%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV425^2 : TPTP v9.3.1. Released v3.6.0.
% 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 : n019.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 10:57:42 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 27
% Syntax : Number of formulae : 90 ( 61 unt; 0 typ; 24 def)
% Number of atoms : 460 ( 126 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 698 ( 92 ~; 126 |; 2 &; 448 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 7 con; 0-3 aty)
% Number of variables : 214 ( 39 ^; 171 !; 4 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_individuals,type,
individuals: $tType ).
thf(tp_a,type,
a: $i > $o ).
thf(tp_current_world,type,
current_world: $i ).
thf(tp_icl_and,type,
icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_icl_atom,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(tp_icl_false,type,
icl_false: $i > $o ).
thf(tp_icl_impl,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_icl_or,type,
icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_icl_princ,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(tp_icl_says,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_icl_true,type,
icl_true: $i > $o ).
thf(tp_iclval,type,
iclval: ( $i > $o ) > $o ).
thf(tp_mall,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mexists,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_miff,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimpl,type,
mimpl: ( $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_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_prop_a,type,
prop_a: $i > $o ).
thf(tp_prop_b,type,
prop_b: $i > $o ).
thf(tp_prop_c,type,
prop_c: $i > $o ).
thf(tp_rel,type,
rel: $i > $i > $o ).
thf(tp_s,type,
s: $i > $o ).
thf(tp_sK1_SY44,type,
sK1_SY44: $i ).
thf(tp_sK2_SY113,type,
sK2_SY113: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY126,type,
sK4_SY126: ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY129,type,
sK5_SY129: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY130,type,
sK6_SY130: $i ).
thf(icl_and,definition,
( icl_and
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_and) ).
thf(icl_atom,definition,
( icl_atom
= ( ^ [P: $i > $o] : ( mbox @ rel @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_atom) ).
thf(icl_false,definition,
icl_false = mfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_false) ).
thf(icl_impl,definition,
( icl_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_impl) ).
thf(icl_or,definition,
( icl_or
= ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_or) ).
thf(icl_princ,definition,
( icl_princ
= ( ^ [P: $i > $o] : P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_princ) ).
thf(icl_says,definition,
( icl_says
= ( ^ [A: $i > $o,S: $i > $o] : ( mbox @ rel @ ( mor @ A @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_says) ).
thf(icl_true,definition,
icl_true = mtrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_true) ).
thf(iclval,definition,
( iclval
= ( ^ [X: $i > $o] : ( mvalid @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',icl_s4_valid) ).
thf(mall,definition,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mall) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
? [Y: $i] :
( ( R @ X @ Y )
& ( P @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',individuals_decl) ).
thf(mexists,definition,
( mexists
= ( ^ [P: individuals > $i > $o,W: $i] :
? [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists) ).
thf(mfalse,definition,
( mfalse
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(miff,definition,
( miff
= ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',miff) ).
thf(mimpl,definition,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimpl) ).
thf(minvalid,definition,
( minvalid
= ( ^ [P: $i > $o] :
! [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mtrue,definition,
( mtrue
= ( ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(1,axiom,
! [B: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ B ) @ ( mbox @ rel @ ( mbox @ rel @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).
thf(2,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).
thf(3,conjecture,
iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unit) ).
