ( irel @ SV8 @ SY305 )
| ( a @ SY305 ) ) )
= $true )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ~ ~ ( ~ ( irel @ SV5 @ SV7 )
| ~ ( irel @ SV7 @ SV9 ) )
| ( irel @ SV5 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV6: $i] :
( ( ( ! [SY293: $i] :
( ~ ( irel @ SV6 @ SY293 )
| ( b @ SY293 ) ) )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( irel @ SV6 @ SY294 )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ( b1 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV3: $i] :
( ( ( ~ ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
| ( b1 @ ( sK4_SY281 @ SV3 ) ) )
= $false )
| ( ( ! [SY282: $i] :
( ~ ( irel @ SV3 @ SY282 )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ( b2 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(50,plain,
( ( ~ ( irel @ sK1_SY63 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(51,plain,
( ( a @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(52,plain,
( ( ~ ( irel @ sK1_SY63 @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(53,plain,
( ( ! [SY300: $i] :
( ~ ( irel @ sK3_SX0 @ SY300 )
| ~ ( ~ ( b @ SY300 )
| ~ ( a1 @ SY300 ) ) )
| ! [SY301: $i] :
( ~ ( irel @ sK3_SX0 @ SY301 )
| ! [SX2: $i] :
( ~ ( irel @ SY301 @ SX2 )
| ~ ( ~ ( b1 @ SX2 )
| ~ ( a2 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY301 @ SX2 )
| ~ ( ~ ( b2 @ SX2 )
| ~ ( a3 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(54,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV8 ) )
= $true )
| ( ( ! [SY304: $i] :
( ~ ( irel @ SV8 @ SY304 )
| ( b @ SY304 ) )
| ! [SY305: $i] :
( ~ ( irel @ SV8 @ SY305 )
| ( a @ SY305 ) ) )
= $true )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( irel @ SV5 @ SV7 )
| ~ ( irel @ SV7 @ SV9 ) ) )
= $true )
| ( ( irel @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV6: $i] :
( ( ( ~ ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
| ( b @ ( sK5_SY293 @ SV6 ) ) )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( irel @ SV6 @ SY294 )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ( b1 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(57,plain,
! [SV3: $i] :
( ( ( ~ ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) ) )
= $false )
| ( ( ! [SY282: $i] :
( ~ ( irel @ SV3 @ SY282 )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ( b2 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(58,plain,
! [SV3: $i] :
( ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false )
| ( ( ! [SY282: $i] :
( ~ ( irel @ SV3 @ SY282 )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ( b2 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(59,plain,
( ( irel @ sK1_SY63 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(60,plain,
( ( irel @ sK1_SY63 @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(61,plain,
( ( ! [SY300: $i] :
( ~ ( irel @ sK3_SX0 @ SY300 )
| ~ ( ~ ( b @ SY300 )
| ~ ( a1 @ SY300 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(62,plain,
( ( ! [SY301: $i] :
( ~ ( irel @ sK3_SX0 @ SY301 )
| ! [SX2: $i] :
( ~ ( irel @ SY301 @ SX2 )
| ~ ( ~ ( b1 @ SX2 )
| ~ ( a2 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY301 @ SX2 )
| ~ ( ~ ( b2 @ SX2 )
| ~ ( a3 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(63,plain,
! [SV8: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY304: $i] :
( ~ ( irel @ SV8 @ SY304 )
| ( b @ SY304 ) )
| ! [SY305: $i] :
( ~ ( irel @ SV8 @ SY305 )
| ( a @ SY305 ) ) )
= $true )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( ~ ( irel @ SV5 @ SV7 )
| ~ ( irel @ SV7 @ SV9 ) ) )
= $false )
| ( ( irel @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV6: $i] :
( ( ( ~ ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) ) )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( irel @ SV6 @ SY294 )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ( b1 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(66,plain,
! [SV6: $i] :
( ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( irel @ SV6 @ SY294 )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ( b1 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(67,plain,
! [SV3: $i] :
( ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true )
| ( ( ! [SY282: $i] :
( ~ ( irel @ SV3 @ SY282 )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY282 @ SX2 )
| ( b2 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(68,plain,
! [SV10: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV10 )
| ! [SY306: $i] :
( ~ ( irel @ SV10 @ SY306 )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
( ( ~ ( irel @ sK3_SX0 @ sK6_SY300 )
| ~ ( ~ ( b @ sK6_SY300 )
| ~ ( a1 @ sK6_SY300 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(70,plain,
( ( ~ ( irel @ sK3_SX0 @ sK7_SY301 )
| ! [SY310: $i] :
( ~ ( irel @ sK7_SY301 @ SY310 )
| ~ ( ~ ( b1 @ SY310 )
| ~ ( a2 @ SY310 ) ) )
| ! [SY311: $i] :
( ~ ( irel @ sK7_SY301 @ SY311 )
| ~ ( ~ ( b2 @ SY311 )
| ~ ( a3 @ SY311 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(71,plain,
! [SV4: $i,SV8: $i] :
( ( ( ! [SY304: $i] :
( ~ ( irel @ SV8 @ SY304 )
| ( b @ SY304 ) ) )
= $true )
| ( ( ! [SY305: $i] :
( ~ ( irel @ SV8 @ SY305 )
| ( a @ SY305 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV7 )
| ~ ( irel @ SV7 @ SV9 ) )
= $true )
| ( ( irel @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(73,plain,
! [SV6: $i] :
( ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true )
| ( ( ! [SY294: $i] :
( ~ ( irel @ SV6 @ SY294 )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY294 @ SX2 )
| ( b1 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( irel @ SV6 @ SV11 )
| ! [SY312: $i] :
( ~ ( irel @ SV11 @ SY312 )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV12 )
| ! [SY316: $i] :
( ~ ( irel @ SV12 @ SY316 )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV10: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV10 ) )
= $true )
| ( ( ! [SY306: $i] :
( ~ ( irel @ SV10 @ SY306 )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(77,plain,
( ( ~ ( irel @ sK3_SX0 @ sK6_SY300 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(78,plain,
( ( ~ ( ~ ( b @ sK6_SY300 )
| ~ ( a1 @ sK6_SY300 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(79,plain,
( ( ~ ( irel @ sK3_SX0 @ sK7_SY301 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [SY310: $i] :
( ~ ( irel @ sK7_SY301 @ SY310 )
| ~ ( ~ ( b1 @ SY310 )
| ~ ( a2 @ SY310 ) ) )
| ! [SY311: $i] :
( ~ ( irel @ sK7_SY301 @ SY311 )
| ~ ( ~ ( b2 @ SY311 )
| ~ ( a3 @ SY311 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(81,plain,
! [SV4: $i,SV13: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV13 )
| ( b @ SV13 ) )
= $true )
| ( ( ! [SY305: $i] :
( ~ ( irel @ SV8 @ SY305 )
| ( a @ SY305 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV7 ) )
= $true )
| ( ( ~ ( irel @ SV7 @ SV9 ) )
= $true )
| ( ( irel @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV14: $i,SV6: $i] :
( ( ( ~ ( irel @ SV6 @ SV14 )
| ! [SY320: $i] :
( ~ ( irel @ SV14 @ SY320 )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( irel @ SV6 @ SV11 ) )
= $true )
| ( ( ! [SY312: $i] :
( ~ ( irel @ SV11 @ SY312 )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV12 ) )
= $true )
| ( ( ! [SY316: $i] :
( ~ ( irel @ SV12 @ SY316 )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV10: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( ! [SY306: $i] :
( ~ ( irel @ SV10 @ SY306 )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(87,plain,
( ( irel @ sK3_SX0 @ sK6_SY300 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(88,plain,
( ( ~ ( b @ sK6_SY300 )
| ~ ( a1 @ sK6_SY300 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(89,plain,
( ( irel @ sK3_SX0 @ sK7_SY301 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(90,plain,
( ( ! [SY310: $i] :
( ~ ( irel @ sK7_SY301 @ SY310 )
