TSTP Solution File: SYN978^4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN978^4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 08:30:57 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 50
% Syntax : Number of formulae : 130 ( 44 unt; 28 typ; 19 def)
% Number of atoms : 734 ( 176 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1033 ( 224 ~; 233 |; 2 &; 572 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 7 con; 0-3 aty)
% Number of variables : 185 ( 31 ^ 152 !; 2 ?; 185 :)
% 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_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY4,type,
sK2_SY4: $i ).
thf(tp_sK3_SY10,type,
sK3_SY10: $i ).
thf(tp_sK4_SY12,type,
sK4_SY12: $i ).
thf(tp_sK5_SY12,type,
sK5_SY12: $i ).
thf(tp_sK6_SY12,type,
sK6_SY12: $i > $i ).
thf(iand,definition,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iand) ).
thf(iatom,definition,
( iatom
= ( ^ [P: $i > $o] : P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iatom) ).
thf(icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icountersatisfiable) ).
thf(iequiv,definition,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iequiv) ).
thf(ifalse,definition,
( ifalse
= ( inot @ itrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifalse) ).
thf(iimplied,definition,
( iimplied
= ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplied) ).
thf(iimplies,definition,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies) ).
thf(iinvalid,definition,
( iinvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iinvalid) ).
thf(inot,definition,
( inot
= ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inot) ).
thf(ior,definition,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ior) ).
thf(isatisfiable,definition,
( isatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isatisfiable) ).
thf(itrue,definition,
( itrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',itrue) ).
thf(ivalid,definition,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ivalid) ).
thf(ixor,definition,
( ixor
= ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ixor) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mimplies,definition,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ X @ Y )
& ( irel @ Y @ Z ) )
=> ( irel @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).
thf(2,axiom,
! [X: $i] : ( irel @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).
thf(3,conjecture,
ivalid @ ( 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,
( ( ~ ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( irel @ X @ Y )
| ~ ( irel @ Y @ Z )
| ( irel @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1]) ).
thf(7,plain,
( ( ! [X: $i] : ( irel @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(8,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( irel @ X @ Y )
| ~ ( irel @ Y @ Z )
| ( irel @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( a @ SX1 )
| ~ ( b @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( a @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( b @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( b @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( a @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,iand,iatom,icountersatisfiable,iequiv,ifalse,iimplied,iimplies,iinvalid,inot,ior,isatisfiable,itrue,ivalid,ixor,mand,mbox_s4,mimplies,mnot,mor]) ).
thf(11,plain,
! [SV1: $i] :
( ( irel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(12,plain,
! [SV2: $i] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ( irel @ SV2 @ SY0 )
| ~ ( irel @ SY0 @ SY1 )
| ( irel @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( a @ SX1 )
| ~ ( b @ SX1 ) ) )
| ! [SX1: $i] :
( ~ ( irel @ SX0 @ SX1 )
| ~ ( ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( a @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( b @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( b @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SX1 @ SX2 )
| ( a @ SX2 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV3: $i,SV2: $i] :
( ( ! [SY2: $i] :
( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SY2 )
| ( irel @ SV2 @ SY2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SY3: $i] :
( ~ ( irel @ sK1_SX0 @ SY3 )
| ~ ( ~ ( a @ SY3 )
| ~ ( b @ SY3 ) ) )
| ! [SY4: $i] :
( ~ ( irel @ sK1_SX0 @ SY4 )
| ~ ( ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( a @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( b @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( b @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( a @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 )
| ( irel @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SY3: $i] :
( ~ ( irel @ sK1_SX0 @ SY3 )
| ~ ( ~ ( a @ SY3 )
| ~ ( b @ SY3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY4: $i] :
( ~ ( irel @ sK1_SX0 @ SY4 )
| ~ ( ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( a @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( b @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( b @ SX2 ) )
| ! [SX2: $i] :
( ~ ( irel @ SY4 @ SX2 )
| ( a @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( irel @ SV2 @ SV3 )
| ~ ( irel @ SV3 @ SV4 ) )
= $true )
| ( ( irel @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SY3: $i] :
( ~ ( irel @ sK1_SX0 @ SY3 )
| ~ ( ~ ( a @ SY3 )
| ~ ( b @ SY3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( irel @ sK1_SX0 @ sK2_SY4 )
| ~ ( ~ ( ~ ! [SY9: $i] :
( ~ ( irel @ sK2_SY4 @ SY9 )
| ( a @ SY9 ) )
| ! [SY10: $i] :
( ~ ( irel @ sK2_SY4 @ SY10 )
| ( b @ SY10 ) ) )
| ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,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)],[19]) ).