thf(4,negated_conjecture,
( ( iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [SY44: $i,SY45: $i] :
( ( rel @ SY44 @ SY45 )
=> ( ~ ! [SY21: $i] :
( ( rel @ SY45 @ SY21 )
=> ( s @ SY21 ) )
| ! [SY42: $i] :
( ( rel @ SY45 @ SY42 )
=> ( ( a @ SY42 )
| ! [SY38: $i] :
( ( rel @ SY42 @ SY38 )
=> ( s @ SY38 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(6,plain,
( ( ! [SY54: $i > $o,SY83: $i] :
( ~ ! [SY84: $i] :
( ( rel @ SY83 @ SY84 )
=> ( SY54 @ SY84 ) )
| ! [SY85: $i] :
( ( rel @ SY83 @ SY85 )
=> ! [SY78: $i] :
( ( rel @ SY85 @ SY78 )
=> ( SY54 @ SY78 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(7,plain,
( ( ! [SY92: $i > $o,SY108: $i] :
( ~ ! [SY109: $i] :
( ( rel @ SY108 @ SY109 )
=> ( SY92 @ SY109 ) )
| ( SY92 @ SY108 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(8,plain,
( ( ! [SY113: $i] :
( ( rel @ sK1_SY44 @ SY113 )
=> ( ~ ! [SY21: $i] :
( ( rel @ SY113 @ SY21 )
=> ( s @ SY21 ) )
| ! [SY42: $i] :
( ( rel @ SY113 @ SY42 )
=> ( ( a @ SY42 )
| ! [SY38: $i] :
( ( rel @ SY42 @ SY38 )
=> ( s @ SY38 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ( rel @ sK1_SY44 @ sK2_SY113 )
=> ( ~ ! [SY117: $i] :
( ( rel @ sK2_SY113 @ SY117 )
=> ( s @ SY117 ) )
| ! [SY118: $i] :
( ( rel @ sK2_SY113 @ SY118 )
=> ( ( a @ SY118 )
| ! [SY38: $i] :
( ( rel @ SY118 @ SY38 )
=> ( s @ SY38 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( rel @ sK1_SY44 @ sK2_SY113 )
= $true ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ! [SY117: $i] :
( ( rel @ sK2_SY113 @ SY117 )
=> ( s @ SY117 ) )
| ! [SY118: $i] :
( ( rel @ sK2_SY113 @ SY118 )
=> ( ( a @ SY118 )
| ! [SY38: $i] :
( ( rel @ SY118 @ SY38 )
=> ( s @ SY38 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ! [SY117: $i] :
( ( rel @ sK2_SY113 @ SY117 )
=> ( s @ SY117 ) )
| ! [SY118: $i] :
( ( rel @ sK2_SY113 @ SY118 )
=> ( ( a @ SY118 )
| ! [SY38: $i] :
( ( rel @ SY118 @ SY38 )
=> ( s @ SY38 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY92: $i > $o,SY108: $i] :
( ~ ! [SY109: $i] :
( ( rel @ SY108 @ SY109 )
=> ( SY92 @ SY109 ) )
| ( SY92 @ SY108 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ! [SY54: $i > $o,SY83: $i] :
( ~ ! [SY84: $i] :
( ( rel @ SY83 @ SY84 )
=> ( SY54 @ SY84 ) )
| ! [SY85: $i] :
( ( rel @ SY83 @ SY85 )
=> ! [SY78: $i] :
( ( rel @ SY85 @ SY78 )
=> ( SY54 @ SY78 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( rel @ sK1_SY44 @ sK2_SY113 )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ~ ( ~ ! [SY117: $i] :
( ( rel @ sK2_SY113 @ SY117 )
=> ( s @ SY117 ) )
| ! [SY118: $i] :
( ( rel @ sK2_SY113 @ SY118 )
=> ( ( a @ SY118 )
| ! [SY38: $i] :
( ( rel @ SY118 @ SY38 )
=> ( s @ SY38 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( rel @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( rel @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( rel @ SX2 @ SX3 )
| ( SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel @ sK2_SY113 @ SX0 )
| ( s @ SX0 ) )
| ! [SX0: $i] :
( ~ ( rel @ sK2_SY113 @ SX0 )
| ( a @ SX0 )
| ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ( s @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(19,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( rel @ SX1 @ SX2 )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,icl_and,icl_atom,icl_false,icl_impl,icl_or,icl_princ,icl_says,icl_true,iclval,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(20,plain,
! [SV1: $i > $o] :
( ( ! [SY120: $i] :
( ~ ! [SY121: $i] :
( ~ ( rel @ SY120 @ SY121 )
| ( SV1 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( rel @ SY120 @ SY122 )
| ! [SY123: $i] :
( ~ ( rel @ SY122 @ SY123 )
