%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV430^2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 10:57:44 AM UTC 2026
% Result : Theorem 0.10s 0.29s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 102 ( 67 unt; 0 typ; 25 def)
% Number of atoms : 603 ( 148 equ; 0 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 952 ( 159 ~; 187 |; 2 &; 568 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 7 con; 0-3 aty)
% Number of variables : 236 ( 41 ^; 191 !; 4 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_individuals,type,
individuals: $tType ).
thf(tp_a,type,
a: $i > $o ).
thf(tp_b,type,
b: $i > $o ).
thf(tp_c,type,
c: $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_impl_princ,type,
icl_impl_princ: ( $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_sK1_SY86,type,
sK1_SY86: $i ).
thf(tp_sK2_SY157,type,
sK2_SY157: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY172,type,
sK4_SY172: ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY175,type,
sK5_SY175: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY177,type,
sK6_SY177: $i ).
thf(icl_and,definition,
( icl_and
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',icl_and) ).
thf(icl_atom,definition,
( icl_atom
= ( ^ [P: $i > $o] : ( mbox @ rel @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',icl_atom) ).
thf(icl_false,definition,
icl_false = mfalse,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',icl_impl) ).
thf(icl_impl_princ,definition,
( icl_impl_princ
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',icl_impl_princ) ).
thf(icl_or,definition,
( icl_or
= ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',icl_or) ).
thf(icl_princ,definition,
( icl_princ
= ( ^ [P: $i > $o] : P ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',icl_says) ).
thf(icl_true,definition,
icl_true = mtrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',icl_true) ).
thf(iclval,definition,
( iclval
= ( ^ [X: $i > $o] : ( mvalid @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',icl_s4_valid) ).
thf(mall,definition,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mall) ).
thf(mand,definition,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',individuals_decl) ).
thf(mexists,definition,
( mexists
= ( ^ [P: individuals > $i > $o,W: $i] :
? [X: individuals] : ( P @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists) ).
thf(mfalse,definition,
( mfalse
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(miff,definition,
( miff
= ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',miff) ).
thf(mimpl,definition,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimpl) ).
thf(minvalid,definition,
( minvalid
= ( ^ [P: $i > $o] :
! [W: $i] :
~ ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [P: $i > $o] :
? [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mtrue,definition,
( mtrue
= ( ^ [X: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(1,axiom,
! [B: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ B ) @ ( mbox @ rel @ ( mbox @ rel @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom) ).
thf(2,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).
thf(3,conjecture,
iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans) ).
thf(4,negated_conjecture,
( ( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ! [SY86: $i,SY87: $i] :
( ( rel @ SY86 @ SY87 )
=> ( ~ ! [SY30: $i] :
( ( rel @ SY87 @ SY30 )
=> ( ~ ( a @ SY30 )
| ( b @ SY30 ) ) )
| ! [SY83: $i] :
( ( rel @ SY87 @ SY83 )
=> ( ~ ! [SY61: $i] :
( ( rel @ SY83 @ SY61 )
=> ( ~ ( b @ SY61 )
| ( c @ SY61 ) ) )
| ! [SY79: $i] :
( ( rel @ SY83 @ SY79 )
=> ( ~ ( a @ SY79 )
| ( c @ SY79 ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4,icl_and,icl_atom,icl_false,icl_impl,icl_impl_princ,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,
( ( ! [SY98: $i > $o,SY127: $i] :
( ~ ! [SY128: $i] :
( ( rel @ SY127 @ SY128 )
=> ( SY98 @ SY128 ) )
| ! [SY129: $i] :
( ( rel @ SY127 @ SY129 )
=> ! [SY122: $i] :
( ( rel @ SY129 @ SY122 )
=> ( SY98 @ SY122 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,icl_and,icl_atom,icl_false,icl_impl,icl_impl_princ,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,
