TSTP Solution File: SYO470^6 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO470^6 : 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 : n021.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 17:34:46 EDT 2022
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 82
% Syntax : Number of formulae : 240 ( 54 unt; 45 typ; 33 def)
% Number of atoms : 1782 ( 463 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 2941 ( 744 ~; 641 |; 8 &;1540 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 190 ( 190 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 44 usr; 6 con; 0-3 aty)
% Number of variables : 563 ( 52 ^ 505 !; 6 ?; 563 :)
% 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_mbox_s5,type,
mbox_s5: ( $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_mdia_s5,type,
mdia_s5: ( $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_p,type,
p: $i > $o ).
thf(tp_rel_s5,type,
rel_s5: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY7,type,
sK2_SY7: $i ).
thf(tp_sK3_SY4,type,
sK3_SY4: $i ).
thf(tp_sK4_SY12,type,
sK4_SY12: $i ).
thf(tp_sK5_SY21,type,
sK5_SY21: $i > $i > $i ).
thf(tp_sK6_SY22,type,
sK6_SY22: $i > $i > $i ).
thf(tp_sK7_SY25,type,
sK7_SY25: $i > $i > $i ).
thf(tp_sK8_SY28,type,
sK8_SY28: $i > $i > $i ).
thf(tp_sK9_SY29,type,
sK9_SY29: $i > $i > $i > $i ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s5,definition,
( mbox_s5
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s5 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s5,definition,
( mdia_s5
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(2,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(4,conjecture,
mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(5,negated_conjecture,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(8,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(9,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(10,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s5 @ SX0 @ SX1 )
| ~ ( rel_s5 @ SX1 @ SX2 ) )
| ( rel_s5 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(12,plain,
( ( ! [SX0: $i] : ( rel_s5 @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(13,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ( rel_s5 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(14,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ~ ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) )
| ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ( p @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(15,plain,
! [SV1: $i] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ~ ( ~ ( rel_s5 @ SV1 @ SY0 )
| ~ ( rel_s5 @ SY0 @ SY1 ) )
| ( rel_s5 @ SV1 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: $i] :
( ( rel_s5 @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV3: $i] :
( ( ! [SY2: $i] :
( ~ ( rel_s5 @ SV3 @ SY2 )
| ( rel_s5 @ SY2 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ~ ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) )
| ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ( p @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY3: $i] :
( ~ ~ ( ~ ( rel_s5 @ SV1 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SY3 ) )
| ( rel_s5 @ SV1 @ SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV5: $i,SV3: $i] :
( ( ~ ( rel_s5 @ SV3 @ SV5 )
| ( rel_s5 @ SV5 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( ~ ( ~ ~ ! [SY4: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY4 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY4 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) )
| ! [SY7: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY7 )
| ( p @ SY7 ) ) )
| ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ~ ~ ( ~ ( rel_s5 @ SV1 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) )
| ( rel_s5 @ SV1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( rel_s5 @ SV3 @ SV5 ) )
= $true )
| ( ( rel_s5 @ SV5 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ~ ! [SY4: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY4 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY4 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) )
| ! [SY7: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY7 )
| ( p @ SY7 ) ) )
| ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( rel_s5 @ SV1 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) ) )
= $true )
| ( ( rel_s5 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV5: $i,SV3: $i] :
( ( ( rel_s5 @ SV3 @ SV5 )
= $false )
| ( ( rel_s5 @ SV5 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ( ~ ( ~ ~ ! [SY4: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY4 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY4 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) )