| ~ ( ~ ( b1 @ SY310 )
| ~ ( a2 @ SY310 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(91,plain,
( ( ! [SY311: $i] :
( ~ ( irel @ sK7_SY301 @ SY311 )
| ~ ( ~ ( b2 @ SY311 )
| ~ ( a3 @ SY311 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(92,plain,
! [SV4: $i,SV13: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV13 ) )
= $true )
| ( ( b @ SV13 )
= $true )
| ( ( ! [SY305: $i] :
( ~ ( irel @ SV8 @ SY305 )
| ( a @ SY305 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( ~ ( irel @ SV7 @ SV9 ) )
= $true )
| ( ( irel @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(94,plain,
! [SV14: $i,SV6: $i] :
( ( ( ~ ( irel @ SV6 @ SV14 ) )
= $true )
| ( ( ! [SY320: $i] :
( ~ ( irel @ SV14 @ SY320 )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(95,plain,
! [SV11: $i,SV6: $i] :
( ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( ! [SY312: $i] :
( ~ ( irel @ SV11 @ SY312 )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(96,plain,
! [SV12: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( ! [SY316: $i] :
( ~ ( irel @ SV12 @ SY316 )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( a2 @ SX3 ) ) )
| ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV3: $i,SV10: $i] :
( ( ( ! [SY306: $i] :
( ~ ( irel @ SV10 @ SY306 )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY306 @ SX3 )
| ( a2 @ SX3 ) ) ) )
= $true )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(98,plain,
( ( ( ~ ( b @ sK6_SY300 ) )
= $true )
| ( ( ~ ( a1 @ sK6_SY300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(99,plain,
( ( ~ ( irel @ sK7_SY301 @ sK8_SY310 )
| ~ ( ~ ( b1 @ sK8_SY310 )
| ~ ( a2 @ sK8_SY310 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(100,plain,
( ( ~ ( irel @ sK7_SY301 @ sK9_SY311 )
| ~ ( ~ ( b2 @ sK9_SY311 )
| ~ ( a3 @ sK9_SY311 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(101,plain,
! [SV4: $i,SV13: $i,SV8: $i] :
( ( ( irel @ SV8 @ SV13 )
= $false )
| ( ( b @ SV13 )
= $true )
| ( ( ! [SY305: $i] :
( ~ ( irel @ SV8 @ SY305 )
| ( a @ SY305 ) ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV5: $i,SV9: $i,SV7: $i] :
( ( ( irel @ SV7 @ SV9 )
= $false )
| ( ( irel @ SV5 @ SV7 )
= $false )
| ( ( irel @ SV5 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV14: $i,SV6: $i] :
( ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( ! [SY320: $i] :
( ~ ( irel @ SV14 @ SY320 )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( a1 @ SX3 ) ) )
| ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV6: $i,SV11: $i] :
( ( ( ! [SY312: $i] :
( ~ ( irel @ SV11 @ SY312 )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY312 @ SX3 )
| ( a1 @ SX3 ) ) ) )
= $true )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV3: $i,SV12: $i] :
( ( ( ! [SY316: $i] :
( ~ ( irel @ SV12 @ SY316 )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( b2 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY316 @ SX3 )
| ( a2 @ SX3 ) ) ) )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV3: $i,SV15: $i,SV10: $i] :
( ( ( ~ ( irel @ SV10 @ SV15 )
| ! [SY324: $i] :
( ~ ( irel @ SV15 @ SY324 )
| ( b2 @ SY324 ) )
| ! [SY325: $i] :
( ~ ( irel @ SV15 @ SY325 )
| ( a2 @ SY325 ) ) )
= $true )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(107,plain,
( ( ( b @ sK6_SY300 )
= $false )
| ( ( ~ ( a1 @ sK6_SY300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
( ( ~ ( irel @ sK7_SY301 @ sK8_SY310 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(109,plain,
( ( ~ ( ~ ( b1 @ sK8_SY310 )
| ~ ( a2 @ sK8_SY310 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(110,plain,
( ( ~ ( irel @ sK7_SY301 @ sK9_SY311 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(111,plain,
( ( ~ ( ~ ( b2 @ sK9_SY311 )
| ~ ( a3 @ sK9_SY311 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(112,plain,
! [SV4: $i,SV13: $i,SV16: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV16 )
