TSTP Solution File: LCL874^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL874^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 : Sun Jul 17 12:27:21 EDT 2022
% Result : Theorem 0.85s 1.05s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 80
% Syntax : Number of formulae : 190 ( 85 unt; 40 typ; 31 def)
% Number of atoms : 804 ( 231 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 1200 ( 212 ~; 208 |; 8 &; 764 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 227 ( 227 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 4 con; 0-3 aty)
% Number of variables : 380 ( 57 ^ 317 !; 6 ?; 380 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meq_ind,type,
meq_ind: mu > mu > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_rb,type,
rb: $i > $i > $o ).
thf(tp_rk,type,
rk: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY16,type,
sK2_SY16: $i > $o ).
thf(tp_sK3_SY0,type,
sK3_SY0: $i > $i ).
thf(tp_sK4_SY29,type,
sK4_SY29: $i ).
thf(tp_sK5_SY23,type,
sK5_SY23: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY26,type,
sK6_SY26: ( $i > $o ) > $i > $i ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_ind) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rb @ ( mbox @ rk @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rk @ A ) @ ( mbox @ rb @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(3,axiom,
meuclidean @ rb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(4,axiom,
meuclidean @ rk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(5,axiom,
mtransitive @ rb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(6,axiom,
mtransitive @ rk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(7,axiom,
mserial @ rb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(8,axiom,
mreflexive @ rk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(9,conjecture,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rk @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(10,negated_conjecture,
( ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rk @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ~ ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rk @ A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( mreflexive @ rk )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( mserial @ rb )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( mtransitive @ rk )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( mtransitive @ rb )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(16,plain,
( ( meuclidean @ rk )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(17,plain,
( ( meuclidean @ rb )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(18,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rk @ A ) @ ( mbox @ rb @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(19,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rb @ ( mbox @ rk @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(20,plain,
( ( ~ ( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ rb @ A ) @ ( mbox @ rk @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(21,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( rb @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( rk @ SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(22,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( rb @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(23,plain,
( ( ! [SX0: $i] : ( rk @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rb @ SX0 @ SX1 )
| ~ ( rb @ SX1 @ SX2 ) )
| ( rb @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(25,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rk @ SX0 @ SX1 )
| ~ ( rk @ SX1 @ SX2 ) )
| ( rk @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rk @ SX0 @ SX1 )
| ~ ( rk @ SX0 @ SX2 ) )
| ( rk @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rb @ SX0 @ SX1 )
| ~ ( rb @ SX0 @ SX2 ) )