| ( SV1 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel @ sK2_SY113 @ SX0 )
| ( s @ SX0 ) )
| ! [SX0: $i] :
( ~ ( rel @ sK2_SY113 @ SX0 )
| ( a @ SX0 )
| ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ( s @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i > $o] :
( ( ! [SY124: $i] :
( ~ ! [SY125: $i] :
( ~ ( rel @ SY124 @ SY125 )
| ( SV2 @ SY125 ) )
| ( SV2 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ~ ! [SY126: $i] :
( ~ ( rel @ SV3 @ SY126 )
| ( SV1 @ SY126 ) )
| ! [SY127: $i] :
( ~ ( rel @ SV3 @ SY127 )
| ! [SY123: $i] :
( ~ ( rel @ SY127 @ SY123 )
| ( SV1 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel @ sK2_SY113 @ SX0 )
| ( s @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ~ ( rel @ sK2_SY113 @ SX0 )
| ( a @ SX0 )
| ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ( s @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ~ ! [SY129: $i] :
( ~ ( rel @ SV4 @ SY129 )
| ( SV2 @ SY129 ) )
| ( SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ! [SY126: $i] :
( ~ ( rel @ SV3 @ SY126 )
| ( SV1 @ SY126 ) ) )
= $true )
| ( ( ! [SY127: $i] :
( ~ ( rel @ SV3 @ SY127 )
| ! [SY123: $i] :
( ~ ( rel @ SY127 @ SY123 )
| ( SV1 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [SX0: $i] :
( ~ ( rel @ sK2_SY113 @ SX0 )
| ( s @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( rel @ sK2_SY113 @ sK3_SX0 )
| ( a @ sK3_SX0 )
| ! [SY130: $i] :
( ~ ( rel @ sK3_SX0 @ SY130 )
| ( s @ SY130 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(30,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ~ ! [SY129: $i] :
( ~ ( rel @ SV4 @ SY129 )
| ( SV2 @ SY129 ) ) )
= $true )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ! [SY126: $i] :
( ~ ( rel @ SV3 @ SY126 )
| ( SV1 @ SY126 ) ) )
= $false )
| ( ( ! [SY127: $i] :
( ~ ( rel @ SV3 @ SY127 )
| ! [SY123: $i] :
( ~ ( rel @ SY127 @ SY123 )
| ( SV1 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV5: $i] :
( ( ~ ( rel @ sK2_SY113 @ SV5 )
| ( s @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( rel @ sK2_SY113 @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ( a @ sK3_SX0 )
| ! [SY130: $i] :
( ~ ( rel @ sK3_SX0 @ SY130 )
| ( s @ SY130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ! [SY129: $i] :
( ~ ( rel @ SV4 @ SY129 )
| ( SV2 @ SY129 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
| ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) ) )
= $false )
| ( ( ! [SY127: $i] :
( ~ ( rel @ SV3 @ SY127 )
| ! [SY123: $i] :
( ~ ( rel @ SY127 @ SY123 )
| ( SV1 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(37,plain,
! [SV5: $i] :
( ( ( ~ ( rel @ sK2_SY113 @ SV5 ) )
= $true )
| ( ( s @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( rel @ sK2_SY113 @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(39,plain,
( ( a @ sK3_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [SY130: $i] :
( ~ ( rel @ sK3_SX0 @ SY130 )
| ( s @ SY130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ ( sK5_SY129 @ SV2 @ SV4 ) )
| ( SV2 @ ( sK5_SY129 @ SV2 @ SV4 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(42,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) ) )
= $false )
| ( ( ! [SY127: $i] :
( ~ ( rel @ SV3 @ SY127 )
| ! [SY123: $i] :
( ~ ( rel @ SY127 @ SY123 )
| ( SV1 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $false )
| ( ( ! [SY127: $i] :
( ~ ( rel @ SV3 @ SY127 )
| ! [SY123: $i] :
( ~ ( rel @ SY127 @ SY123 )
| ( SV1 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(44,plain,
! [SV5: $i] :
( ( ( rel @ sK2_SY113 @ SV5 )
= $false )
| ( ( s @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(45,plain,
( ( ~ ( rel @ sK3_SX0 @ sK6_SY130 )
