%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO066^4.002 : 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 : n014.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 11:07:32 AM UTC 2026
% Result : Theorem 0.51s 0.31s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 25
% Syntax : Number of formulae : 156 ( 106 unt; 0 typ; 19 def)
% Number of atoms : 1124 ( 218 equ; 0 cnn)
% Maximal formula atoms : 36 ( 7 avg)
% Number of connectives : 1845 ( 429 ~; 364 |; 28 &; 968 @)
% ( 0 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 13 con; 0-3 aty)
% Number of variables : 309 ( 31 ^; 276 !; 2 ?; 309 :)
% 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_o11,type,
o11: $i > $o ).
thf(tp_o12,type,
o12: $i > $o ).
thf(tp_o21,type,
o21: $i > $o ).
thf(tp_o22,type,
o22: $i > $o ).
thf(tp_o31,type,
o31: $i > $o ).
thf(tp_o32,type,
o32: $i > $o ).
thf(tp_sK10_SY243,type,
sK10_SY243: $i ).
thf(tp_sK11_SY244,type,
sK11_SY244: $i ).
thf(tp_sK1_SY120,type,
sK1_SY120: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY225,type,
sK4_SY225: $i ).
thf(tp_sK5_SY226,type,
sK5_SY226: $i ).
thf(tp_sK6_SY233,type,
sK6_SY233: $i ).
thf(tp_sK7_SY234,type,
sK7_SY234: $i ).
thf(tp_sK8_SY239,type,
sK8_SY239: $i ).
thf(tp_sK9_SY240,type,
sK9_SY240: $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 @ ( iatom @ o31 ) @ ( iatom @ o32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(2,axiom,
ivalid @ ( ior @ ( iatom @ o21 ) @ ( iatom @ o22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(3,axiom,
ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(4,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(5,axiom,
! [X: $i] : ( irel @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).
thf(6,conjecture,
ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(7,negated_conjecture,
( ( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [SY120: $i] :
( ! [SY121: $i] :
( ( irel @ SY120 @ SY121 )
=> ( ( o11 @ SY121 )
& ( o21 @ SY121 ) ) )
| ! [SY122: $i] :
( ( irel @ SY120 @ SY122 )
=> ( ! [SY112: $i] :
( ( irel @ SY122 @ SY112 )
=> ( ( o11 @ SY112 )
& ( o31 @ SY112 ) ) )
| ! [SY113: $i] :
( ( irel @ SY122 @ SY113 )
=> ( ! [SY103: $i] :
( ( irel @ SY113 @ SY103 )
=> ( ( o21 @ SY103 )
& ( o31 @ SY103 ) ) )
| ! [SY104: $i] :
( ( irel @ SY113 @ SY104 )
=> ( ! [SY96: $i] :
( ( irel @ SY104 @ SY96 )
=> ( ( o12 @ SY96 )
& ( o22 @ SY96 ) ) )
| ! [SY97: $i] :
( ( irel @ SY104 @ SY97 )
=> ( ! [SY91: $i] :
( ( irel @ SY97 @ SY91 )
=> ( ( o12 @ SY91 )
& ( o32 @ SY91 ) ) )
| ! [SY92: $i] :
( ( irel @ SY97 @ SY92 )
=> ( ( o22 @ SY92 )
& ( o32 @ SY92 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(9,plain,
( ( ! [SY156: $i] :
( ! [SY157: $i] :
( ( irel @ SY156 @ SY157 )
=> ( o31 @ SY157 ) )
| ! [SY158: $i] :
( ( irel @ SY156 @ SY158 )
=> ( o32 @ SY158 ) ) ) )
= $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(10,plain,
( ( ! [SY176: $i] :
( ! [SY177: $i] :
( ( irel @ SY176 @ SY177 )
=> ( o21 @ SY177 ) )
| ! [SY178: $i] :
( ( irel @ SY176 @ SY178 )
=> ( o22 @ SY178 ) ) ) )
= $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(11,plain,
( ( ! [SY196: $i] :
( ! [SY197: $i] :
( ( irel @ SY196 @ SY197 )
=> ( o11 @ SY197 ) )
| ! [SY198: $i] :
( ( irel @ SY196 @ SY198 )
=> ( o12 @ SY198 ) ) ) )
= $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(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $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(13,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $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(14,plain,
( ( ! [SY206: $i] :
( ( irel @ sK1_SY120 @ SY206 )
=> ( ( o11 @ SY206 )
& ( o21 @ SY206 ) ) )
| ! [SY207: $i] :
( ( irel @ sK1_SY120 @ SY207 )
=> ( ! [SY112: $i] :
( ( irel @ SY207 @ SY112 )