| ! [SY7: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY7 )
| ( p @ SY7 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( ~ ( rel_s5 @ SV1 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) ) )
= $false )
| ( ( rel_s5 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ( ~ ~ ! [SY4: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY4 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY4 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) )
| ! [SY7: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY7 )
| ( p @ SY7 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( rel_s5 @ SV1 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) )
= $true )
| ( ( rel_s5 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( ( ~ ~ ! [SY4: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY4 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY4 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ( ! [SY7: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY7 )
| ( p @ SY7 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( rel_s5 @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( rel_s5 @ SV4 @ SV6 ) )
= $true )
| ( ( rel_s5 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ( ~ ! [SY4: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY4 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY4 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ( ~ ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
| ( p @ sK2_SY7 ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(36,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ( rel_s5 @ SV1 @ SV4 )
= $false )
| ( ( ~ ( rel_s5 @ SV4 @ SV6 ) )
= $true )
| ( ( rel_s5 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( ( ! [SY4: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY4 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY4 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ( ~ ( rel_s5 @ sK1_SX0 @ sK2_SY7 ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ( p @ sK2_SY7 )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV1: $i,SV6: $i,SV4: $i] :
( ( ( rel_s5 @ SV4 @ SV6 )
= $false )
| ( ( rel_s5 @ SV1 @ SV4 )
= $false )
| ( ( rel_s5 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( ( ~ ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
| ~ ~ ! [SY12: $i] :
( ~ ( rel_s5 @ sK3_SY4 @ SY12 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY12 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(42,plain,
( ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ( ~ ( rel_s5 @ sK1_SX0 @ sK3_SY4 ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( ( ~ ~ ! [SY12: $i] :
( ~ ( rel_s5 @ sK3_SY4 @ SY12 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY12 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( ( ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
( ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
( ( ( ~ ! [SY12: $i] :
( ~ ( rel_s5 @ sK3_SY4 @ SY12 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY12 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
( ( ( ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(53,plain,
( ( ( ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(54,plain,
( ( ( ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(55,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
( ( ( ! [SY12: $i] :
( ~ ( rel_s5 @ sK3_SY4 @ SY12 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY12 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
( ( ( ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(58,plain,
( ( ( ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(59,plain,
! [SV7: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV7 )
| ( p @ SV7 ) )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV8: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV8 )
| ~ ~ ! [SY14: $i] :
( ~ ( rel_s5 @ SV8 @ SY14 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY14 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(61,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(62,plain,
( ( ( ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(63,plain,
( ( ( ~ ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
| ~ ! [SY16: $i] :
( ~ ( rel_s5 @ sK4_SY12 @ SY16 )
| ( p @ SY16 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(64,plain,
! [SV9: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV9 )
| ( p @ SV9 ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV10: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV10 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SV10 @ SY17 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY17 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV7: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV7 ) )
