%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO404^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:08:14 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 34
% Syntax : Number of formulae : 242 ( 40 unt; 0 typ; 33 def)
% Number of atoms : 2900 ( 788 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 3972 ( 895 ~;1070 |; 8 &;1991 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 12 con; 0-3 aty)
% Number of variables : 408 ( 52 ^; 350 !; 6 ?; 408 :)
% 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_k,type,
mbox_k: ( $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_k,type,
mdia_k: ( $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_q,type,
q: $i > $o ).
thf(tp_rel_k,type,
rel_k: $i > $i > $o ).
thf(tp_sK10_SY102,type,
sK10_SY102: $i ).
thf(tp_sK11_SY101,type,
sK11_SY101: $i > $i ).
thf(tp_sK12_SY101,type,
sK12_SY101: $i > $i ).
thf(tp_sK13_SY102,type,
sK13_SY102: $i > $i ).
thf(tp_sK14_SY102,type,
sK14_SY102: $i > $i ).
thf(tp_sK15_SY102,type,
sK15_SY102: $i > $i ).
thf(tp_sK16_SY102,type,
sK16_SY102: $i > $i ).
thf(tp_sK17_SY102,type,
sK17_SY102: $i > $i ).
thf(tp_sK18_SY102,type,
sK18_SY102: $i > $i ).
thf(tp_sK1_SY83,type,
sK1_SY83: $i ).
thf(tp_sK2_SY99,type,
sK2_SY99: $i ).
thf(tp_sK3_SY101,type,
sK3_SY101: $i ).
thf(tp_sK4_SY101,type,
sK4_SY101: $i ).
thf(tp_sK5_SY102,type,
sK5_SY102: $i ).
thf(tp_sK6_SY102,type,
sK6_SY102: $i ).
thf(tp_sK7_SY102,type,
sK7_SY102: $i ).
thf(tp_sK8_SY102,type,
sK8_SY102: $i ).
thf(tp_sK9_SY102,type,
sK9_SY102: $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(mbox_k,definition,
( mbox_k
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_k @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k) ).
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(mdia_k,definition,
( mdia_k
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_k) ).
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,conjecture,
mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
( ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY83: $i] :
~ ( ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( rel_k @ SY83 @ SY84 )
| ~ ( q @ SY84 )
| ( p @ SY84 ) )
| ~ ! [SY85: $i] :
( ~ ( rel_k @ SY83 @ SY85 )
| ~ ~ ( q @ SY85 )
| ( p @ SY85 ) ) )
| ! [SY86: $i] :
( ~ ( rel_k @ SY83 @ SY86 )
| ( p @ SY86 ) ) )
| ~ ( ~ ! [SY87: $i] :
( ~ ( rel_k @ SY83 @ SY87 )
| ( p @ SY87 ) )
| ~ ( ~ ! [SY88: $i] :
( ~ ( rel_k @ SY83 @ SY88 )
| ~ ( q @ SY88 )
| ( p @ SY88 ) )
| ~ ! [SY89: $i] :
( ~ ( rel_k @ SY83 @ SY89 )
| ~ ~ ( q @ SY89 )
| ( p @ SY89 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mbox_k,mcountersatisfiable,mdia,mdia_k,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(4,plain,
( ( ~ ( ~ ( ~ ~ ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
| ! [SY99: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY99 )
| ( p @ SY99 ) ) )
| ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ~ ( ~ ~ ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
| ! [SY99: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY99 )
| ( p @ SY99 ) ) )
| ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( ~ ~ ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
| ! [SY99: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY99 )
| ( p @ SY99 ) ) )
| ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ( ~ ( ~ ~ ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
| ! [SY99: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY99 )
| ( p @ SY99 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ~ ~ ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
| ! [SY99: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY99 )
| ( p @ SY99 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ~ ~ ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ! [SY99: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY99 )
| ( p @ SY99 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ( ~ ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK2_SY99 )
| ( p @ sK2_SY99 ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(13,plain,
( ( ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) )
| ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK2_SY99 ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ( p @ sK2_SY99 )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(16,plain,
( ( ( ~ ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ( ~ ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(18,plain,
( ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ( ! [SY97: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY97 )
| ~ ( q @ SY97 )
| ( p @ SY97 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ( ! [SY98: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY98 )
| ~ ~ ( q @ SY98 )
| ( p @ SY98 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV1 )
| ~ ( q @ SV1 )
| ( p @ SV1 ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV2 )
| ~ ~ ( q @ SV2 )
| ( p @ SV2 ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
( ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(29,plain,
( ( ( ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(30,plain,
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV1 ) )
= $true )
| ( ( ~ ( q @ SV1 )
| ( p @ SV1 ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV2 ) )
= $true )
| ( ( ~ ~ ( q @ SV2 )
| ( p @ SV2 ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(33,plain,
( ( ( ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV3 )
| ( p @ SV3 ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( ~ ( q @ SV1 )
| ( p @ SV1 ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( ~ ~ ( q @ SV2 )
| ( p @ SV2 ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV4 )
| ( p @ SV4 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV3 ) )
= $true )
| ( ( p @ SV3 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( ( ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV1: $i] :
( ( ( ~ ( q @ SV1 ) )
= $true )
| ( ( p @ SV1 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( ~ ~ ( q @ SV2 ) )
= $true )
| ( ( p @ SV2 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV4: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV4 ) )
= $true )
| ( ( p @ SV4 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ( ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV3: $i] :
( ( ( rel_k @ sK1_SY83 @ SV3 )
= $false )
| ( ( p @ SV3 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(48,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK3_SY101 )