| ( s @ sK6_SY130 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(46,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ ( sK5_SY129 @ SV2 @ SV4 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK5_SY129 @ SV2 @ SV4 ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(48,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $true )
| ( ( ! [SY127: $i] :
( ~ ( rel @ SV3 @ SY127 )
| ! [SY123: $i] :
( ~ ( rel @ SY127 @ SY123 )
| ( SV1 @ SY123 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(49,plain,
! [SV1: $i > $o,SV6: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV6 )
| ! [SY131: $i] :
( ~ ( rel @ SV6 @ SY131 )
| ( SV1 @ SY131 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( ~ ( rel @ sK3_SX0 @ sK6_SY130 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
( ( s @ sK6_SY130 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( rel @ SV4 @ ( sK5_SY129 @ SV2 @ SV4 ) )
= $true )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV1: $i > $o,SV7: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV7 )
| ! [SY132: $i] :
( ~ ( rel @ SV7 @ SY132 )
| ( SV1 @ SY132 ) ) )
= $true )
| ( ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV1: $i > $o,SV6: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY131: $i] :
( ~ ( rel @ SV6 @ SY131 )
| ( SV1 @ SY131 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
( ( rel @ sK3_SX0 @ sK6_SY130 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV1: $i > $o,SV7: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV7 ) )
= $true )
| ( ( ! [SY132: $i] :
( ~ ( rel @ SV7 @ SY132 )
| ( SV1 @ SY132 ) ) )
= $true )
| ( ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV1: $i > $o,SV6: $i,SV3: $i] :
( ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( ! [SY131: $i] :
( ~ ( rel @ SV6 @ SY131 )
| ( SV1 @ SY131 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV1: $i > $o,SV7: $i,SV3: $i] :
( ( ( rel @ SV3 @ SV7 )
= $false )
| ( ( ! [SY132: $i] :
( ~ ( rel @ SV7 @ SY132 )
| ( SV1 @ SY132 ) ) )
= $true )
| ( ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV3: $i,SV1: $i > $o,SV8: $i,SV6: $i] :
( ( ( ~ ( rel @ SV6 @ SV8 )
| ( SV1 @ SV8 ) )
= $true )
| ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV3: $i,SV1: $i > $o,SV9: $i,SV7: $i] :
( ( ( ~ ( rel @ SV7 @ SV9 )
| ( SV1 @ SV9 ) )
= $true )
| ( ( rel @ SV3 @ SV7 )
= $false )
| ( ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV3: $i,SV1: $i > $o,SV8: $i,SV6: $i] :
( ( ( ~ ( rel @ SV6 @ SV8 ) )
= $true )
| ( ( SV1 @ SV8 )
= $true )
| ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV3: $i,SV1: $i > $o,SV9: $i,SV7: $i] :
( ( ( ~ ( rel @ SV7 @ SV9 ) )
= $true )
| ( ( SV1 @ SV9 )
= $true )
| ( ( rel @ SV3 @ SV7 )
= $false )
| ( ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV3: $i,SV1: $i > $o,SV8: $i,SV6: $i] :
( ( ( rel @ SV6 @ SV8 )
= $false )
| ( ( SV1 @ SV8 )
= $true )
| ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV3: $i,SV1: $i > $o,SV9: $i,SV7: $i] :
( ( ( rel @ SV7 @ SV9 )
= $false )
| ( ( SV1 @ SV9 )
= $true )
| ( ( rel @ SV3 @ SV7 )
= $false )
| ( ( rel @ SV3 @ ( sK4_SY126 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,64,63,55,52,51,47,44,39,38]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV425^2 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 16:30:16 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 2
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 3449
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 ..
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 66 ****
% 0.07/0.23 %**** clause counter: 65 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------