| ( a @ SV16 ) )
= $true )
| ( ( b @ SV13 )
= $true )
| ( ( irel @ SV8 @ SV13 )
= $false )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV6: $i,SV14: $i] :
( ( ( ! [SY320: $i] :
( ~ ( irel @ SV14 @ SY320 )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( b1 @ SX3 ) )
| ! [SX3: $i] :
( ~ ( irel @ SY320 @ SX3 )
| ( a1 @ SX3 ) ) ) )
= $true )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV6: $i,SV17: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV17 )
| ! [SY326: $i] :
( ~ ( irel @ SV17 @ SY326 )
| ( b1 @ SY326 ) )
| ! [SY327: $i] :
( ~ ( irel @ SV17 @ SY327 )
| ( a1 @ SY327 ) ) )
= $true )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV3: $i,SV18: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV18 )
| ! [SY328: $i] :
( ~ ( irel @ SV18 @ SY328 )
| ( b2 @ SY328 ) )
| ! [SY329: $i] :
( ~ ( irel @ SV18 @ SY329 )
| ( a2 @ SY329 ) ) )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV3: $i,SV15: $i,SV10: $i] :
( ( ( ~ ( irel @ SV10 @ SV15 ) )
= $true )
| ( ( ! [SY324: $i] :
( ~ ( irel @ SV15 @ SY324 )
| ( b2 @ SY324 ) )
| ! [SY325: $i] :
( ~ ( irel @ SV15 @ SY325 )
| ( a2 @ SY325 ) ) )
= $true )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(117,plain,
( ( ( a1 @ sK6_SY300 )
= $false )
| ( ( b @ sK6_SY300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
( ( irel @ sK7_SY301 @ sK8_SY310 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
( ( ~ ( b1 @ sK8_SY310 )
| ~ ( a2 @ sK8_SY310 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(120,plain,
( ( irel @ sK7_SY301 @ sK9_SY311 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(121,plain,
( ( ~ ( b2 @ sK9_SY311 )
| ~ ( a3 @ sK9_SY311 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV4: $i,SV13: $i,SV16: $i,SV8: $i] :
( ( ( ~ ( irel @ SV8 @ SV16 ) )
= $true )
| ( ( a @ SV16 )
= $true )
| ( ( b @ SV13 )
= $true )
| ( ( irel @ SV8 @ SV13 )
= $false )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV6: $i,SV19: $i,SV14: $i] :
( ( ( ~ ( irel @ SV14 @ SV19 )
| ! [SY330: $i] :
( ~ ( irel @ SV19 @ SY330 )
| ( b1 @ SY330 ) )
| ! [SY331: $i] :
( ~ ( irel @ SV19 @ SY331 )
| ( a1 @ SY331 ) ) )
= $true )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV6: $i,SV17: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV17 ) )
= $true )
| ( ( ! [SY326: $i] :
( ~ ( irel @ SV17 @ SY326 )
| ( b1 @ SY326 ) )
| ! [SY327: $i] :
( ~ ( irel @ SV17 @ SY327 )
| ( a1 @ SY327 ) ) )
= $true )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV3: $i,SV18: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV18 ) )
= $true )
| ( ( ! [SY328: $i] :
( ~ ( irel @ SV18 @ SY328 )
| ( b2 @ SY328 ) )
| ! [SY329: $i] :
( ~ ( irel @ SV18 @ SY329 )
| ( a2 @ SY329 ) ) )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV3: $i,SV15: $i,SV10: $i] :
( ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY324: $i] :
( ~ ( irel @ SV15 @ SY324 )
| ( b2 @ SY324 ) )
| ! [SY325: $i] :
( ~ ( irel @ SV15 @ SY325 )
| ( a2 @ SY325 ) ) )
= $true )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
( ( ( ~ ( b1 @ sK8_SY310 ) )
= $true )
| ( ( ~ ( a2 @ sK8_SY310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(128,plain,
( ( ( ~ ( b2 @ sK9_SY311 ) )
= $true )
| ( ( ~ ( a3 @ sK9_SY311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(129,plain,
! [SV4: $i,SV13: $i,SV16: $i,SV8: $i] :
( ( ( irel @ SV8 @ SV16 )
= $false )
| ( ( a @ SV16 )
= $true )
| ( ( b @ SV13 )
= $true )
| ( ( irel @ SV8 @ SV13 )
= $false )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( ! [SY290: $i] :
( ~ ( irel @ SV4 @ SY290 )
| ( b @ SY290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV6: $i,SV19: $i,SV14: $i] :
( ( ( ~ ( irel @ SV14 @ SV19 ) )
= $true )
| ( ( ! [SY330: $i] :
( ~ ( irel @ SV19 @ SY330 )
| ( b1 @ SY330 ) )
| ! [SY331: $i] :
( ~ ( irel @ SV19 @ SY331 )
| ( a1 @ SY331 ) ) )
= $true )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV6: $i,SV17: $i,SV11: $i] :
( ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY326: $i] :
( ~ ( irel @ SV17 @ SY326 )
| ( b1 @ SY326 ) )
| ! [SY327: $i] :
( ~ ( irel @ SV17 @ SY327 )
| ( a1 @ SY327 ) ) )
= $true )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV3: $i,SV18: $i,SV12: $i] :
( ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY328: $i] :
( ~ ( irel @ SV18 @ SY328 )
| ( b2 @ SY328 ) )
| ! [SY329: $i] :
( ~ ( irel @ SV18 @ SY329 )
| ( a2 @ SY329 ) ) )
= $true )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV3: $i,SV10: $i,SV15: $i] :
( ( ( ! [SY324: $i] :
( ~ ( irel @ SV15 @ SY324 )
| ( b2 @ SY324 ) ) )
= $true )
| ( ( ! [SY325: $i] :
( ~ ( irel @ SV15 @ SY325 )
| ( a2 @ SY325 ) ) )
= $true )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
( ( ( b1 @ sK8_SY310 )
= $false )
| ( ( ~ ( a2 @ sK8_SY310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(135,plain,
( ( ( b2 @ sK9_SY311 )
= $false )
| ( ( ~ ( a3 @ sK9_SY311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV16: $i,SV13: $i,SV8: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV20 )
| ( b @ SV20 ) )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV8 @ SV13 )
= $false )
| ( ( b @ SV13 )
= $true )
| ( ( a @ SV16 )
= $true )
| ( ( irel @ SV8 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV6: $i,SV19: $i,SV14: $i] :
( ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY330: $i] :
( ~ ( irel @ SV19 @ SY330 )
| ( b1 @ SY330 ) )
| ! [SY331: $i] :
( ~ ( irel @ SV19 @ SY331 )
| ( a1 @ SY331 ) ) )
= $true )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV6: $i,SV11: $i,SV17: $i] :
( ( ( ! [SY326: $i] :
( ~ ( irel @ SV17 @ SY326 )
| ( b1 @ SY326 ) ) )
= $true )
| ( ( ! [SY327: $i] :
( ~ ( irel @ SV17 @ SY327 )
| ( a1 @ SY327 ) ) )
= $true )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV3: $i,SV12: $i,SV18: $i] :
( ( ( ! [SY328: $i] :
( ~ ( irel @ SV18 @ SY328 )
| ( b2 @ SY328 ) ) )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( irel @ SV18 @ SY329 )
| ( a2 @ SY329 ) ) )
= $true )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV3: $i,SV10: $i,SV21: $i,SV15: $i] :
( ( ( ~ ( irel @ SV15 @ SV21 )
| ( b2 @ SV21 ) )
= $true )
| ( ( ! [SY325: $i] :
( ~ ( irel @ SV15 @ SY325 )
| ( a2 @ SY325 ) ) )
= $true )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(141,plain,
( ( ( a2 @ sK8_SY310 )
= $false )
| ( ( b1 @ sK8_SY310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(142,plain,
( ( ( a3 @ sK9_SY311 )
= $false )
| ( ( b2 @ sK9_SY311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(143,plain,
! [SV16: $i,SV13: $i,SV8: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV20 ) )
= $true )
| ( ( b @ SV20 )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV8 @ SV13 )
= $false )
| ( ( b @ SV13 )
= $true )
| ( ( a @ SV16 )
= $true )
| ( ( irel @ SV8 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV6: $i,SV14: $i,SV19: $i] :
( ( ( ! [SY330: $i] :
( ~ ( irel @ SV19 @ SY330 )
| ( b1 @ SY330 ) ) )
= $true )
| ( ( ! [SY331: $i] :
( ~ ( irel @ SV19 @ SY331 )
| ( a1 @ SY331 ) ) )
= $true )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(145,plain,
! [SV6: $i,SV11: $i,SV22: $i,SV17: $i] :
( ( ( ~ ( irel @ SV17 @ SV22 )
| ( b1 @ SV22 ) )
= $true )
| ( ( ! [SY327: $i] :
( ~ ( irel @ SV17 @ SY327 )
| ( a1 @ SY327 ) ) )
= $true )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(146,plain,
! [SV3: $i,SV12: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( irel @ SV18 @ SV23 )
| ( b2 @ SV23 ) )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( irel @ SV18 @ SY329 )
| ( a2 @ SY329 ) ) )
= $true )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(147,plain,
! [SV3: $i,SV10: $i,SV21: $i,SV15: $i] :
( ( ( ~ ( irel @ SV15 @ SV21 ) )
= $true )
| ( ( b2 @ SV21 )
= $true )
| ( ( ! [SY325: $i] :
( ~ ( irel @ SV15 @ SY325 )
| ( a2 @ SY325 ) ) )