| ~ ( q @ sK3_SY101 )
| ( p @ sK3_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(49,plain,
! [SV1: $i] :
( ( ( q @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( ~ ( q @ SV2 ) )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV4: $i] :
( ( ( rel_k @ sK1_SY83 @ SV4 )
= $false )
| ( ( p @ SV4 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(52,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK4_SY101 )
| ~ ( q @ sK4_SY101 )
| ( p @ sK4_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(53,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK3_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
( ( ( ~ ( q @ sK3_SY101 )
| ( p @ sK3_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV1: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( q @ SV2 )
= $true )
| ( ( p @ SV2 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( ~ ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(57,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK4_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(58,plain,
( ( ( ~ ( q @ sK4_SY101 )
| ( p @ sK4_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(59,plain,
( ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
( ( ( ~ ( q @ sK3_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(61,plain,
( ( ( p @ sK3_SY101 )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(62,plain,
! [SV1: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(63,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) )
| ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(65,plain,
( ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(66,plain,
( ( ( ~ ( q @ sK4_SY101 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(67,plain,
( ( ( p @ sK4_SY101 )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(68,plain,
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
( ( ( q @ sK3_SY101 )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(70,plain,
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV1: $i] :
( ( ( ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(72,plain,
! [SV1: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(73,plain,
! [SV2: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(74,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(75,plain,
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(76,plain,
( ( ( q @ sK4_SY101 )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(77,plain,
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(78,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK5_SY102 )
| ~ ~ ( q @ sK5_SY102 )
| ( p @ sK5_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(79,plain,
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(80,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK6_SY102 )
| ~ ~ ( q @ sK6_SY102 )
| ( p @ sK6_SY102 ) )
= $false )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(81,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV5 )
| ( p @ SV5 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV1: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV2: $i] :
( ( ( ! [SY100: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY100 )
| ( p @ SY100 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(84,plain,
! [SV2: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(85,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK7_SY102 )
| ~ ~ ( q @ sK7_SY102 )
| ( p @ sK7_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(86,plain,
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(87,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK8_SY102 )
| ~ ~ ( q @ sK8_SY102 )
| ( p @ sK8_SY102 ) )
= $false )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(88,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK5_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(89,plain,
( ( ( ~ ~ ( q @ sK5_SY102 )
| ( p @ sK5_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(90,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK9_SY102 )
| ~ ~ ( q @ sK9_SY102 )
| ( p @ sK9_SY102 ) )
= $false )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(91,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK6_SY102 ) )
= $false )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(92,plain,
( ( ( ~ ~ ( q @ sK6_SY102 )
| ( p @ sK6_SY102 ) )
= $false )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(93,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV5 ) )
= $true )
| ( ( p @ SV5 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV1: $i] :
( ( ( ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV6 )
| ( p @ SV6 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV2: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(97,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK7_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(98,plain,
( ( ( ~ ~ ( q @ sK7_SY102 )
| ( p @ sK7_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(99,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK10_SY102 )
| ~ ~ ( q @ sK10_SY102 )
| ( p @ sK10_SY102 ) )
= $false )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(100,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK8_SY102 ) )
= $false )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(101,plain,
( ( ( ~ ~ ( q @ sK8_SY102 )
| ( p @ sK8_SY102 ) )
= $false )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(102,plain,
( ( ( rel_k @ sK1_SY83 @ sK5_SY102 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(103,plain,
( ( ( ~ ~ ( q @ sK5_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(104,plain,
( ( ( p @ sK5_SY102 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(105,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK9_SY102 ) )
= $false )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(106,plain,
( ( ( ~ ~ ( q @ sK9_SY102 )
| ( p @ sK9_SY102 ) )
= $false )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(107,plain,
( ( ( rel_k @ sK1_SY83 @ sK6_SY102 )
= $true )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(108,plain,
( ( ( ~ ~ ( q @ sK6_SY102 ) )
= $false )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(109,plain,
( ( ( p @ sK6_SY102 )
= $false )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(110,plain,
! [SV1: $i,SV5: $i] :
( ( ( rel_k @ sK1_SY83 @ SV5 )
= $false )
| ( ( p @ SV5 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(111,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
| ~ ( q @ ( sK11_SY101 @ SV1 ) )
| ( p @ ( sK11_SY101 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[94]) ).