=> ( ( o11 @ SY112 )
& ( o31 @ SY112 ) ) )
| ! [SY113: $i] :
( ( irel @ SY207 @ SY113 )
=> ( ! [SY103: $i] :
( ( irel @ SY113 @ SY103 )
=> ( ( o21 @ SY103 )
& ( o31 @ SY103 ) ) )
| ! [SY104: $i] :
( ( irel @ SY113 @ SY104 )
=> ( ! [SY96: $i] :
( ( irel @ SY104 @ SY96 )
=> ( ( o12 @ SY96 )
& ( o22 @ SY96 ) ) )
| ! [SY97: $i] :
( ( irel @ SY104 @ SY97 )
=> ( ! [SY91: $i] :
( ( irel @ SY97 @ SY91 )
=> ( ( o12 @ SY91 )
& ( o32 @ SY91 ) ) )
| ! [SY92: $i] :
( ( irel @ SY97 @ SY92 )
=> ( ( o22 @ SY92 )
& ( o32 @ SY92 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ~ ( ! [SY206: $i] :
( ( irel @ sK1_SY120 @ SY206 )
=> ( ( o11 @ SY206 )
& ( o21 @ SY206 ) ) )
| ! [SY207: $i] :
( ( irel @ sK1_SY120 @ SY207 )
=> ( ! [SY112: $i] :
( ( irel @ SY207 @ SY112 )
=> ( ( o11 @ SY112 )
& ( o31 @ SY112 ) ) )
| ! [SY113: $i] :
( ( irel @ SY207 @ SY113 )
=> ( ! [SY103: $i] :
( ( irel @ SY113 @ SY103 )
=> ( ( o21 @ SY103 )
& ( o31 @ SY103 ) ) )
| ! [SY104: $i] :
( ( irel @ SY113 @ SY104 )
=> ( ! [SY96: $i] :
( ( irel @ SY104 @ SY96 )
=> ( ( o12 @ SY96 )
& ( o22 @ SY96 ) ) )
| ! [SY97: $i] :
( ( irel @ SY104 @ SY97 )
=> ( ! [SY91: $i] :
( ( irel @ SY97 @ SY91 )
=> ( ( o12 @ SY91 )
& ( o32 @ SY91 ) ) )
| ! [SY92: $i] :
( ( irel @ SY97 @ SY92 )
=> ( ( o22 @ SY92 )
& ( o32 @ SY92 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SY196: $i] :
( ! [SY197: $i] :
( ( irel @ SY196 @ SY197 )
=> ( o11 @ SY197 ) )
| ! [SY198: $i] :
( ( irel @ SY196 @ SY198 )
=> ( o12 @ SY198 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [SY176: $i] :
( ! [SY177: $i] :
( ( irel @ SY176 @ SY177 )
=> ( o21 @ SY177 ) )
| ! [SY178: $i] :
( ( irel @ SY176 @ SY178 )
=> ( o22 @ SY178 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [SY156: $i] :
( ! [SY157: $i] :
( ( irel @ SY156 @ SY157 )
=> ( o31 @ SY157 ) )
| ! [SY158: $i] :
( ( irel @ SY156 @ SY158 )
=> ( o32 @ SY158 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(21,plain,
( ( ~ ( ! [SY206: $i] :
( ( irel @ sK1_SY120 @ SY206 )
=> ( ( o11 @ SY206 )
& ( o21 @ SY206 ) ) )
| ! [SY207: $i] :
( ( irel @ sK1_SY120 @ SY207 )
=> ( ! [SY112: $i] :
( ( irel @ SY207 @ SY112 )
=> ( ( o11 @ SY112 )
& ( o31 @ SY112 ) ) )
| ! [SY113: $i] :
( ( irel @ SY207 @ SY113 )
=> ( ! [SY103: $i] :
( ( irel @ SY113 @ SY103 )
=> ( ( o21 @ SY103 )
& ( o31 @ SY103 ) ) )
| ! [SY104: $i] :
( ( irel @ SY113 @ SY104 )
=> ( ! [SY96: $i] :
( ( irel @ SY104 @ SY96 )
=> ( ( o12 @ SY96 )
& ( o22 @ SY96 ) ) )
| ! [SY97: $i] :
( ( irel @ SY104 @ SY97 )
=> ( ! [SY91: $i] :
( ( irel @ SY97 @ SY91 )
=> ( ( o12 @ SY91 )
& ( o32 @ SY91 ) ) )
| ! [SY92: $i] :
( ( irel @ SY97 @ SY92 )
=> ( ( o22 @ SY92 )
& ( o32 @ SY92 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( o31 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( o32 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(23,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY120 @ SX0 )
| ~ ( ~ ( o11 @ SX0 )
| ~ ( o21 @ SX0 ) ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY120 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( o11 @ SX1 )
| ~ ( o31 @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( o21 @ SX2 )
| ~ ( o31 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) ) ) ) )
= $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(24,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( irel @ SX0 @ SX1 )
| ~ ( irel @ SX1 @ SX2 ) )
| ( irel @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( o21 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( o22 @ SX1 ) ) ) )
= $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(26,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( o11 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ( o12 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(27,plain,
