%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN978^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 11:07:17 AM UTC 2026
% Result : Theorem 0.11s 0.22s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 22
% Syntax : Number of formulae : 141 ( 85 unt; 0 typ; 19 def)
% Number of atoms : 1096 ( 205 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 2107 ( 763 ~; 462 |; 35 &; 820 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 11 con; 0-3 aty)
% Number of variables : 204 ( 31 ^; 171 !; 2 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i > $o ).
thf(tp_b,type,
b: $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_SY85,type,
sK1_SY85: $i ).
thf(tp_sK2_SY104,type,
sK2_SY104: $i ).
thf(tp_sK3_SY116,type,
sK3_SY116: $i ).
thf(tp_sK4_SY115,type,
sK4_SY115: $i ).
thf(tp_sK5_SY113,type,
sK5_SY113: $i ).
thf(tp_sK6_SY112,type,
sK6_SY112: $i ).
thf(tp_sK7_REN,type,
sK7_REN: $o ).
thf(tp_sK8_REN,type,
sK8_REN: $o ).
thf(tp_sK9_REN,type,
sK9_REN: $o ).
thf(iand,definition,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iand) ).
thf(iatom,definition,
( iatom
= ( ^ [P: $i > $o] : P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iatom) ).
thf(icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icountersatisfiable) ).
thf(iequiv,definition,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iequiv) ).
thf(ifalse,definition,
( ifalse
= ( inot @ itrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifalse) ).
thf(iimplied,definition,
( iimplied
= ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplied) ).
thf(iimplies,definition,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies) ).
thf(iinvalid,definition,
( iinvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iinvalid) ).
thf(inot,definition,
( inot
= ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inot) ).
thf(ior,definition,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ior) ).
thf(isatisfiable,definition,
( isatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isatisfiable) ).
thf(itrue,definition,
( itrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',itrue) ).
thf(ivalid,definition,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ivalid) ).
thf(ixor,definition,
( ixor
= ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ixor) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mimplies,definition,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).
thf(2,axiom,
! [X: $i] : ( irel @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).
thf(3,conjecture,
ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(4,negated_conjecture,
( ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [SY85: $i] :
( ~ ! [SY86: $i] :
( ( irel @ SY85 @ SY86 )
=> ( ( a @ SY86 )
& ( b @ SY86 ) ) )
| ! [SY87: $i] :
( ( irel @ SY85 @ SY87 )
=> ( ( ~ ! [SY81: $i] :
( ( irel @ SY87 @ SY81 )
=> ( a @ SY81 ) )
| ! [SY82: $i] :
( ( irel @ SY87 @ SY82 )
=> ( b @ SY82 ) ) )
& ( ~ ! [SY83: $i] :
( ( irel @ SY87 @ SY83 )
=> ( b @ SY83 ) )
| ! [SY84: $i] :
( ( irel @ SY87 @ SY84 )
=> ( a @ SY84 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(7,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[2,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(8,plain,
( ( ~ ! [SY103: $i] :
( ( irel @ sK1_SY85 @ SY103 )
=> ( ( a @ SY103 )
& ( b @ SY103 ) ) )
| ! [SY104: $i] :
( ( irel @ sK1_SY85 @ SY104 )
=> ( ( ~ ! [SY81: $i] :
( ( irel @ SY104 @ SY81 )
=> ( a @ SY81 ) )
| ! [SY82: $i] :
( ( irel @ SY104 @ SY82 )
=> ( b @ SY82 ) ) )
& ( ~ ! [SY83: $i] :
( ( irel @ SY104 @ SY83 )
=> ( b @ SY83 ) )
| ! [SY84: $i] :
( ( irel @ SY104 @ SY84 )
=> ( a @ SY84 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ~ ( ~ ! [SY103: $i] :
( ( irel @ sK1_SY85 @ SY103 )
=> ( ( a @ SY103 )
& ( b @ SY103 ) ) )
| ! [SY104: $i] :
( ( irel @ sK1_SY85 @ SY104 )
=> ( ( ~ ! [SY81: $i] :
( ( irel @ SY104 @ SY81 )
=> ( a @ SY81 ) )
| ! [SY82: $i] :
( ( irel @ SY104 @ SY82 )
=> ( b @ SY82 ) ) )
& ( ~ ! [SY83: $i] :
( ( irel @ SY104 @ SY83 )
=> ( b @ SY83 ) )
| ! [SY84: $i] :
( ( irel @ SY104 @ SY84 )
=> ( a @ SY84 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY103: $i] :
( ~ ( irel @ sK1_SY85 @ SY103 )
| ( a @ SY103 ) )
& ! [SY103: $i] :
( ~ ( irel @ sK1_SY85 @ SY103 )
| ( b @ SY103 ) )
& ( irel @ sK1_SY85 @ sK2_SY104 )
& ( ! [SY109: $i] :