thf(112,plain,
! [SV2: $i,SV6: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ SV6 ) )
= $true )
| ( ( p @ SV6 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(113,plain,
! [SV2: $i] :
( ( ( ! [SY101: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY101 )
| ~ ( q @ SY101 )
| ( p @ SY101 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(114,plain,
( ( ( rel_k @ sK1_SY83 @ sK7_SY102 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(115,plain,
( ( ( ~ ~ ( q @ sK7_SY102 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(116,plain,
( ( ( p @ sK7_SY102 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(117,plain,
( ( ( ~ ( rel_k @ sK1_SY83 @ sK10_SY102 ) )
= $false )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(118,plain,
( ( ( ~ ~ ( q @ sK10_SY102 )
| ( p @ sK10_SY102 ) )
= $false )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(119,plain,
( ( ( rel_k @ sK1_SY83 @ sK8_SY102 )
= $true )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(120,plain,
( ( ( ~ ~ ( q @ sK8_SY102 ) )
= $false )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(121,plain,
( ( ( p @ sK8_SY102 )
= $false )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(122,plain,
( ( ( ~ ( q @ sK5_SY102 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(123,plain,
( ( ( rel_k @ sK1_SY83 @ sK9_SY102 )
= $true )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(124,plain,
( ( ( ~ ~ ( q @ sK9_SY102 ) )
= $false )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(125,plain,
( ( ( p @ sK9_SY102 )
= $false )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(126,plain,
( ( ( ~ ( q @ sK6_SY102 ) )
= $true )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(127,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(128,plain,
! [SV1: $i] :
( ( ( ~ ( q @ ( sK11_SY101 @ SV1 ) )
| ( p @ ( sK11_SY101 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(129,plain,
! [SV2: $i,SV6: $i] :
( ( ( rel_k @ sK1_SY83 @ SV6 )
= $false )
| ( ( p @ SV6 )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(130,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
| ~ ( q @ ( sK12_SY101 @ SV2 ) )
| ( p @ ( sK12_SY101 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[113]) ).
thf(131,plain,
( ( ( ~ ( q @ sK7_SY102 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(132,plain,
( ( ( rel_k @ sK1_SY83 @ sK10_SY102 )
= $true )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(133,plain,
( ( ( ~ ~ ( q @ sK10_SY102 ) )
= $false )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(134,plain,
( ( ( p @ sK10_SY102 )
= $false )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(135,plain,
( ( ( ~ ( q @ sK8_SY102 ) )
= $true )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(136,plain,
( ( ( q @ sK5_SY102 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(137,plain,
( ( ( ~ ( q @ sK9_SY102 ) )
= $true )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(138,plain,
( ( ( q @ sK6_SY102 )
= $false )
| ( ( p @ sK3_SY101 )
= $false )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV1: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV1: $i] :
( ( ( ~ ( q @ ( sK11_SY101 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(141,plain,
! [SV1: $i] :
( ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(142,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(143,plain,
! [SV2: $i] :
( ( ( ~ ( q @ ( sK12_SY101 @ SV2 ) )
| ( p @ ( sK12_SY101 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(144,plain,
( ( ( q @ sK7_SY102 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(145,plain,
( ( ( ~ ( q @ sK10_SY102 ) )
= $true )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(146,plain,
( ( ( q @ sK8_SY102 )
= $false )
| ( ( p @ sK4_SY101 )
= $false )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(147,plain,
( ( ( q @ sK9_SY102 )
= $false )
| ( ( q @ sK3_SY101 )
= $true )
| ( ( p @ sK2_SY99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV1: $i] :
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV1: $i] :
( ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(150,plain,
! [SV1: $i] :
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV2: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(152,plain,
! [SV2: $i] :
( ( ( ~ ( q @ ( sK12_SY101 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(153,plain,
! [SV2: $i] :
( ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(154,plain,
( ( ( q @ sK10_SY102 )
= $false )
| ( ( q @ sK4_SY101 )
= $true )
| ( ( rel_k @ sK1_SY83 @ sK2_SY99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK13_SY102 @ SV1 ) )
| ~ ~ ( q @ ( sK13_SY102 @ SV1 ) )
| ( p @ ( sK13_SY102 @ SV1 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[148]) ).