! [SV1: $i] :
( ( irel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY216: $i] :
( ~ ( irel @ SV2 @ SY216 )
| ( o31 @ SY216 ) )
| ! [SY217: $i] :
( ~ ( irel @ SV2 @ SY217 )
| ( o32 @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY120 @ SX0 )
| ~ ( ~ ( o11 @ SX0 )
| ~ ( o21 @ SX0 ) ) )
| ! [SX0: $i] :
( ~ ( irel @ sK1_SY120 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( o11 @ SX1 )
| ~ ( o31 @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( o21 @ SX2 )
| ~ ( o31 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV3: $i] :
( ( ! [SY218: $i,SY219: $i] :
( ~ ~ ( ~ ( irel @ SV3 @ SY218 )
| ~ ( irel @ SY218 @ SY219 ) )
| ( irel @ SV3 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV4: $i] :
( ( ! [SY220: $i] :
( ~ ( irel @ SV4 @ SY220 )
| ( o21 @ SY220 ) )
| ! [SY221: $i] :
( ~ ( irel @ SV4 @ SY221 )
| ( o22 @ SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV5: $i] :
( ( ! [SY222: $i] :
( ~ ( irel @ SV5 @ SY222 )
| ( o11 @ SY222 ) )
| ! [SY223: $i] :
( ~ ( irel @ SV5 @ SY223 )
| ( o12 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( ! [SY216: $i] :
( ~ ( irel @ SV2 @ SY216 )
| ( o31 @ SY216 ) ) )
= $true )
| ( ( ! [SY217: $i] :
( ~ ( irel @ SV2 @ SY217 )
| ( o32 @ SY217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY120 @ SX0 )
| ~ ( ~ ( o11 @ SX0 )
| ~ ( o21 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY120 @ SX0 )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( o11 @ SX1 )
| ~ ( o31 @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ~ ( ~ ( o21 @ SX2 )
| ~ ( o31 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(36,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY224: $i] :
( ~ ~ ( ~ ( irel @ SV3 @ SV6 )
| ~ ( irel @ SV6 @ SY224 ) )
| ( irel @ SV3 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( ! [SY220: $i] :
( ~ ( irel @ SV4 @ SY220 )
| ( o21 @ SY220 ) ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( irel @ SV4 @ SY221 )
| ( o22 @ SY221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV5: $i] :
( ( ( ! [SY222: $i] :
( ~ ( irel @ SV5 @ SY222 )
| ( o11 @ SY222 ) ) )
= $true )
| ( ( ! [SY223: $i] :
( ~ ( irel @ SV5 @ SY223 )
| ( o12 @ SY223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV7 )
| ( o31 @ SV7 ) )
= $true )
| ( ( ! [SY217: $i] :
( ~ ( irel @ SV2 @ SY217 )
| ( o32 @ SY217 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ( irel @ sK1_SY120 @ sK2_SX0 )
| ~ ( ~ ( o11 @ sK2_SX0 )
| ~ ( o21 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(41,plain,
( ( ~ ( irel @ sK1_SY120 @ sK3_SX0 )
| ! [SY225: $i] :
( ~ ( irel @ sK3_SX0 @ SY225 )
| ~ ( ~ ( o11 @ SY225 )
| ~ ( o31 @ SY225 ) ) )
| ! [SY226: $i] :
( ~ ( irel @ sK3_SX0 @ SY226 )
| ! [SX2: $i] :
( ~ ( irel @ SY226 @ SX2 )
| ~ ( ~ ( o21 @ SX2 )
| ~ ( o31 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY226 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(42,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ~ ~ ( ~ ( irel @ SV3 @ SV6 )
| ~ ( irel @ SV6 @ SV8 ) )
| ( irel @ SV3 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV9 )
| ( o21 @ SV9 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( irel @ SV4 @ SY221 )
| ( o22 @ SY221 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV10 )
| ( o11 @ SV10 ) )
= $true )
| ( ( ! [SY223: $i] :
( ~ ( irel @ SV5 @ SY223 )
| ( o12 @ SY223 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV7 ) )
= $true )
| ( ( o31 @ SV7 )
= $true )
| ( ( ! [SY217: $i] :
( ~ ( irel @ SV2 @ SY217 )
| ( o32 @ SY217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ( irel @ sK1_SY120 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(47,plain,
( ( ~ ( ~ ( o11 @ sK2_SX0 )