= $true )
| ( ( p @ SV7 )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV8: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV8 ) )
= $true )
| ( ( ~ ~ ! [SY14: $i] :
( ~ ( rel_s5 @ SV8 @ SY14 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY14 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( ( ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(69,plain,
( ( ( ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(70,plain,
( ( ( ~ ( rel_s5 @ sK3_SY4 @ sK4_SY12 ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(71,plain,
( ( ( ~ ! [SY16: $i] :
( ~ ( rel_s5 @ sK4_SY12 @ SY16 )
| ( p @ SY16 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(72,plain,
! [SV9: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV9 ) )
= $true )
| ( ( p @ SV9 )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV10: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV10 ) )
= $true )
| ( ( ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SV10 @ SY17 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY17 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV7: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV7 )
= $false )
| ( ( p @ SV7 )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV8: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( ~ ~ ! [SY14: $i] :
( ~ ( rel_s5 @ SV8 @ SY14 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY14 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV11 )
| ( p @ SV11 ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV12 )
| ~ ~ ! [SY19: $i] :
( ~ ( rel_s5 @ SV12 @ SY19 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY19 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
( ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(79,plain,
( ( ( ! [SY16: $i] :
( ~ ( rel_s5 @ sK4_SY12 @ SY16 )
| ( p @ SY16 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV9: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV10: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SV10 @ SY17 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY17 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV8: $i] :
( ( ( ~ ! [SY14: $i] :
( ~ ( rel_s5 @ SV8 @ SY14 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY14 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV11 ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV12 ) )
= $true )
| ( ( ~ ~ ! [SY19: $i] :
( ~ ( rel_s5 @ SV12 @ SY19 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY19 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(85,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV13: $i] :
( ( ( ~ ( rel_s5 @ sK4_SY12 @ SV13 )
| ( p @ SV13 ) )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV10: $i] :
( ( ( ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SV10 @ SY17 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY17 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV8: $i] :
( ( ( ! [SY14: $i] :
( ~ ( rel_s5 @ SV8 @ SY14 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY14 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(89,plain,
! [SV11: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV11 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV12: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( ~ ~ ! [SY19: $i] :
( ~ ( rel_s5 @ SV12 @ SY19 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY19 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(91,plain,
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(92,plain,
( ( ( ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(93,plain,
! [SV13: $i] :
( ( ( ~ ( rel_s5 @ sK4_SY12 @ SV13 ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV10: $i] :
( ( ( ! [SY17: $i] :
( ~ ( rel_s5 @ SV10 @ SY17 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY17 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(95,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( rel_s5 @ SV8 @ SV14 )
| ~ ! [SY21: $i] :
( ~ ( rel_s5 @ SV14 @ SY21 )
| ( p @ SY21 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV12: $i] :
( ( ( ~ ! [SY19: $i] :
( ~ ( rel_s5 @ SV12 @ SY19 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY19 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
( ( ( ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(98,plain,
( ( ( ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV13: $i] :
( ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( ~ ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV15: $i,SV10: $i] :
( ( ( ~ ( rel_s5 @ SV10 @ SV15 )
| ~ ! [SY22: $i] :
( ~ ( rel_s5 @ SV15 @ SY22 )
| ( p @ SY22 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( rel_s5 @ SV8 @ SV14 ) )