thf(156,plain,
! [SV1: $i] :
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK14_SY102 @ SV1 ) )
| ~ ~ ( q @ ( sK14_SY102 @ SV1 ) )
| ( p @ ( sK14_SY102 @ SV1 ) ) )
= $false )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(158,plain,
! [SV2: $i] :
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV2: $i] :
( ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( ~ ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(160,plain,
! [SV2: $i] :
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK13_SY102 @ SV1 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(162,plain,
! [SV1: $i] :
( ( ( ~ ~ ( q @ ( sK13_SY102 @ SV1 ) )
| ( p @ ( sK13_SY102 @ SV1 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(163,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK15_SY102 @ SV1 ) )
| ~ ~ ( q @ ( sK15_SY102 @ SV1 ) )
| ( p @ ( sK15_SY102 @ SV1 ) ) )
= $false )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[156]) ).
thf(164,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK14_SY102 @ SV1 ) ) )
= $false )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(165,plain,
! [SV1: $i] :
( ( ( ~ ~ ( q @ ( sK14_SY102 @ SV1 ) )
| ( p @ ( sK14_SY102 @ SV1 ) ) )
= $false )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(166,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK16_SY102 @ SV2 ) )
| ~ ~ ( q @ ( sK16_SY102 @ SV2 ) )
| ( p @ ( sK16_SY102 @ SV2 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[158]) ).
thf(167,plain,
! [SV2: $i] :
( ( ( ! [SY102: $i] :
( ~ ( rel_k @ sK1_SY83 @ SY102 )
| ~ ~ ( q @ SY102 )
| ( p @ SY102 ) ) )
= $false )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK17_SY102 @ SV2 ) )
| ~ ~ ( q @ ( sK17_SY102 @ SV2 ) )
| ( p @ ( sK17_SY102 @ SV2 ) ) )
= $false )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[160]) ).
thf(169,plain,
! [SV1: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK13_SY102 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(170,plain,
! [SV1: $i] :
( ( ( ~ ~ ( q @ ( sK13_SY102 @ SV1 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(171,plain,
! [SV1: $i] :
( ( ( p @ ( sK13_SY102 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(172,plain,
! [SV1: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK15_SY102 @ SV1 ) ) )
= $false )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(173,plain,
! [SV1: $i] :
( ( ( ~ ~ ( q @ ( sK15_SY102 @ SV1 ) )
| ( p @ ( sK15_SY102 @ SV1 ) ) )
= $false )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(174,plain,
! [SV1: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK14_SY102 @ SV1 ) )
= $true )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(175,plain,
! [SV1: $i] :
( ( ( ~ ~ ( q @ ( sK14_SY102 @ SV1 ) ) )
= $false )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(176,plain,
! [SV1: $i] :
( ( ( p @ ( sK14_SY102 @ SV1 ) )
= $false )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(177,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK16_SY102 @ SV2 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(178,plain,
! [SV2: $i] :
( ( ( ~ ~ ( q @ ( sK16_SY102 @ SV2 ) )
| ( p @ ( sK16_SY102 @ SV2 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(179,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK18_SY102 @ SV2 ) )
| ~ ~ ( q @ ( sK18_SY102 @ SV2 ) )
| ( p @ ( sK18_SY102 @ SV2 ) ) )
= $false )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[167]) ).