| ~ ( o21 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ ( irel @ sK1_SY120 @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
( ( ! [SY225: $i] :
( ~ ( irel @ sK3_SX0 @ SY225 )
| ~ ( ~ ( o11 @ SY225 )
| ~ ( o31 @ SY225 ) ) )
| ! [SY226: $i] :
( ~ ( irel @ sK3_SX0 @ SY226 )
| ! [SX2: $i] :
( ~ ( irel @ SY226 @ SX2 )
| ~ ( ~ ( o21 @ SX2 )
| ~ ( o31 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY226 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(50,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( irel @ SV3 @ SV6 )
| ~ ( irel @ SV6 @ SV8 ) ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV9 ) )
= $true )
| ( ( o21 @ SV9 )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( irel @ SV4 @ SY221 )
| ( o22 @ SY221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV10 ) )
= $true )
| ( ( o11 @ SV10 )
= $true )
| ( ( ! [SY223: $i] :
( ~ ( irel @ SV5 @ SY223 )
| ( o12 @ SY223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV7: $i,SV2: $i] :
( ( ( irel @ SV2 @ SV7 )
= $false )
| ( ( o31 @ SV7 )
= $true )
| ( ( ! [SY217: $i] :
( ~ ( irel @ SV2 @ SY217 )
| ( o32 @ SY217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(54,plain,
( ( irel @ sK1_SY120 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(55,plain,
( ( ~ ( o11 @ sK2_SX0 )
| ~ ( o21 @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(56,plain,
( ( irel @ sK1_SY120 @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(57,plain,
( ( ! [SY225: $i] :
( ~ ( irel @ sK3_SX0 @ SY225 )
| ~ ( ~ ( o11 @ SY225 )
| ~ ( o31 @ SY225 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(58,plain,
( ( ! [SY226: $i] :
( ~ ( irel @ sK3_SX0 @ SY226 )
| ! [SX2: $i] :
( ~ ( irel @ SY226 @ SX2 )
| ~ ( ~ ( o21 @ SX2 )
| ~ ( o31 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( irel @ SY226 @ SX2 )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SX2 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(59,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( irel @ SV3 @ SV6 )
| ~ ( irel @ SV6 @ SV8 ) ) )
= $false )
| ( ( irel @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV9: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV9 )
= $false )
| ( ( o21 @ SV9 )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( irel @ SV4 @ SY221 )
| ( o22 @ SY221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV10: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV10 )
= $false )
| ( ( o11 @ SV10 )
= $true )
| ( ( ! [SY223: $i] :
( ~ ( irel @ SV5 @ SY223 )
| ( o12 @ SY223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV11 )
| ( o32 @ SV11 ) )
= $true )
| ( ( o31 @ SV7 )
= $true )
| ( ( irel @ SV2 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(63,plain,
( ( ( ~ ( o11 @ sK2_SX0 ) )
= $true )
| ( ( ~ ( o21 @ sK2_SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(64,plain,
( ( ~ ( irel @ sK3_SX0 @ sK4_SY225 )
| ~ ( ~ ( o11 @ sK4_SY225 )
| ~ ( o31 @ sK4_SY225 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(65,plain,
( ( ~ ( irel @ sK3_SX0 @ sK5_SY226 )
| ! [SY233: $i] :
( ~ ( irel @ sK5_SY226 @ SY233 )
| ~ ( ~ ( o21 @ SY233 )
| ~ ( o31 @ SY233 ) ) )
| ! [SY234: $i] :
( ~ ( irel @ sK5_SY226 @ SY234 )
| ! [SX3: $i] :
( ~ ( irel @ SY234 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SY234 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(66,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV6 )
| ~ ( irel @ SV6 @ SV8 ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(67,plain,
! [SV9: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV12 )
| ( o22 @ SV12 ) )
= $true )
| ( ( o21 @ SV9 )
= $true )
| ( ( irel @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV10: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV13 )
| ( o12 @ SV13 ) )
= $true )
| ( ( o11 @ SV10 )