= $true )
| ( ( ~ ! [SY21: $i] :
( ~ ( rel_s5 @ SV14 @ SY21 )
| ( p @ SY21 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV12: $i] :
( ( ( ! [SY19: $i] :
( ~ ( rel_s5 @ SV12 @ SY19 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY19 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
! [SV16: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV16 )
| ( p @ SV16 ) )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV17: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV17 )
| ~ ~ ! [SY23: $i] :
( ~ ( rel_s5 @ SV17 @ SY23 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY23 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV13: $i] :
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) )
| ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV15: $i,SV10: $i] :
( ( ( ~ ( rel_s5 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ! [SY22: $i] :
( ~ ( rel_s5 @ SV15 @ SY22 )
| ( p @ SY22 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV14: $i,SV8: $i] :
( ( ( rel_s5 @ SV8 @ SV14 )
= $false )
| ( ( ~ ! [SY21: $i] :
( ~ ( rel_s5 @ SV14 @ SY21 )
| ( p @ SY21 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV18: $i,SV12: $i] :
( ( ( ~ ( rel_s5 @ SV12 @ SV18 )
| ~ ! [SY25: $i] :
( ~ ( rel_s5 @ SV18 @ SY25 )
| ( p @ SY25 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV16: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV16 ) )
= $true )
| ( ( p @ SV16 )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV17: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV17 ) )
= $true )
| ( ( ~ ~ ! [SY23: $i] :
( ~ ( rel_s5 @ SV17 @ SY23 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY23 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV13: $i] :
( ( ( ~ ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV13: $i] :
( ( ( ~ ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(113,plain,
! [SV15: $i,SV10: $i] :
( ( ( rel_s5 @ SV10 @ SV15 )
= $false )
| ( ( ~ ! [SY22: $i] :
( ~ ( rel_s5 @ SV15 @ SY22 )
| ( p @ SY22 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV8: $i,SV14: $i] :
( ( ( ! [SY21: $i] :
( ~ ( rel_s5 @ SV14 @ SY21 )
| ( p @ SY21 ) ) )
= $false )
| ( ( rel_s5 @ SV8 @ SV14 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV18: $i,SV12: $i] :
( ( ( ~ ( rel_s5 @ SV12 @ SV18 ) )
= $true )
| ( ( ~ ! [SY25: $i] :
( ~ ( rel_s5 @ SV18 @ SY25 )
| ( p @ SY25 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV16: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV16 )
= $false )
| ( ( p @ SV16 )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV17: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( ~ ~ ! [SY23: $i] :
( ~ ( rel_s5 @ SV17 @ SY23 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY23 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV13: $i] :
( ( ( ! [SY8: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY8 )
| ( p @ SY8 ) ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(119,plain,
! [SV13: $i] :
( ( ( ! [SY9: $i] :
( ~ ( rel_s5 @ sK1_SX0 @ SY9 )
| ~ ~ ! [SX2: $i] :
( ~ ( rel_s5 @ SY9 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(120,plain,
! [SV10: $i,SV15: $i] :
( ( ( ! [SY22: $i] :
( ~ ( rel_s5 @ SV15 @ SY22 )
| ( p @ SY22 ) ) )
= $false )
| ( ( rel_s5 @ SV10 @ SV15 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( rel_s5 @ SV14 @ ( sK5_SY21 @ SV8 @ SV14 ) )
| ( p @ ( sK5_SY21 @ SV8 @ SV14 ) ) )
= $false )
| ( ( rel_s5 @ SV8 @ SV14 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(122,plain,
! [SV18: $i,SV12: $i] :
( ( ( rel_s5 @ SV12 @ SV18 )
= $false )
| ( ( ~ ! [SY25: $i] :
( ~ ( rel_s5 @ SV18 @ SY25 )
| ( p @ SY25 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV17: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( rel_s5 @ SV17 @ SY23 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY23 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(124,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV19 )
| ( p @ SV19 ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV13: $i,SV20: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV20 )
| ~ ~ ! [SY26: $i] :
( ~ ( rel_s5 @ SV20 @ SY26 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY26 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV10: $i,SV15: $i] :
( ( ( ~ ( rel_s5 @ SV15 @ ( sK6_SY22 @ SV10 @ SV15 ) )
| ( p @ ( sK6_SY22 @ SV10 @ SV15 ) ) )
= $false )
| ( ( rel_s5 @ SV10 @ SV15 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[120]) ).
thf(127,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( rel_s5 @ SV14 @ ( sK5_SY21 @ SV8 @ SV14 ) ) )
= $false )
| ( ( rel_s5 @ SV8 @ SV14 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV14: $i,SV8: $i] :