thf(23,plain,
! [SV5: $i] :
( ( ~ ( irel @ sK1_SX0 @ SV5 )
| ~ ( ~ ( a @ SV5 )
| ~ ( b @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( irel @ sK1_SX0 @ sK2_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( ~ ( ~ ! [SY9: $i] :
( ~ ( irel @ sK2_SY4 @ SY9 )
| ( a @ SY9 ) )
| ! [SY10: $i] :
( ~ ( irel @ sK2_SY4 @ SY10 )
| ( b @ SY10 ) ) )
| ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,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)],[22]) ).
thf(27,plain,
! [SV5: $i] :
( ( ( ~ ( irel @ sK1_SX0 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( a @ SV5 )
| ~ ( b @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( irel @ sK1_SX0 @ sK2_SY4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( ~ ! [SY9: $i] :
( ~ ( irel @ sK2_SY4 @ SY9 )
| ( a @ SY9 ) )
| ! [SY10: $i] :
( ~ ( irel @ sK2_SY4 @ SY10 )
| ( b @ SY10 ) ) )
| ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,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)],[26]) ).
thf(31,plain,
! [SV5: $i] :
( ( ( irel @ sK1_SX0 @ SV5 )
= $false )
| ( ( ~ ( ~ ( a @ SV5 )
| ~ ( b @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( ( ~ ( ~ ! [SY9: $i] :
( ~ ( irel @ sK2_SY4 @ SY9 )
| ( a @ SY9 ) )
| ! [SY10: $i] :
( ~ ( irel @ sK2_SY4 @ SY10 )
| ( b @ SY10 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV5: $i] :
( ( ( ~ ( a @ SV5 )
| ~ ( b @ SV5 ) )
= $false )
| ( ( irel @ sK1_SX0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
( ( ( ~ ! [SY9: $i] :
( ~ ( irel @ sK2_SY4 @ SY9 )
| ( a @ SY9 ) )
| ! [SY10: $i] :
( ~ ( irel @ sK2_SY4 @ SY10 )
| ( b @ SY10 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV5: $i] :
( ( ( ~ ( a @ SV5 ) )
= $false )
| ( ( irel @ sK1_SX0 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV5: $i] :
( ( ( ~ ( b @ SV5 ) )
= $false )
| ( ( irel @ sK1_SX0 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ( ~ ! [SY9: $i] :
( ~ ( irel @ sK2_SY4 @ SY9 )
| ( a @ SY9 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ( ! [SY10: $i] :
( ~ ( irel @ sK2_SY4 @ SY10 )
| ( b @ SY10 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( a @ SV5 )
= $true )
| ( ( irel @ sK1_SX0 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV5: $i] :
( ( ( b @ SV5 )
= $true )
| ( ( irel @ sK1_SX0 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( ( ! [SY9: $i] :
( ~ ( irel @ sK2_SY4 @ SY9 )
| ( a @ SY9 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( ( ~ ( irel @ sK2_SY4 @ sK3_SY10 )
| ( b @ sK3_SY10 ) )
= $false )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(43,plain,
! [SV6: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV6 )
| ( a @ SV6 ) )
= $true )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
( ( ( ~ ( irel @ sK2_SY4 @ sK3_SY10 ) )
= $false )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(45,plain,
( ( ( b @ sK3_SY10 )
= $false )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV6: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV6 ) )
= $true )
| ( ( a @ SV6 )
= $true )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(47,plain,
( ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) )
= $false )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV6: $i] :
( ( ( irel @ sK2_SY4 @ SV6 )
= $false )
| ( ( a @ SV6 )
= $true )
| ( ( ~ ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) )
= $false )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) ) )
= $false )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
( ( ( ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) )
= $false )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
! [SV6: $i] :
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) )
| ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) )
= $false )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) ) )
= $false )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
( ( ( ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) )
= $false )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(56,plain,
( ( ( ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) ) )
= $true )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
( ( ( ~ ( irel @ sK2_SY4 @ sK4_SY12 )
| ( a @ sK4_SY12 ) )
= $false )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(58,plain,
! [SV6: $i] :
( ( ( ~ ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) ) )