= $true )
| ( ( irel @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(69,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV11 ) )
= $true )
| ( ( o32 @ SV11 )
= $true )
| ( ( o31 @ SV7 )
= $true )
| ( ( irel @ SV2 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(70,plain,
( ( ( o11 @ sK2_SX0 )
= $false )
| ( ( ~ ( o21 @ sK2_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(71,plain,
( ( ~ ( irel @ sK3_SX0 @ sK4_SY225 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,plain,
( ( ~ ( ~ ( o11 @ sK4_SY225 )
| ~ ( o31 @ sK4_SY225 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(73,plain,
( ( ~ ( irel @ sK3_SX0 @ sK5_SY226 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
( ( ! [SY233: $i] :
( ~ ( irel @ sK5_SY226 @ SY233 )
| ~ ( ~ ( o21 @ SY233 )
| ~ ( o31 @ SY233 ) ) )
| ! [SY234: $i] :
( ~ ( irel @ sK5_SY226 @ SY234 )
| ! [SX3: $i] :
( ~ ( irel @ SY234 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SY234 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( irel @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( irel @ SV6 @ SV8 ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV9: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( irel @ SV4 @ SV12 ) )
= $true )
| ( ( o22 @ SV12 )
= $true )
| ( ( o21 @ SV9 )
= $true )
| ( ( irel @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV10: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( irel @ SV5 @ SV13 ) )
= $true )
| ( ( o12 @ SV13 )
= $true )
| ( ( o11 @ SV10 )
= $true )
| ( ( irel @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV7: $i,SV11: $i,SV2: $i] :
( ( ( irel @ SV2 @ SV11 )
= $false )
| ( ( o32 @ SV11 )
= $true )
| ( ( o31 @ SV7 )
= $true )
| ( ( irel @ SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(79,plain,
( ( ( o21 @ sK2_SX0 )
= $false )
| ( ( o11 @ sK2_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
( ( irel @ sK3_SX0 @ sK4_SY225 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(81,plain,
( ( ~ ( o11 @ sK4_SY225 )
| ~ ( o31 @ sK4_SY225 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(82,plain,
( ( irel @ sK3_SX0 @ sK5_SY226 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(83,plain,
( ( ! [SY233: $i] :
( ~ ( irel @ sK5_SY226 @ SY233 )
| ~ ( ~ ( o21 @ SY233 )
| ~ ( o31 @ SY233 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(84,plain,
( ( ! [SY234: $i] :
( ~ ( irel @ sK5_SY226 @ SY234 )
| ! [SX3: $i] :
( ~ ( irel @ SY234 @ SX3 )
| ~ ( ~ ( o12 @ SX3 )
| ~ ( o22 @ SX3 ) ) )
| ! [SX3: $i] :
( ~ ( irel @ SY234 @ SX3 )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SX3 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(85,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV6 )
= $false )
| ( ( ~ ( irel @ SV6 @ SV8 ) )
= $true )
| ( ( irel @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV9: $i,SV12: $i,SV4: $i] :
( ( ( irel @ SV4 @ SV12 )
= $false )
| ( ( o22 @ SV12 )
= $true )
| ( ( o21 @ SV9 )
= $true )
| ( ( irel @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV10: $i,SV13: $i,SV5: $i] :
( ( ( irel @ SV5 @ SV13 )
= $false )
| ( ( o12 @ SV13 )
= $true )
| ( ( o11 @ SV10 )
= $true )
| ( ( irel @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(88,plain,
( ( ( ~ ( o11 @ sK4_SY225 ) )
= $true )
| ( ( ~ ( o31 @ sK4_SY225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(89,plain,
( ( ~ ( irel @ sK5_SY226 @ sK6_SY233 )
| ~ ( ~ ( o21 @ sK6_SY233 )
| ~ ( o31 @ sK6_SY233 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(90,plain,
( ( ~ ( irel @ sK5_SY226 @ sK7_SY234 )
| ! [SY239: $i] :
( ~ ( irel @ sK7_SY234 @ SY239 )
| ~ ( ~ ( o12 @ SY239 )
| ~ ( o22 @ SY239 ) ) )
| ! [SY240: $i] :
( ~ ( irel @ sK7_SY234 @ SY240 )
| ! [SX4: $i] :