( ~ ( irel @ sK2_SY104 @ SY109 )
| ( a @ SY109 ) )
| ! [SY110: $i] :
( ~ ( irel @ sK2_SY104 @ SY110 )
| ( b @ SY110 ) ) )
& ( ! [SY111: $i] :
( ~ ( irel @ sK2_SY104 @ SY111 )
| ( a @ SY111 ) )
| sK9_REN )
& ( sK9_REN
=> ( ( irel @ sK2_SY104 @ sK6_SY112 )
& ~ ( a @ sK6_SY112 ) ) )
& ( sK8_REN
| ! [SY114: $i] :
( ~ ( irel @ sK2_SY104 @ SY114 )
| ( b @ SY114 ) ) )
& ( sK8_REN
=> ( ( irel @ sK2_SY104 @ sK5_SY113 )
& ~ ( b @ sK5_SY113 ) ) )
& ( sK7_REN
| ( ( irel @ sK2_SY104 @ sK3_SY116 )
& ~ ( a @ sK3_SY116 ) ) )
& ( sK7_REN
=> ( ( irel @ sK2_SY104 @ sK4_SY115 )
& ~ ( b @ sK4_SY115 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( irel @ X @ Y )
| ~ ( irel @ Y @ Z )
| ( irel @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(12,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( irel @ X @ Y )
| ~ ( irel @ Y @ Z )
| ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SY103: $i] :
( ~ ( irel @ sK1_SY85 @ SY103 )
| ( a @ SY103 ) )
& ! [SY103: $i] :
( ~ ( irel @ sK1_SY85 @ SY103 )
| ( b @ SY103 ) )
& ( irel @ sK1_SY85 @ sK2_SY104 )
& ( ! [SY109: $i] :
( ~ ( irel @ sK2_SY104 @ SY109 )
| ( a @ SY109 ) )
| ! [SY110: $i] :
( ~ ( irel @ sK2_SY104 @ SY110 )
| ( b @ SY110 ) ) )
& ( ! [SY111: $i] :
( ~ ( irel @ sK2_SY104 @ SY111 )
| ( a @ SY111 ) )
| sK9_REN )
& ( sK9_REN
=> ( ( irel @ sK2_SY104 @ sK6_SY112 )
& ~ ( a @ sK6_SY112 ) ) )
& ( sK8_REN
| ! [SY114: $i] :
( ~ ( irel @ sK2_SY104 @ SY114 )
| ( b @ SY114 ) ) )
& ( sK8_REN
=> ( ( irel @ sK2_SY104 @ sK5_SY113 )
& ~ ( b @ sK5_SY113 ) ) )
& ( sK7_REN
| ( ( irel @ sK2_SY104 @ sK3_SY116 )
& ~ ( a @ sK3_SY116 ) ) )
& ( sK7_REN
=> ( ( irel @ sK2_SY104 @ sK4_SY115 )
& ~ ( b @ sK4_SY115 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( a @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( irel @ sK1_SY85 @ sK2_SY104 )
| ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(16,plain,
! [SV1: $i] :
( ( irel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV2: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( irel @ SV2 @ SY117 )
| ~ ( irel @ SY117 @ SY118 )
| ( irel @ SV2 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( a @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( irel @ sK1_SY85 @ sK2_SY104 )
| ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV3: $i,SV2: $i] :
( ( ! [SY119: $i] :
( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SY119 )
| ( irel @ SV2 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( a @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( b @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( irel @ sK1_SY85 @ sK2_SY104 )
| ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 )
| ( irel @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( a @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( b @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ( irel @ sK1_SY85 @ sK2_SY104 )
| ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( a @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( b @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( irel @ sK1_SY85 @ sK2_SY104 )
| ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( irel @ SV3 @ SV4 ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( a @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( b @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( irel @ sK1_SY85 @ sK2_SY104 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( irel @ SV2 @ SV3 )
= $false )
| ( ( ~ ( irel @ SV3 @ SV4 ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( a @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK1_SY85 @ SX0 )
| ( b @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(36,plain,
( ( irel @ sK1_SY85 @ sK2_SY104 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(37,plain,
( ( ~ ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV2: $i,SV4: $i,SV3: $i] :
( ( ( irel @ SV3 @ SV4 )
= $false )
| ( ( irel @ SV2 @ SV3 )
= $false )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV5: $i] :
( ( ~ ( irel @ sK1_SY85 @ SV5 )
| ( a @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV6: $i] :
( ( ~ ( irel @ sK1_SY85 @ SV6 )
| ( b @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV5: $i] :
( ( ( ~ ( irel @ sK1_SY85 @ SV5 ) )
= $true )
| ( ( a @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV6: $i] :
( ( ( ~ ( irel @ sK1_SY85 @ SV6 ) )