( ( ( p @ ( sK5_SY21 @ SV8 @ SV14 ) )
= $false )
| ( ( rel_s5 @ SV8 @ SV14 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV12: $i,SV18: $i] :
( ( ( ! [SY25: $i] :
( ~ ( rel_s5 @ SV18 @ SY25 )
| ( p @ SY25 ) ) )
= $false )
| ( ( rel_s5 @ SV12 @ SV18 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(130,plain,
! [SV17: $i] :
( ( ( ! [SY23: $i] :
( ~ ( rel_s5 @ SV17 @ SY23 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY23 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(131,plain,
! [SV13: $i,SV19: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV19 ) )
= $true )
| ( ( p @ SV19 )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV13: $i,SV20: $i] :
( ( ( ~ ( rel_s5 @ sK1_SX0 @ SV20 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
( ~ ( rel_s5 @ SV20 @ SY26 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY26 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV10: $i,SV15: $i] :
( ( ( ~ ( rel_s5 @ SV15 @ ( sK6_SY22 @ SV10 @ SV15 ) ) )
= $false )
| ( ( rel_s5 @ SV10 @ SV15 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(134,plain,
! [SV15: $i,SV10: $i] :
( ( ( p @ ( sK6_SY22 @ SV10 @ SV15 ) )
= $false )
| ( ( rel_s5 @ SV10 @ SV15 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(135,plain,
! [SV8: $i,SV14: $i] :
( ( ( rel_s5 @ SV14 @ ( sK5_SY21 @ SV8 @ SV14 ) )
= $true )
| ( ( rel_s5 @ SV8 @ SV14 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV8 )
= $false )
| ( ( p @ sK2_SY7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(136,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( rel_s5 @ SV18 @ ( sK7_SY25 @ SV12 @ SV18 ) )
| ( p @ ( sK7_SY25 @ SV12 @ SV18 ) ) )
= $false )
| ( ( rel_s5 @ SV12 @ SV18 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(137,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ( rel_s5 @ SV17 @ SV21 )
| ~ ! [SY28: $i] :
( ~ ( rel_s5 @ SV21 @ SY28 )
| ( p @ SY28 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV13: $i,SV19: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV19 )
= $false )
| ( ( p @ SV19 )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV13: $i,SV20: $i] :
( ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( ~ ~ ! [SY26: $i] :
( ~ ( rel_s5 @ SV20 @ SY26 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY26 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV10: $i,SV15: $i] :
( ( ( rel_s5 @ SV15 @ ( sK6_SY22 @ SV10 @ SV15 ) )
= $true )
| ( ( rel_s5 @ SV10 @ SV15 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV10 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK2_SY7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(141,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( rel_s5 @ SV18 @ ( sK7_SY25 @ SV12 @ SV18 ) ) )
= $false )
| ( ( rel_s5 @ SV12 @ SV18 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(142,plain,
! [SV18: $i,SV12: $i] :
( ( ( p @ ( sK7_SY25 @ SV12 @ SV18 ) )
= $false )
| ( ( rel_s5 @ SV12 @ SV18 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(143,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ( rel_s5 @ SV17 @ SV21 ) )
= $true )
| ( ( ~ ! [SY28: $i] :
( ~ ( rel_s5 @ SV21 @ SY28 )
| ( p @ SY28 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(144,plain,
! [SV13: $i,SV20: $i] :
( ( ( ~ ! [SY26: $i] :
( ~ ( rel_s5 @ SV20 @ SY26 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY26 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(145,plain,
! [SV12: $i,SV18: $i] :
( ( ( rel_s5 @ SV18 @ ( sK7_SY25 @ SV12 @ SV18 ) )
= $true )
| ( ( rel_s5 @ SV12 @ SV18 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV12 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ sK3_SY4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(146,plain,
! [SV21: $i,SV17: $i] :
( ( ( rel_s5 @ SV17 @ SV21 )
= $false )
| ( ( ~ ! [SY28: $i] :
( ~ ( rel_s5 @ SV21 @ SY28 )
| ( p @ SY28 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(147,plain,
! [SV13: $i,SV20: $i] :
( ( ( ! [SY26: $i] :
( ~ ( rel_s5 @ SV20 @ SY26 )
| ~ ! [SX3: $i] :
( ~ ( rel_s5 @ SY26 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(148,plain,
! [SV17: $i,SV21: $i] :
( ( ( ! [SY28: $i] :
( ~ ( rel_s5 @ SV21 @ SY28 )
| ( p @ SY28 ) ) )
= $false )
| ( ( rel_s5 @ SV17 @ SV21 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(149,plain,
! [SV13: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( rel_s5 @ SV20 @ SV22 )
| ~ ! [SY29: $i] :
( ~ ( rel_s5 @ SV22 @ SY29 )
| ( p @ SY29 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(150,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( rel_s5 @ SV21 @ ( sK8_SY28 @ SV17 @ SV21 ) )
| ( p @ ( sK8_SY28 @ SV17 @ SV21 ) ) )
= $false )
| ( ( rel_s5 @ SV17 @ SV21 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[148]) ).