thf(180,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK17_SY102 @ SV2 ) ) )
= $false )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(181,plain,
! [SV2: $i] :
( ( ( ~ ~ ( q @ ( sK17_SY102 @ SV2 ) )
| ( p @ ( sK17_SY102 @ SV2 ) ) )
= $false )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(182,plain,
! [SV1: $i] :
( ( ( ~ ( q @ ( sK13_SY102 @ SV1 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(183,plain,
! [SV1: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK15_SY102 @ SV1 ) )
= $true )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(184,plain,
! [SV1: $i] :
( ( ( ~ ~ ( q @ ( sK15_SY102 @ SV1 ) ) )
= $false )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(185,plain,
! [SV1: $i] :
( ( ( p @ ( sK15_SY102 @ SV1 ) )
= $false )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(186,plain,
! [SV1: $i] :
( ( ( ~ ( q @ ( sK14_SY102 @ SV1 ) ) )
= $true )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(187,plain,
! [SV2: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK16_SY102 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(188,plain,
! [SV2: $i] :
( ( ( ~ ~ ( q @ ( sK16_SY102 @ SV2 ) ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(189,plain,
! [SV2: $i] :
( ( ( p @ ( sK16_SY102 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(190,plain,
! [SV2: $i] :
( ( ( ~ ( rel_k @ sK1_SY83 @ ( sK18_SY102 @ SV2 ) ) )
= $false )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(191,plain,
! [SV2: $i] :
( ( ( ~ ~ ( q @ ( sK18_SY102 @ SV2 ) )
| ( p @ ( sK18_SY102 @ SV2 ) ) )
= $false )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(192,plain,
! [SV2: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK17_SY102 @ SV2 ) )
= $true )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(193,plain,
! [SV2: $i] :
( ( ( ~ ~ ( q @ ( sK17_SY102 @ SV2 ) ) )
= $false )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(194,plain,
! [SV2: $i] :
( ( ( p @ ( sK17_SY102 @ SV2 ) )
= $false )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(195,plain,
! [SV1: $i] :
( ( ( q @ ( sK13_SY102 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(196,plain,
! [SV1: $i] :
( ( ( ~ ( q @ ( sK15_SY102 @ SV1 ) ) )
= $true )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(197,plain,
! [SV1: $i] :
( ( ( q @ ( sK14_SY102 @ SV1 ) )
= $false )
| ( ( p @ ( sK11_SY101 @ SV1 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV2: $i] :
( ( ( ~ ( q @ ( sK16_SY102 @ SV2 ) ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(199,plain,
! [SV2: $i] :
( ( ( rel_k @ sK1_SY83 @ ( sK18_SY102 @ SV2 ) )
= $true )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(200,plain,
! [SV2: $i] :
( ( ( ~ ~ ( q @ ( sK18_SY102 @ SV2 ) ) )
= $false )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(201,plain,
! [SV2: $i] :
( ( ( p @ ( sK18_SY102 @ SV2 ) )
= $false )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(202,plain,
! [SV2: $i] :
( ( ( ~ ( q @ ( sK17_SY102 @ SV2 ) ) )
= $true )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(203,plain,
! [SV1: $i] :
( ( ( q @ ( sK15_SY102 @ SV1 ) )
= $false )
| ( ( q @ ( sK11_SY101 @ SV1 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV1 )
= $false )
| ( ( p @ SV1 )
= $true )
| ( ( q @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(204,plain,
! [SV2: $i] :
( ( ( q @ ( sK16_SY102 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV2: $i] :
( ( ( ~ ( q @ ( sK18_SY102 @ SV2 ) ) )
= $true )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(206,plain,
! [SV2: $i] :
( ( ( q @ ( sK17_SY102 @ SV2 ) )
= $false )
| ( ( p @ ( sK12_SY101 @ SV2 ) )
= $false )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(207,plain,
! [SV2: $i] :
( ( ( q @ ( sK18_SY102 @ SV2 ) )
= $false )
| ( ( q @ ( sK12_SY101 @ SV2 ) )
= $true )
| ( ( rel_k @ sK1_SY83 @ SV2 )
= $false )
| ( ( p @ SV2 )
= $true )
| ( ( q @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(208,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,207,206,204,203,201,199,197,195,194,192,189,187,185,183,176,174,171,169,154,147,146,144,138,136,134,132,129,125,123,121,119,116,114,110,109,107,104,102,51]) ).
thf(209,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO404^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n026.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 17:42:02 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
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% 0.10/0.26 No.of.Axioms: 0
% 0.10/0.26
% 0.10/0.26 Length.of.Defs: 5604
% 0.10/0.26
% 0.10/0.26 Contains.Choice.Funs: false
% 0.10/0.26 .....
% 0.10/0.26
% 0.10/0.26 ********************************
% 0.10/0.26 * All subproblems solved! *
% 0.10/0.26 ********************************
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:208,loop_count:0,foatp_calls:1,translation:fof_full)
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% 0.10/0.26 %**** Beginning of derivation protocol ****
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26
% 0.10/0.26 %**** End of derivation protocol ****
% 0.10/0.26 %**** no. of clauses in derivation: 209 ****
% 0.10/0.26 %**** clause counter: 208 ****
% 0.10/0.26
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:208,loop_count:0,foatp_calls:1,translation:fof_full)
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