= $true )
| ( ( b @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( ~ ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV5: $i] :
( ( ( irel @ sK1_SY85 @ SV5 )
= $false )
| ( ( a @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV6: $i] :
( ( ( irel @ sK1_SY85 @ SV6 )
= $false )
| ( ( b @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( ~ ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
( ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
| ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(53,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
( ( ~ ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
( ( ~ ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
( ( ~ ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
( ( ~ ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
( ( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(61,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
( ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
| ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
( ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
| ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV7: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV7 )
| ( a @ SV7 ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(65,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(66,plain,
( ( ~ ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(67,plain,
( ( ~ ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(68,plain,
( ( ~ ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(69,plain,
( ( ~ ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(70,plain,
( ( ~ ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(71,plain,
! [SV7: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV7 ) )
= $true )
| ( ( a @ SV7 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(72,plain,
( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) )
| sK9_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(73,plain,
( ( ~ sK9_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(74,plain,
( ( sK8_REN
| ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(75,plain,
( ( ~ sK8_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(76,plain,
( ( sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(77,plain,
( ( ~ sK7_REN
| ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(78,plain,
! [SV7: $i] :
( ( ( irel @ sK2_SY104 @ SV7 )
= $false )
| ( ( a @ SV7 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(79,plain,
( ( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( a @ SX0 ) ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
( ( ( ~ sK9_REN ) = $true )
| ( ( ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(81,plain,
( ( sK8_REN = $true )
| ( ( ! [SX0: $i] :
( ~ ( irel @ sK2_SY104 @ SX0 )
| ( b @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
( ( ( ~ sK8_REN ) = $true )
| ( ( ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(83,plain,
( ( sK7_REN = $true )
| ( ( ~ ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(84,plain,
( ( ( ~ sK7_REN ) = $true )
| ( ( ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV7: $i,SV8: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV8 )
| ( b @ SV8 ) )
= $true )
| ( ( a @ SV7 )
= $true )
| ( ( irel @ sK2_SY104 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV9: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV9 )
| ( a @ SV9 ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
( ( sK9_REN = $false )
| ( ( ~ ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV10: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV10 )
| ( b @ SV10 ) )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(89,plain,
( ( sK8_REN = $false )
| ( ( ~ ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(90,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK3_SY116 )
| ~ ~ ( a @ sK3_SY116 ) )
= $false )
| ( sK7_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(91,plain,
( ( sK7_REN = $false )
| ( ( ~ ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV7: $i,SV8: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV8 ) )
= $true )
| ( ( b @ SV8 )
= $true )
| ( ( a @ SV7 )
= $true )
| ( ( irel @ sK2_SY104 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV9: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV9 ) )