= $true )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV16: $i,SV13: $i,SV8: $i,SV20: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV20 )
= $false )
| ( ( b @ SV20 )
= $true )
| ( ( irel @ SV4 @ SV8 )
= $false )
| ( ( irel @ SV8 @ SV13 )
= $false )
| ( ( b @ SV13 )
= $true )
| ( ( a @ SV16 )
= $true )
| ( ( irel @ SV8 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV6: $i,SV14: $i,SV24: $i,SV19: $i] :
( ( ( ~ ( irel @ SV19 @ SV24 )
| ( b1 @ SV24 ) )
= $true )
| ( ( ! [SY331: $i] :
( ~ ( irel @ SV19 @ SY331 )
| ( a1 @ SY331 ) ) )
= $true )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(150,plain,
! [SV6: $i,SV11: $i,SV22: $i,SV17: $i] :
( ( ( ~ ( irel @ SV17 @ SV22 ) )
= $true )
| ( ( b1 @ SV22 )
= $true )
| ( ( ! [SY327: $i] :
( ~ ( irel @ SV17 @ SY327 )
| ( a1 @ SY327 ) ) )
= $true )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV3: $i,SV12: $i,SV23: $i,SV18: $i] :
( ( ( ~ ( irel @ SV18 @ SV23 ) )
= $true )
| ( ( b2 @ SV23 )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( irel @ SV18 @ SY329 )
| ( a2 @ SY329 ) ) )
= $true )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(152,plain,
! [SV3: $i,SV10: $i,SV21: $i,SV15: $i] :
( ( ( irel @ SV15 @ SV21 )
= $false )
| ( ( b2 @ SV21 )
= $true )
| ( ( ! [SY325: $i] :
( ~ ( irel @ SV15 @ SY325 )
| ( a2 @ SY325 ) ) )
= $true )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(153,plain,
! [SV6: $i,SV14: $i,SV24: $i,SV19: $i] :
( ( ( ~ ( irel @ SV19 @ SV24 ) )
= $true )
| ( ( b1 @ SV24 )
= $true )
| ( ( ! [SY331: $i] :
( ~ ( irel @ SV19 @ SY331 )
| ( a1 @ SY331 ) ) )
= $true )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(154,plain,
! [SV6: $i,SV11: $i,SV22: $i,SV17: $i] :
( ( ( irel @ SV17 @ SV22 )
= $false )
| ( ( b1 @ SV22 )
= $true )
| ( ( ! [SY327: $i] :
( ~ ( irel @ SV17 @ SY327 )
| ( a1 @ SY327 ) ) )
= $true )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(155,plain,
! [SV3: $i,SV12: $i,SV23: $i,SV18: $i] :
( ( ( irel @ SV18 @ SV23 )
= $false )
| ( ( b2 @ SV23 )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( irel @ SV18 @ SY329 )
| ( a2 @ SY329 ) ) )
= $true )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(156,plain,
! [SV3: $i,SV10: $i,SV21: $i,SV25: $i,SV15: $i] :
( ( ( ~ ( irel @ SV15 @ SV25 )
| ( a2 @ SV25 ) )
= $true )
| ( ( b2 @ SV21 )
= $true )
| ( ( irel @ SV15 @ SV21 )
= $false )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(157,plain,
! [SV6: $i,SV14: $i,SV24: $i,SV19: $i] :
( ( ( irel @ SV19 @ SV24 )
= $false )
| ( ( b1 @ SV24 )
= $true )
| ( ( ! [SY331: $i] :
( ~ ( irel @ SV19 @ SY331 )
| ( a1 @ SY331 ) ) )
= $true )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV6: $i,SV11: $i,SV22: $i,SV26: $i,SV17: $i] :
( ( ( ~ ( irel @ SV17 @ SV26 )
| ( a1 @ SV26 ) )
= $true )
| ( ( b1 @ SV22 )
= $true )
| ( ( irel @ SV17 @ SV22 )
= $false )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV3: $i,SV12: $i,SV23: $i,SV27: $i,SV18: $i] :
( ( ( ~ ( irel @ SV18 @ SV27 )
| ( a2 @ SV27 ) )
= $true )
| ( ( b2 @ SV23 )
= $true )
| ( ( irel @ SV18 @ SV23 )
= $false )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(160,plain,
! [SV3: $i,SV10: $i,SV21: $i,SV25: $i,SV15: $i] :
( ( ( ~ ( irel @ SV15 @ SV25 ) )
= $true )
| ( ( a2 @ SV25 )
= $true )
| ( ( b2 @ SV21 )
= $true )
| ( ( irel @ SV15 @ SV21 )
= $false )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(161,plain,
! [SV6: $i,SV14: $i,SV24: $i,SV28: $i,SV19: $i] :
( ( ( ~ ( irel @ SV19 @ SV28 )
| ( a1 @ SV28 ) )
= $true )
| ( ( b1 @ SV24 )
= $true )
| ( ( irel @ SV19 @ SV24 )
= $false )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(162,plain,
! [SV6: $i,SV11: $i,SV22: $i,SV26: $i,SV17: $i] :
( ( ( ~ ( irel @ SV17 @ SV26 ) )
= $true )
| ( ( a1 @ SV26 )
= $true )
| ( ( b1 @ SV22 )
= $true )
| ( ( irel @ SV17 @ SV22 )
= $false )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(163,plain,
! [SV3: $i,SV12: $i,SV23: $i,SV27: $i,SV18: $i] :