( ~ ( irel @ SY240 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SY240 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(91,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( irel @ SV6 @ SV8 )
= $false )
| ( ( irel @ SV3 @ SV6 )
= $false )
| ( ( irel @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
( ( ( o11 @ sK4_SY225 )
= $false )
| ( ( ~ ( o31 @ sK4_SY225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(93,plain,
( ( ~ ( irel @ sK5_SY226 @ sK6_SY233 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(94,plain,
( ( ~ ( ~ ( o21 @ sK6_SY233 )
| ~ ( o31 @ sK6_SY233 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(95,plain,
( ( ~ ( irel @ sK5_SY226 @ sK7_SY234 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(96,plain,
( ( ! [SY239: $i] :
( ~ ( irel @ sK7_SY234 @ SY239 )
| ~ ( ~ ( o12 @ SY239 )
| ~ ( o22 @ SY239 ) ) )
| ! [SY240: $i] :
( ~ ( irel @ sK7_SY234 @ SY240 )
| ! [SX4: $i] :
( ~ ( irel @ SY240 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SY240 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(97,plain,
( ( ( o31 @ sK4_SY225 )
= $false )
| ( ( o11 @ sK4_SY225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
( ( irel @ sK5_SY226 @ sK6_SY233 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(99,plain,
( ( ~ ( o21 @ sK6_SY233 )
| ~ ( o31 @ sK6_SY233 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(100,plain,
( ( irel @ sK5_SY226 @ sK7_SY234 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
( ( ! [SY239: $i] :
( ~ ( irel @ sK7_SY234 @ SY239 )
| ~ ( ~ ( o12 @ SY239 )
| ~ ( o22 @ SY239 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(102,plain,
( ( ! [SY240: $i] :
( ~ ( irel @ sK7_SY234 @ SY240 )
| ! [SX4: $i] :
( ~ ( irel @ SY240 @ SX4 )
| ~ ( ~ ( o12 @ SX4 )
| ~ ( o32 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( irel @ SY240 @ SX4 )
| ~ ( ~ ( o22 @ SX4 )
| ~ ( o32 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(103,plain,
( ( ( ~ ( o21 @ sK6_SY233 ) )
= $true )
| ( ( ~ ( o31 @ sK6_SY233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(104,plain,
( ( ~ ( irel @ sK7_SY234 @ sK8_SY239 )
| ~ ( ~ ( o12 @ sK8_SY239 )
| ~ ( o22 @ sK8_SY239 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(105,plain,
( ( ~ ( irel @ sK7_SY234 @ sK9_SY240 )
| ! [SY243: $i] :
( ~ ( irel @ sK9_SY240 @ SY243 )
| ~ ( ~ ( o12 @ SY243 )
| ~ ( o32 @ SY243 ) ) )
| ! [SY244: $i] :
( ~ ( irel @ sK9_SY240 @ SY244 )
| ~ ( ~ ( o22 @ SY244 )
| ~ ( o32 @ SY244 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(106,plain,
( ( ( o21 @ sK6_SY233 )
= $false )
| ( ( ~ ( o31 @ sK6_SY233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(107,plain,
( ( ~ ( irel @ sK7_SY234 @ sK8_SY239 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(108,plain,
( ( ~ ( ~ ( o12 @ sK8_SY239 )
| ~ ( o22 @ sK8_SY239 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(109,plain,
( ( ~ ( irel @ sK7_SY234 @ sK9_SY240 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(110,plain,
( ( ! [SY243: $i] :
( ~ ( irel @ sK9_SY240 @ SY243 )
| ~ ( ~ ( o12 @ SY243 )
| ~ ( o32 @ SY243 ) ) )
| ! [SY244: $i] :
( ~ ( irel @ sK9_SY240 @ SY244 )
| ~ ( ~ ( o22 @ SY244 )
| ~ ( o32 @ SY244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(111,plain,
( ( ( o31 @ sK6_SY233 )
= $false )
| ( ( o21 @ sK6_SY233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(112,plain,
( ( irel @ sK7_SY234 @ sK8_SY239 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(113,plain,
( ( ~ ( o12 @ sK8_SY239 )
| ~ ( o22 @ sK8_SY239 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(114,plain,
( ( irel @ sK7_SY234 @ sK9_SY240 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(115,plain,
( ( ! [SY243: $i] :
( ~ ( irel @ sK9_SY240 @ SY243 )
| ~ ( ~ ( o12 @ SY243 )