| ( rb @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( rb @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( rb @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( rk @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( rk @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( rb @ SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( rb @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( rk @ SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(31,plain,
! [SV1: $i] :
( ( ~ ! [SY0: $i] :
~ ( rb @ SV1 @ SY0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(32,plain,
! [SV2: $i] :
( ( rk @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY1: $i,SY2: $i] :
( ~ ~ ( ~ ( rb @ SV3 @ SY1 )
| ~ ( rb @ SY1 @ SY2 ) )
| ( rb @ SV3 @ SY2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV4: $i] :
( ( ! [SY3: $i,SY4: $i] :
( ~ ~ ( ~ ( rk @ SV4 @ SY3 )
| ~ ( rk @ SY3 @ SY4 ) )
| ( rk @ SV4 @ SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV5: $i] :
( ( ! [SY5: $i,SY6: $i] :
( ~ ~ ( ~ ( rk @ SV5 @ SY5 )
| ~ ( rk @ SV5 @ SY6 ) )
| ( rk @ SY5 @ SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV6: $i] :
( ( ! [SY7: $i,SY8: $i] :
( ~ ~ ( ~ ( rb @ SV6 @ SY7 )
| ~ ( rb @ SV6 @ SY8 ) )
| ( rb @ SY7 @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV7: $i] :
( ( ! [SY9: $i > $o] :
( ~ ! [SY10: $i] :
( ~ ( rb @ SV7 @ SY10 )
| ( SY9 @ SY10 ) )
| ! [SY11: $i] :
( ~ ( rb @ SV7 @ SY11 )
| ! [SX3: $i] :
( ~ ( rk @ SY11 @ SX3 )
| ( SY9 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV8: $i] :
( ( ! [SY13: $i > $o] :
( ~ ! [SY14: $i] :
( ~ ( rk @ SV8 @ SY14 )
| ( SY13 @ SY14 ) )
| ! [SY15: $i] :
( ~ ( rb @ SV8 @ SY15 )
| ( SY13 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(39,plain,
( ( ! [SY16: $i > $o] :
( ~ ! [SY17: $i] :
( ~ ( rb @ sK1_SX0 @ SY17 )
| ( SY16 @ SY17 ) )
| ! [SY18: $i] :
( ~ ( rk @ sK1_SX0 @ SY18 )
| ( SY16 @ SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(40,plain,
! [SV1: $i] :
( ( ! [SY0: $i] :
~ ( rb @ SV1 @ SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY19: $i] :
( ~ ~ ( ~ ( rb @ SV3 @ SV9 )
| ~ ( rb @ SV9 @ SY19 ) )
| ( rb @ SV3 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY20: $i] :
( ~ ~ ( ~ ( rk @ SV4 @ SV10 )
| ~ ( rk @ SV10 @ SY20 ) )
| ( rk @ SV4 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY21: $i] :
( ~ ~ ( ~ ( rk @ SV5 @ SV11 )
| ~ ( rk @ SV5 @ SY21 ) )
| ( rk @ SV11 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY22: $i] :
( ~ ~ ( ~ ( rb @ SV6 @ SV12 )
| ~ ( rb @ SV6 @ SY22 ) )
| ( rb @ SV12 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV13: $i > $o,SV7: $i] :
( ( ~ ! [SY23: $i] :
( ~ ( rb @ SV7 @ SY23 )
| ( SV13 @ SY23 ) )
| ! [SY24: $i] :
( ~ ( rb @ SV7 @ SY24 )
| ! [SY25: $i] :
( ~ ( rk @ SY24 @ SY25 )
| ( SV13 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV14: $i > $o,SV8: $i] :
( ( ~ ! [SY26: $i] :
( ~ ( rk @ SV8 @ SY26 )
| ( SV14 @ SY26 ) )
| ! [SY27: $i] :
( ~ ( rb @ SV8 @ SY27 )
| ( SV14 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
( ( ~ ! [SY28: $i] :
( ~ ( rb @ sK1_SX0 @ SY28 )
| ( sK2_SY16 @ SY28 ) )
| ! [SY29: $i] :
( ~ ( rk @ sK1_SX0 @ SY29 )
| ( sK2_SY16 @ SY29 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(48,plain,
! [SV1: $i] :
( ( ~ ( rb @ SV1 @ ( sK3_SY0 @ SV1 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(49,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ~ ~ ( ~ ( rb @ SV3 @ SV9 )
| ~ ( rb @ SV9 @ SV15 ) )
| ( rb @ SV3 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV16: $i,SV10: $i,SV4: $i] :
( ( ~ ~ ( ~ ( rk @ SV4 @ SV10 )
| ~ ( rk @ SV10 @ SV16 ) )
| ( rk @ SV4 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV17: $i,SV11: $i,SV5: $i] :
( ( ~ ~ ( ~ ( rk @ SV5 @ SV11 )
| ~ ( rk @ SV5 @ SV17 ) )
| ( rk @ SV11 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ~ ~ ( ~ ( rb @ SV6 @ SV12 )
| ~ ( rb @ SV6 @ SV18 ) )
| ( rb @ SV12 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV13: $i > $o,SV7: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( rb @ SV7 @ SY23 )
| ( SV13 @ SY23 ) ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( rb @ SV7 @ SY24 )
| ! [SY25: $i] :
( ~ ( rk @ SY24 @ SY25 )
| ( SV13 @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV14: $i > $o,SV8: $i] :
( ( ( ~ ! [SY26: $i] :
( ~ ( rk @ SV8 @ SY26 )
| ( SV14 @ SY26 ) ) )
= $true )
| ( ( ! [SY27: $i] :