( ( ( ~ ( irel @ SV18 @ SV27 ) )
= $true )
| ( ( a2 @ SV27 )
= $true )
| ( ( b2 @ SV23 )
= $true )
| ( ( irel @ SV18 @ SV23 )
= $false )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV3: $i,SV10: $i,SV21: $i,SV25: $i,SV15: $i] :
( ( ( irel @ SV15 @ SV25 )
= $false )
| ( ( a2 @ SV25 )
= $true )
| ( ( b2 @ SV21 )
= $true )
| ( ( irel @ SV15 @ SV21 )
= $false )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( ! [SY309: $i] :
( ~ ( irel @ SV10 @ SY309 )
| ( b2 @ SY309 ) ) )
= $true )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV6: $i,SV14: $i,SV24: $i,SV28: $i,SV19: $i] :
( ( ( ~ ( irel @ SV19 @ SV28 ) )
= $true )
| ( ( a1 @ SV28 )
= $true )
| ( ( b1 @ SV24 )
= $true )
| ( ( irel @ SV19 @ SV24 )
= $false )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV6: $i,SV11: $i,SV22: $i,SV26: $i,SV17: $i] :
( ( ( irel @ SV17 @ SV26 )
= $false )
| ( ( a1 @ SV26 )
= $true )
| ( ( b1 @ SV22 )
= $true )
| ( ( irel @ SV17 @ SV22 )
= $false )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( ! [SY315: $i] :
( ~ ( irel @ SV11 @ SY315 )
| ( b1 @ SY315 ) ) )
= $true )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV3: $i,SV12: $i,SV23: $i,SV27: $i,SV18: $i] :
( ( ( irel @ SV18 @ SV27 )
= $false )
| ( ( a2 @ SV27 )
= $true )
| ( ( b2 @ SV23 )
= $true )
| ( ( irel @ SV18 @ SV23 )
= $false )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( ! [SY319: $i] :
( ~ ( irel @ SV12 @ SY319 )
| ( b2 @ SY319 ) ) )
= $true )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(168,plain,
! [SV3: $i,SV25: $i,SV21: $i,SV15: $i,SV29: $i,SV10: $i] :
( ( ( ~ ( irel @ SV10 @ SV29 )
| ( b2 @ SV29 ) )
= $true )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( irel @ SV15 @ SV21 )
= $false )
| ( ( b2 @ SV21 )
= $true )
| ( ( a2 @ SV25 )
= $true )
| ( ( irel @ SV15 @ SV25 )
= $false )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(169,plain,
! [SV6: $i,SV14: $i,SV24: $i,SV28: $i,SV19: $i] :
( ( ( irel @ SV19 @ SV28 )
= $false )
| ( ( a1 @ SV28 )
= $true )
| ( ( b1 @ SV24 )
= $true )
| ( ( irel @ SV19 @ SV24 )
= $false )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( irel @ SV14 @ SY323 )
| ( b1 @ SY323 ) ) )
= $true )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(170,plain,
! [SV6: $i,SV26: $i,SV22: $i,SV17: $i,SV30: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV30 )
| ( b1 @ SV30 ) )
= $true )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( irel @ SV17 @ SV22 )
= $false )
| ( ( b1 @ SV22 )
= $true )
| ( ( a1 @ SV26 )
= $true )
| ( ( irel @ SV17 @ SV26 )
= $false )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV3: $i,SV27: $i,SV23: $i,SV18: $i,SV31: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV31 )
| ( b2 @ SV31 ) )
= $true )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( irel @ SV18 @ SV23 )
= $false )
| ( ( b2 @ SV23 )
= $true )
| ( ( a2 @ SV27 )
= $true )
| ( ( irel @ SV18 @ SV27 )
= $false )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(172,plain,
! [SV3: $i,SV25: $i,SV21: $i,SV15: $i,SV29: $i,SV10: $i] :
( ( ( ~ ( irel @ SV10 @ SV29 ) )
= $true )
| ( ( b2 @ SV29 )
= $true )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( irel @ SV15 @ SV21 )
= $false )
| ( ( b2 @ SV21 )
= $true )
| ( ( a2 @ SV25 )
= $true )
| ( ( irel @ SV15 @ SV25 )
= $false )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(173,plain,
! [SV6: $i,SV28: $i,SV24: $i,SV19: $i,SV32: $i,SV14: $i] :
( ( ( ~ ( irel @ SV14 @ SV32 )
| ( b1 @ SV32 ) )
= $true )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( irel @ SV19 @ SV24 )
= $false )
| ( ( b1 @ SV24 )
= $true )
| ( ( a1 @ SV28 )
= $true )
| ( ( irel @ SV19 @ SV28 )
= $false )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(174,plain,
! [SV6: $i,SV26: $i,SV22: $i,SV17: $i,SV30: $i,SV11: $i] :
( ( ( ~ ( irel @ SV11 @ SV30 ) )
= $true )
| ( ( b1 @ SV30 )