= $true )
| ( ( a @ SV9 )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK6_SY112 )
| ~ ~ ( a @ sK6_SY112 ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV10: $i] :
( ( ( ~ ( irel @ sK2_SY104 @ SV10 ) )
= $true )
| ( ( b @ SV10 )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(96,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK5_SY113 )
| ~ ~ ( b @ sK5_SY113 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(97,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK3_SY116 ) )
= $false )
| ( sK7_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(98,plain,
( ( ( ~ ~ ( a @ sK3_SY116 ) )
= $false )
| ( sK7_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(99,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK4_SY115 )
| ~ ~ ( b @ sK4_SY115 ) )
= $false )
| ( sK7_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV7: $i,SV8: $i] :
( ( ( irel @ sK2_SY104 @ SV8 )
= $false )
| ( ( b @ SV8 )
= $true )
| ( ( a @ SV7 )
= $true )
| ( ( irel @ sK2_SY104 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV9: $i] :
( ( ( irel @ sK2_SY104 @ SV9 )
= $false )
| ( ( a @ SV9 )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(102,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK6_SY112 ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(103,plain,
( ( ( ~ ~ ( a @ sK6_SY112 ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(104,plain,
! [SV10: $i] :
( ( ( irel @ sK2_SY104 @ SV10 )
= $false )
| ( ( b @ SV10 )
= $true )
| ( sK8_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK5_SY113 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(106,plain,
( ( ( ~ ~ ( b @ sK5_SY113 ) )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(107,plain,
( ( ( irel @ sK2_SY104 @ sK3_SY116 )
= $true )
| ( sK7_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(108,plain,
( ( ( ~ ( a @ sK3_SY116 ) )
= $true )
| ( sK7_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(109,plain,
( ( ( ~ ( irel @ sK2_SY104 @ sK4_SY115 ) )
= $false )
| ( sK7_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(110,plain,
( ( ( ~ ~ ( b @ sK4_SY115 ) )
= $false )
| ( sK7_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(111,plain,
( ( ( irel @ sK2_SY104 @ sK6_SY112 )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(112,plain,
( ( ( ~ ( a @ sK6_SY112 ) )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(113,plain,
( ( ( irel @ sK2_SY104 @ sK5_SY113 )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(114,plain,
( ( ( ~ ( b @ sK5_SY113 ) )
= $true )
| ( sK8_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(115,plain,
( ( ( a @ sK3_SY116 )
= $false )
| ( sK7_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(116,plain,
( ( ( irel @ sK2_SY104 @ sK4_SY115 )
= $true )
| ( sK7_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(117,plain,
( ( ( ~ ( b @ sK4_SY115 ) )
= $true )
| ( sK7_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(118,plain,
( ( ( a @ sK6_SY112 )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(119,plain,
( ( ( b @ sK5_SY113 )
= $false )
| ( sK8_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(120,plain,
( ( ( b @ sK4_SY115 )
= $false )
| ( sK7_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(121,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,120,119,118,116,115,113,111,107,104,101,100,47,46,38,36]) ).
thf(122,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN978^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n018.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 17:32:52 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
% 0.11/0.22
% 0.11/0.22 No.of.Axioms: 2
% 0.11/0.22
% 0.11/0.22 Length.of.Defs: 2734
% 0.11/0.22
% 0.11/0.22 Contains.Choice.Funs: false
% 0.11/0.22 .....
% 0.11/0.22
% 0.11/0.22 ********************************
% 0.11/0.22 * All subproblems solved! *
% 0.11/0.22 ********************************
% 0.11/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.22
% 0.11/0.22 %**** Beginning of derivation protocol ****
% 0.11/0.22 % SZS output start CNFRefutation
% See solution above
% 0.11/0.22
% 0.11/0.22 %**** End of derivation protocol ****
% 0.11/0.22 %**** no. of clauses in derivation: 122 ****
% 0.11/0.22 %**** clause counter: 121 ****
% 0.11/0.22
% 0.11/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------