= $false )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV6: $i] :
( ( ( ! [SY12: $i] :
( ~ ( irel @ sK2_SY4 @ SY12 )
| ( a @ SY12 ) ) )
= $false )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(60,plain,
( ( ( ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) ) )
= $true )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
( ( ( ~ ( irel @ sK2_SY4 @ sK5_SY12 )
| ( a @ sK5_SY12 ) )
= $false )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(62,plain,
! [SV7: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV7 )
| ( b @ SV7 ) )
= $true )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(63,plain,
( ( ( ~ ( irel @ sK2_SY4 @ sK4_SY12 ) )
= $false )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(64,plain,
( ( ( a @ sK4_SY12 )
= $false )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(65,plain,
! [SV6: $i] :
( ( ( ! [SY11: $i] :
( ~ ( irel @ sK2_SY4 @ SY11 )
| ( b @ SY11 ) ) )
= $true )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(66,plain,
! [SV6: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ ( sK6_SY12 @ SV6 ) )
| ( a @ ( sK6_SY12 @ SV6 ) ) )
= $false )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(67,plain,
! [SV8: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV8 )
| ( b @ SV8 ) )
= $true )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( ( ~ ( irel @ sK2_SY4 @ sK5_SY12 ) )
= $false )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(69,plain,
( ( ( a @ sK5_SY12 )
= $false )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(70,plain,
! [SV7: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV7 ) )
= $true )
| ( ( b @ SV7 )
= $true )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(71,plain,
( ( ( irel @ sK2_SY4 @ sK4_SY12 )
= $true )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(72,plain,
! [SV6: $i,SV9: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV9 )
| ( b @ SV9 ) )
= $true )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV6: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ ( sK6_SY12 @ SV6 ) ) )
= $false )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV6: $i] :
( ( ( a @ ( sK6_SY12 @ SV6 ) )
= $false )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(75,plain,
! [SV8: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV8 ) )
= $true )
| ( ( b @ SV8 )
= $true )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(76,plain,
( ( ( irel @ sK2_SY4 @ sK5_SY12 )
= $true )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV7: $i] :
( ( ( irel @ sK2_SY4 @ SV7 )
= $false )
| ( ( b @ SV7 )
= $true )
| ( ( b @ sK3_SY10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(78,plain,
! [SV6: $i,SV9: $i] :
( ( ( ~ ( irel @ sK2_SY4 @ SV9 ) )
= $true )
| ( ( b @ SV9 )
= $true )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV6: $i] :
( ( ( irel @ sK2_SY4 @ ( sK6_SY12 @ SV6 ) )
= $true )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV8: $i] :
( ( ( irel @ sK2_SY4 @ SV8 )
= $false )
| ( ( b @ SV8 )
= $true )
| ( ( irel @ sK2_SY4 @ sK3_SY10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV6: $i,SV9: $i] :
( ( ( irel @ sK2_SY4 @ SV9 )
= $false )
| ( ( b @ SV9 )
= $true )
| ( ( a @ SV6 )
= $true )
| ( ( irel @ sK2_SY4 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,81,80,79,77,76,74,71,69,64,40,39,30,28]) ).
thf(83,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN978^4 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 14:05:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 2
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 2734
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.21/0.41
% 0.21/0.41 ********************************
% 0.21/0.41 * All subproblems solved! *
% 0.21/0.41 ********************************
% 0.21/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:82,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.41
% 0.21/0.41 %**** Beginning of derivation protocol ****
% 0.21/0.41 % SZS output start CNFRefutation
% See solution above
% 0.21/0.42
% 0.21/0.42 %**** End of derivation protocol ****
% 0.21/0.42 %**** no. of clauses in derivation: 83 ****
% 0.21/0.42 %**** clause counter: 82 ****
% 0.21/0.42
% 0.21/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:82,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------