( ~ ( rb @ SV8 @ SY27 )
| ( SV14 @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(55,plain,
( ( ~ ! [SY28: $i] :
( ~ ( rb @ sK1_SX0 @ SY28 )
| ( sK2_SY16 @ SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(56,plain,
( ( ! [SY29: $i] :
( ~ ( rk @ sK1_SX0 @ SY29 )
| ( sK2_SY16 @ SY29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(57,plain,
! [SV1: $i] :
( ( rb @ SV1 @ ( sK3_SY0 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(58,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rb @ SV3 @ SV9 )
| ~ ( rb @ SV9 @ SV15 ) ) )
= $true )
| ( ( rb @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV16: $i,SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( rk @ SV4 @ SV10 )
| ~ ( rk @ SV10 @ SV16 ) ) )
= $true )
| ( ( rk @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV17: $i,SV11: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( rk @ SV5 @ SV11 )
| ~ ( rk @ SV5 @ SV17 ) ) )
= $true )
| ( ( rk @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( rb @ SV6 @ SV12 )
| ~ ( rb @ SV6 @ SV18 ) ) )
= $true )
| ( ( rb @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV13: $i > $o,SV7: $i] :
( ( ( ! [SY23: $i] :
( ~ ( rb @ SV7 @ SY23 )
| ( SV13 @ SY23 ) ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( rb @ SV7 @ SY24 )
| ! [SY25: $i] :
( ~ ( rk @ SY24 @ SY25 )
| ( SV13 @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV14: $i > $o,SV8: $i] :
( ( ( ! [SY26: $i] :
( ~ ( rk @ SV8 @ SY26 )
| ( SV14 @ SY26 ) ) )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( rb @ SV8 @ SY27 )
| ( SV14 @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(64,plain,
( ( ! [SY28: $i] :
( ~ ( rb @ sK1_SX0 @ SY28 )
| ( sK2_SY16 @ SY28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(65,plain,
( ( ~ ( rk @ sK1_SX0 @ sK4_SY29 )
| ( sK2_SY16 @ sK4_SY29 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(66,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( rb @ SV3 @ SV9 )
| ~ ( rb @ SV9 @ SV15 ) ) )
= $false )
| ( ( rb @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV16: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( rk @ SV4 @ SV10 )
| ~ ( rk @ SV10 @ SV16 ) ) )
= $false )
| ( ( rk @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV17: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( ~ ( rk @ SV5 @ SV11 )
| ~ ( rk @ SV5 @ SV17 ) ) )
= $false )
| ( ( rk @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( rb @ SV6 @ SV12 )
| ~ ( rb @ SV6 @ SV18 ) ) )
= $false )
| ( ( rb @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV13: $i > $o,SV7: $i] :
( ( ( ~ ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
| ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( rb @ SV7 @ SY24 )
| ! [SY25: $i] :
( ~ ( rk @ SY24 @ SY25 )
| ( SV13 @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(71,plain,
! [SV14: $i > $o,SV8: $i] :
( ( ( ~ ( rk @ SV8 @ ( sK6_SY26 @ SV14 @ SV8 ) )
| ( SV14 @ ( sK6_SY26 @ SV14 @ SV8 ) ) )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( rb @ SV8 @ SY27 )
| ( SV14 @ SY27 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(72,plain,
! [SV19: $i] :
( ( ~ ( rb @ sK1_SX0 @ SV19 )
| ( sK2_SY16 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
( ( ~ ( rk @ sK1_SX0 @ sK4_SY29 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
( ( sK2_SY16 @ sK4_SY29 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( rb @ SV3 @ SV9 )
| ~ ( rb @ SV9 @ SV15 ) )
= $true )
| ( ( rb @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(76,plain,
! [SV16: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( rk @ SV4 @ SV10 )
| ~ ( rk @ SV10 @ SV16 ) )
= $true )
| ( ( rk @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(77,plain,
! [SV17: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( rk @ SV5 @ SV11 )
| ~ ( rk @ SV5 @ SV17 ) )
= $true )
| ( ( rk @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(78,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( rb @ SV6 @ SV12 )
| ~ ( rb @ SV6 @ SV18 ) )
= $true )
| ( ( rb @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(79,plain,
! [SV13: $i > $o,SV7: $i] :