= $true )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( irel @ SV17 @ SV22 )
= $false )
| ( ( b1 @ SV22 )
= $true )
| ( ( a1 @ SV26 )
= $true )
| ( ( irel @ SV17 @ SV26 )
= $false )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(175,plain,
! [SV3: $i,SV27: $i,SV23: $i,SV18: $i,SV31: $i,SV12: $i] :
( ( ( ~ ( irel @ SV12 @ SV31 ) )
= $true )
| ( ( b2 @ SV31 )
= $true )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( irel @ SV18 @ SV23 )
= $false )
| ( ( b2 @ SV23 )
= $true )
| ( ( a2 @ SV27 )
= $true )
| ( ( irel @ SV18 @ SV27 )
= $false )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(176,plain,
! [SV3: $i,SV25: $i,SV21: $i,SV15: $i,SV29: $i,SV10: $i] :
( ( ( irel @ SV10 @ SV29 )
= $false )
| ( ( b2 @ SV29 )
= $true )
| ( ( irel @ SV10 @ SV15 )
= $false )
| ( ( irel @ SV15 @ SV21 )
= $false )
| ( ( b2 @ SV21 )
= $true )
| ( ( a2 @ SV25 )
= $true )
| ( ( irel @ SV15 @ SV25 )
= $false )
| ( ( irel @ SV3 @ SV10 )
= $false )
| ( ( b1 @ ( sK4_SY281 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV6: $i,SV28: $i,SV24: $i,SV19: $i,SV32: $i,SV14: $i] :
( ( ( ~ ( irel @ SV14 @ SV32 ) )
= $true )
| ( ( b1 @ SV32 )
= $true )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( irel @ SV19 @ SV24 )
= $false )
| ( ( b1 @ SV24 )
= $true )
| ( ( a1 @ SV28 )
= $true )
| ( ( irel @ SV19 @ SV28 )
= $false )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(178,plain,
! [SV6: $i,SV26: $i,SV22: $i,SV17: $i,SV30: $i,SV11: $i] :
( ( ( irel @ SV11 @ SV30 )
= $false )
| ( ( b1 @ SV30 )
= $true )
| ( ( irel @ SV11 @ SV17 )
= $false )
| ( ( irel @ SV17 @ SV22 )
= $false )
| ( ( b1 @ SV22 )
= $true )
| ( ( a1 @ SV26 )
= $true )
| ( ( irel @ SV17 @ SV26 )
= $false )
| ( ( irel @ SV6 @ SV11 )
= $false )
| ( ( b @ ( sK5_SY293 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV3: $i,SV27: $i,SV23: $i,SV18: $i,SV31: $i,SV12: $i] :
( ( ( irel @ SV12 @ SV31 )
= $false )
| ( ( b2 @ SV31 )
= $true )
| ( ( irel @ SV12 @ SV18 )
= $false )
| ( ( irel @ SV18 @ SV23 )
= $false )
| ( ( b2 @ SV23 )
= $true )
| ( ( a2 @ SV27 )
= $true )
| ( ( irel @ SV18 @ SV27 )
= $false )
| ( ( irel @ SV3 @ SV12 )
= $false )
| ( ( irel @ SV3 @ ( sK4_SY281 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(180,plain,
! [SV6: $i,SV28: $i,SV24: $i,SV19: $i,SV32: $i,SV14: $i] :
( ( ( irel @ SV14 @ SV32 )
= $false )
| ( ( b1 @ SV32 )
= $true )
| ( ( irel @ SV14 @ SV19 )
= $false )
| ( ( irel @ SV19 @ SV24 )
= $false )
| ( ( b1 @ SV24 )
= $true )
| ( ( a1 @ SV28 )
= $true )
| ( ( irel @ SV19 @ SV28 )
= $false )
| ( ( irel @ SV6 @ SV14 )
= $false )
| ( ( irel @ SV6 @ ( sK5_SY293 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(181,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,180,179,178,176,148,142,141,120,118,117,102,89,87,60,59,51,31]) ).
thf(182,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO064^4.003 : 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
% 0.12/0.18 % Computer : n002.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 17:35:12 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.12/0.82
% 3.12/0.82 No.of.Axioms: 6
% 3.12/0.82
% 3.12/0.82 Length.of.Defs: 2734
% 3.12/0.82
% 3.12/0.82 Contains.Choice.Funs: false
% 3.12/0.82 .........
% 3.12/0.82
% 3.12/0.82 ********************************
% 3.12/0.82 * All subproblems solved! *
% 3.12/0.82 ********************************
% 3.12/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:181,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.12/0.82
% 3.12/0.82 %**** Beginning of derivation protocol ****
% 3.12/0.82 % SZS output start CNFRefutation
% See solution above
% 3.12/0.82
% 3.12/0.82 %**** End of derivation protocol ****
% 3.12/0.82 %**** no. of clauses in derivation: 182 ****
% 3.12/0.82 %**** clause counter: 181 ****
% 3.12/0.82
% 3.12/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:181,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------