thf(151,plain,
! [SV13: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( rel_s5 @ SV20 @ SV22 ) )
= $true )
| ( ( ~ ! [SY29: $i] :
( ~ ( rel_s5 @ SV22 @ SY29 )
| ( p @ SY29 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(152,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( rel_s5 @ SV21 @ ( sK8_SY28 @ SV17 @ SV21 ) ) )
= $false )
| ( ( rel_s5 @ SV17 @ SV21 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(153,plain,
! [SV21: $i,SV17: $i] :
( ( ( p @ ( sK8_SY28 @ SV17 @ SV21 ) )
= $false )
| ( ( rel_s5 @ SV17 @ SV21 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(154,plain,
! [SV13: $i,SV22: $i,SV20: $i] :
( ( ( rel_s5 @ SV20 @ SV22 )
= $false )
| ( ( ~ ! [SY29: $i] :
( ~ ( rel_s5 @ SV22 @ SY29 )
| ( p @ SY29 ) ) )
= $true )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(155,plain,
! [SV17: $i,SV21: $i] :
( ( ( rel_s5 @ SV21 @ ( sK8_SY28 @ SV17 @ SV21 ) )
= $true )
| ( ( rel_s5 @ SV17 @ SV21 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV17 )
= $false )
| ( ( rel_s5 @ sK3_SY4 @ sK4_SY12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(156,plain,
! [SV13: $i,SV20: $i,SV22: $i] :
( ( ( ! [SY29: $i] :
( ~ ( rel_s5 @ SV22 @ SY29 )
| ( p @ SY29 ) ) )
= $false )
| ( ( rel_s5 @ SV20 @ SV22 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(157,plain,
! [SV20: $i,SV13: $i,SV22: $i] :
( ( ( ~ ( rel_s5 @ SV22 @ ( sK9_SY29 @ SV13 @ SV20 @ SV22 ) )
| ( p @ ( sK9_SY29 @ SV13 @ SV20 @ SV22 ) ) )
= $false )
| ( ( rel_s5 @ SV20 @ SV22 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[156]) ).
thf(158,plain,
! [SV20: $i,SV13: $i,SV22: $i] :
( ( ( ~ ( rel_s5 @ SV22 @ ( sK9_SY29 @ SV13 @ SV20 @ SV22 ) ) )
= $false )
| ( ( rel_s5 @ SV20 @ SV22 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(159,plain,
! [SV22: $i,SV20: $i,SV13: $i] :
( ( ( p @ ( sK9_SY29 @ SV13 @ SV20 @ SV22 ) )
= $false )
| ( ( rel_s5 @ SV20 @ SV22 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(160,plain,
! [SV20: $i,SV13: $i,SV22: $i] :
( ( ( rel_s5 @ SV22 @ ( sK9_SY29 @ SV13 @ SV20 @ SV22 ) )
= $true )
| ( ( rel_s5 @ SV20 @ SV22 )
= $false )
| ( ( rel_s5 @ sK1_SX0 @ SV20 )
= $false )
| ( ( p @ SV13 )
= $true )
| ( ( rel_s5 @ sK4_SY12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(161,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,160,159,155,153,145,142,140,138,135,134,128,116,89,80,74,40,26]) ).
thf(162,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO470^6 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Fri Jul 8 18:34:20 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33
% 0.12/0.33 No.of.Axioms: 3
% 0.12/0.33
% 0.12/0.33 Length.of.Defs: 5645
% 0.12/0.33
% 0.12/0.33 Contains.Choice.Funs: false
% 0.12/0.33 (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 0.17/0.46
% 0.17/0.46 ********************************
% 0.17/0.46 * All subproblems solved! *
% 0.17/0.46 ********************************
% 0.17/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:161,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.47
% 0.17/0.47 %**** Beginning of derivation protocol ****
% 0.17/0.47 % SZS output start CNFRefutation
% See solution above
% 0.17/0.47
% 0.17/0.47 %**** End of derivation protocol ****
% 0.17/0.47 %**** no. of clauses in derivation: 162 ****
% 0.17/0.47 %**** clause counter: 161 ****
% 0.17/0.47
% 0.17/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:161,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------