( ( ( ~ ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( rb @ SV7 @ SY24 )
| ! [SY25: $i] :
( ~ ( rk @ SY24 @ SY25 )
| ( SV13 @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(80,plain,
! [SV7: $i,SV13: $i > $o] :
( ( ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( rb @ SV7 @ SY24 )
| ! [SY25: $i] :
( ~ ( rk @ SY24 @ SY25 )
| ( SV13 @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(81,plain,
! [SV14: $i > $o,SV8: $i] :
( ( ( ~ ( rk @ SV8 @ ( sK6_SY26 @ SV14 @ SV8 ) ) )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( rb @ SV8 @ SY27 )
| ( SV14 @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(82,plain,
! [SV8: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $false )
| ( ( ! [SY27: $i] :
( ~ ( rb @ SV8 @ SY27 )
| ( SV14 @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(83,plain,
! [SV19: $i] :
( ( ( ~ ( rb @ sK1_SX0 @ SV19 ) )
= $true )
| ( ( sK2_SY16 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(84,plain,
( ( rk @ sK1_SX0 @ sK4_SY29 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(85,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( rb @ SV3 @ SV9 ) )
= $true )
| ( ( ~ ( rb @ SV9 @ SV15 ) )
= $true )
| ( ( rb @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV16: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( rk @ SV4 @ SV10 ) )
= $true )
| ( ( ~ ( rk @ SV10 @ SV16 ) )
= $true )
| ( ( rk @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV17: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( rk @ SV5 @ SV11 ) )
= $true )
| ( ( ~ ( rk @ SV5 @ SV17 ) )
= $true )
| ( ( rk @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( rb @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( rb @ SV6 @ SV18 ) )
= $true )
| ( ( rb @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV13: $i > $o,SV7: $i] :
( ( ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( rb @ SV7 @ SY24 )
| ! [SY25: $i] :
( ~ ( rk @ SY24 @ SY25 )
| ( SV13 @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(90,plain,
! [SV13: $i > $o,SV20: $i,SV7: $i] :
( ( ( ~ ( rb @ SV7 @ SV20 )
| ! [SY30: $i] :
( ~ ( rk @ SV20 @ SY30 )
| ( SV13 @ SY30 ) ) )
= $true )
| ( ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV14: $i > $o,SV8: $i] :
( ( ( rk @ SV8 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $true )
| ( ( ! [SY27: $i] :
( ~ ( rb @ SV8 @ SY27 )
| ( SV14 @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(92,plain,
! [SV14: $i > $o,SV21: $i,SV8: $i] :
( ( ( ~ ( rb @ SV8 @ SV21 )
| ( SV14 @ SV21 ) )
= $true )
| ( ( SV14 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV19: $i] :
( ( ( rb @ sK1_SX0 @ SV19 )
= $false )
| ( ( sK2_SY16 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ( rb @ SV3 @ SV9 )
= $false )
| ( ( ~ ( rb @ SV9 @ SV15 ) )
= $true )
| ( ( rb @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV16: $i,SV10: $i,SV4: $i] :
( ( ( rk @ SV4 @ SV10 )
= $false )
| ( ( ~ ( rk @ SV10 @ SV16 ) )
= $true )
| ( ( rk @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV17: $i,SV11: $i,SV5: $i] :
( ( ( rk @ SV5 @ SV11 )
= $false )
| ( ( ~ ( rk @ SV5 @ SV17 ) )
= $true )
| ( ( rk @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV18: $i,SV12: $i,SV6: $i] :
( ( ( rb @ SV6 @ SV12 )
= $false )
| ( ( ~ ( rb @ SV6 @ SV18 ) )
= $true )
| ( ( rb @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV13: $i > $o,SV22: $i,SV7: $i] :
( ( ( ~ ( rb @ SV7 @ SV22 )
| ! [SY31: $i] :
( ~ ( rk @ SV22 @ SY31 )
| ( SV13 @ SY31 ) ) )
= $true )
| ( ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV13: $i > $o,SV20: $i,SV7: $i] :
( ( ( ~ ( rb @ SV7 @ SV20 ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( rk @ SV20 @ SY30 )
| ( SV13 @ SY30 ) ) )
= $true )
| ( ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV14: $i > $o,SV23: $i,SV8: $i] :
( ( ( ~ ( rb @ SV8 @ SV23 )
| ( SV14 @ SV23 ) )
= $true )
| ( ( rk @ SV8 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV14: $i > $o,SV21: $i,SV8: $i] :
( ( ( ~ ( rb @ SV8 @ SV21 ) )
= $true )
| ( ( SV14 @ SV21 )
= $true )
| ( ( SV14 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV3: $i,SV15: $i,SV9: $i] :
( ( ( rb @ SV9 @ SV15 )
= $false )