| ~ ( o32 @ SY243 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(116,plain,
( ( ! [SY244: $i] :
( ~ ( irel @ sK9_SY240 @ SY244 )
| ~ ( ~ ( o22 @ SY244 )
| ~ ( o32 @ SY244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(117,plain,
( ( ( ~ ( o12 @ sK8_SY239 ) )
= $true )
| ( ( ~ ( o22 @ sK8_SY239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(118,plain,
( ( ~ ( irel @ sK9_SY240 @ sK10_SY243 )
| ~ ( ~ ( o12 @ sK10_SY243 )
| ~ ( o32 @ sK10_SY243 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(119,plain,
( ( ~ ( irel @ sK9_SY240 @ sK11_SY244 )
| ~ ( ~ ( o22 @ sK11_SY244 )
| ~ ( o32 @ sK11_SY244 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(120,plain,
( ( ( o12 @ sK8_SY239 )
= $false )
| ( ( ~ ( o22 @ sK8_SY239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(121,plain,
( ( ~ ( irel @ sK9_SY240 @ sK10_SY243 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(122,plain,
( ( ~ ( ~ ( o12 @ sK10_SY243 )
| ~ ( o32 @ sK10_SY243 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(123,plain,
( ( ~ ( irel @ sK9_SY240 @ sK11_SY244 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(124,plain,
( ( ~ ( ~ ( o22 @ sK11_SY244 )
| ~ ( o32 @ sK11_SY244 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(125,plain,
( ( ( o22 @ sK8_SY239 )
= $false )
| ( ( o12 @ sK8_SY239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(126,plain,
( ( irel @ sK9_SY240 @ sK10_SY243 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(127,plain,
( ( ~ ( o12 @ sK10_SY243 )
| ~ ( o32 @ sK10_SY243 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(128,plain,
( ( irel @ sK9_SY240 @ sK11_SY244 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(129,plain,
( ( ~ ( o22 @ sK11_SY244 )
| ~ ( o32 @ sK11_SY244 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(130,plain,
( ( ( ~ ( o12 @ sK10_SY243 ) )
= $true )
| ( ( ~ ( o32 @ sK10_SY243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(131,plain,
( ( ( ~ ( o22 @ sK11_SY244 ) )
= $true )
| ( ( ~ ( o32 @ sK11_SY244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(132,plain,
( ( ( o12 @ sK10_SY243 )
= $false )
| ( ( ~ ( o32 @ sK10_SY243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(133,plain,
( ( ( o22 @ sK11_SY244 )
= $false )
| ( ( ~ ( o32 @ sK11_SY244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(134,plain,
( ( ( o32 @ sK10_SY243 )
= $false )
| ( ( o12 @ sK10_SY243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(135,plain,
( ( ( o32 @ sK11_SY244 )
= $false )
| ( ( o22 @ sK11_SY244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,135,134,128,126,125,114,112,111,100,98,97,91,87,86,82,80,79,78,56,54]) ).
thf(137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO066^4.002 : 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
% 0.11/0.17 % Computer : n014.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 17:31:11 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.31
% 0.51/0.31 No.of.Axioms: 5
% 0.51/0.31
% 0.51/0.31 Length.of.Defs: 2734
% 0.51/0.31
% 0.51/0.31 Contains.Choice.Funs: false
% 0.51/0.31 .......
% 0.51/0.31
% 0.51/0.31 ********************************
% 0.51/0.31 * All subproblems solved! *
% 0.51/0.31 ********************************
% 0.51/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:136,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.51/0.31
% 0.51/0.31 %**** Beginning of derivation protocol ****
% 0.51/0.31 % SZS output start CNFRefutation
% See solution above
% 0.51/0.31
% 0.51/0.31 %**** End of derivation protocol ****
% 0.51/0.31 %**** no. of clauses in derivation: 137 ****
% 0.51/0.31 %**** clause counter: 136 ****
% 0.51/0.31
% 0.51/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:136,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------