| ( ( rb @ SV3 @ SV9 )
= $false )
| ( ( rb @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV4: $i,SV16: $i,SV10: $i] :
( ( ( rk @ SV10 @ SV16 )
= $false )
| ( ( rk @ SV4 @ SV10 )
= $false )
| ( ( rk @ SV4 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV11: $i,SV17: $i,SV5: $i] :
( ( ( rk @ SV5 @ SV17 )
= $false )
| ( ( rk @ SV5 @ SV11 )
= $false )
| ( ( rk @ SV11 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV12: $i,SV18: $i,SV6: $i] :
( ( ( rb @ SV6 @ SV18 )
= $false )
| ( ( rb @ SV6 @ SV12 )
= $false )
| ( ( rb @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV13: $i > $o,SV22: $i,SV7: $i] :
( ( ( ~ ( rb @ SV7 @ SV22 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( rk @ SV22 @ SY31 )
| ( SV13 @ SY31 ) ) )
= $true )
| ( ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(107,plain,
! [SV13: $i > $o,SV20: $i,SV7: $i] :
( ( ( rb @ SV7 @ SV20 )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( rk @ SV20 @ SY30 )
| ( SV13 @ SY30 ) ) )
= $true )
| ( ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(108,plain,
! [SV14: $i > $o,SV23: $i,SV8: $i] :
( ( ( ~ ( rb @ SV8 @ SV23 ) )
= $true )
| ( ( SV14 @ SV23 )
= $true )
| ( ( rk @ SV8 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV14: $i > $o,SV21: $i,SV8: $i] :
( ( ( rb @ SV8 @ SV21 )
= $false )
| ( ( SV14 @ SV21 )
= $true )
| ( ( SV14 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV13: $i > $o,SV22: $i,SV7: $i] :
( ( ( rb @ SV7 @ SV22 )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( rk @ SV22 @ SY31 )
| ( SV13 @ SY31 ) ) )
= $true )
| ( ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV7: $i,SV13: $i > $o,SV24: $i,SV20: $i] :
( ( ( ~ ( rk @ SV20 @ SV24 )
| ( SV13 @ SV24 ) )
= $true )
| ( ( rb @ SV7 @ SV20 )
= $false )
| ( ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV14: $i > $o,SV23: $i,SV8: $i] :
( ( ( rb @ SV8 @ SV23 )
= $false )
| ( ( SV14 @ SV23 )
= $true )
| ( ( rk @ SV8 @ ( sK6_SY26 @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV7: $i,SV13: $i > $o,SV25: $i,SV22: $i] :
( ( ( ~ ( rk @ SV22 @ SV25 )
| ( SV13 @ SV25 ) )
= $true )
| ( ( rb @ SV7 @ SV22 )
= $false )
| ( ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV7: $i,SV13: $i > $o,SV24: $i,SV20: $i] :
( ( ( ~ ( rk @ SV20 @ SV24 ) )
= $true )
| ( ( SV13 @ SV24 )
= $true )
| ( ( rb @ SV7 @ SV20 )
= $false )
| ( ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(115,plain,
! [SV7: $i,SV13: $i > $o,SV25: $i,SV22: $i] :
( ( ( ~ ( rk @ SV22 @ SV25 ) )
= $true )
| ( ( SV13 @ SV25 )
= $true )
| ( ( rb @ SV7 @ SV22 )
= $false )
| ( ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV7: $i,SV13: $i > $o,SV24: $i,SV20: $i] :
( ( ( rk @ SV20 @ SV24 )
= $false )
| ( ( SV13 @ SV24 )
= $true )
| ( ( rb @ SV7 @ SV20 )
= $false )
| ( ( SV13 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV7: $i,SV13: $i > $o,SV25: $i,SV22: $i] :
( ( ( rk @ SV22 @ SV25 )
= $false )
| ( ( SV13 @ SV25 )
= $true )
| ( ( rb @ SV7 @ SV22 )
= $false )
| ( ( rb @ SV7 @ ( sK5_SY23 @ SV13 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(118,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,117,116,112,109,105,104,103,102,93,84,74,57]) ).
thf(119,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL874^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n025.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 : Sun Jul 3 17:49:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 8
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 5293
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.85/1.05
% 0.85/1.05 ********************************
% 0.85/1.05 * All subproblems solved! *
% 0.85/1.05 ********************************
% 0.85/1.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.85/1.06
% 0.85/1.06 %**** Beginning of derivation protocol ****
% 0.85/1.06 % SZS output start CNFRefutation
% See solution above
% 0.85/1.06
% 0.85/1.06 %**** End of derivation protocol ****
% 0.85/1.06 %**** no. of clauses in derivation: 119 ****
% 0.85/1.06 %**** clause counter: 118 ****
% 0.85/1.06
% 0.85/1.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------