( ( ! [SY136: $i > $o,SY152: $i] :
( ~ ! [SY153: $i] :
( ( rel @ SY152 @ SY153 )
=> ( SY136 @ SY153 ) )
| ( SY136 @ SY152 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,icl_and,icl_atom,icl_false,icl_impl,icl_impl_princ,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,
( ( ! [SY157: $i] :
( ( rel @ sK1_SY86 @ SY157 )
=> ( ~ ! [SY30: $i] :
( ( rel @ SY157 @ SY30 )
=> ( ~ ( a @ SY30 )
| ( b @ SY30 ) ) )
| ! [SY83: $i] :
( ( rel @ SY157 @ SY83 )
=> ( ~ ! [SY61: $i] :
( ( rel @ SY83 @ SY61 )
=> ( ~ ( b @ SY61 )
| ( c @ SY61 ) ) )
| ! [SY79: $i] :
( ( rel @ SY83 @ SY79 )
=> ( ~ ( a @ SY79 )
| ( c @ SY79 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(9,plain,
( ( ( rel @ sK1_SY86 @ sK2_SY157 )
=> ( ~ ! [SY162: $i] :
( ( rel @ sK2_SY157 @ SY162 )
=> ( ~ ( a @ SY162 )
| ( b @ SY162 ) ) )
| ! [SY163: $i] :
( ( rel @ sK2_SY157 @ SY163 )
=> ( ~ ! [SY61: $i] :
( ( rel @ SY163 @ SY61 )
=> ( ~ ( b @ SY61 )
| ( c @ SY61 ) ) )
| ! [SY79: $i] :
( ( rel @ SY163 @ SY79 )
=> ( ~ ( a @ SY79 )
| ( c @ SY79 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(10,plain,
( ( rel @ sK1_SY86 @ sK2_SY157 )
= $true ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ! [SY162: $i] :
( ( rel @ sK2_SY157 @ SY162 )
=> ( ~ ( a @ SY162 )
| ( b @ SY162 ) ) )
| ! [SY163: $i] :
( ( rel @ sK2_SY157 @ SY163 )
=> ( ~ ! [SY61: $i] :
( ( rel @ SY163 @ SY61 )
=> ( ~ ( b @ SY61 )
| ( c @ SY61 ) ) )
| ! [SY79: $i] :
( ( rel @ SY163 @ SY79 )
=> ( ~ ( a @ SY79 )
| ( c @ SY79 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ! [SY162: $i] :
( ( rel @ sK2_SY157 @ SY162 )
=> ( ~ ( a @ SY162 )
| ( b @ SY162 ) ) )
| ! [SY163: $i] :
( ( rel @ sK2_SY157 @ SY163 )
=> ( ~ ! [SY61: $i] :
( ( rel @ SY163 @ SY61 )
=> ( ~ ( b @ SY61 )
| ( c @ SY61 ) ) )
| ! [SY79: $i] :
( ( rel @ SY163 @ SY79 )
=> ( ~ ( a @ SY79 )
| ( c @ SY79 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY136: $i > $o,SY152: $i] :
( ~ ! [SY153: $i] :
( ( rel @ SY152 @ SY153 )
=> ( SY136 @ SY153 ) )
| ( SY136 @ SY152 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ! [SY98: $i > $o,SY127: $i] :
( ~ ! [SY128: $i] :
( ( rel @ SY127 @ SY128 )
=> ( SY98 @ SY128 ) )
| ! [SY129: $i] :
( ( rel @ SY127 @ SY129 )
=> ! [SY122: $i] :
( ( rel @ SY129 @ SY122 )
=> ( SY98 @ SY122 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( rel @ sK1_SY86 @ sK2_SY157 )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ~ ( ~ ! [SY162: $i] :
( ( rel @ sK2_SY157 @ SY162 )
=> ( ~ ( a @ SY162 )
| ( b @ SY162 ) ) )
| ! [SY163: $i] :
( ( rel @ sK2_SY157 @ SY163 )
=> ( ~ ! [SY61: $i] :
( ( rel @ SY163 @ SY61 )
=> ( ~ ( b @ SY61 )
| ( c @ SY61 ) ) )
| ! [SY79: $i] :
( ( rel @ SY163 @ SY79 )
=> ( ~ ( a @ SY79 )
| ( c @ SY79 ) ) ) ) ) ) )
= $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_impl_princ,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_SY157 @ SX0 )
| ~ ( a @ SX0 )
| ( b @ SX0 ) )
| ! [SX0: $i] :
( ~ ( rel @ sK2_SY157 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ~ ( b @ SX1 )
| ( c @ SX1 ) )
| ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ~ ( a @ SX1 )
| ( c @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,icl_and,icl_atom,icl_false,icl_impl,icl_impl_princ,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_impl_princ,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] :
( ( ! [SY166: $i] :
( ~ ! [SY167: $i] :
( ~ ( rel @ SY166 @ SY167 )
| ( SV1 @ SY167 ) )
| ! [SY168: $i] :
( ~ ( rel @ SY166 @ SY168 )
| ! [SY169: $i] :
( ~ ( rel @ SY168 @ SY169 )
| ( SV1 @ SY169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel @ sK2_SY157 @ SX0 )
| ~ ( a @ SX0 )
| ( b @ SX0 ) )
| ! [SX0: $i] :
( ~ ( rel @ sK2_SY157 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ~ ( b @ SX1 )
| ( c @ SX1 ) )
| ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ~ ( a @ SX1 )
| ( c @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i > $o] :
( ( ! [SY170: $i] :
( ~ ! [SY171: $i] :
( ~ ( rel @ SY170 @ SY171 )
| ( SV2 @ SY171 ) )
| ( SV2 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ~ ! [SY172: $i] :
( ~ ( rel @ SV3 @ SY172 )
| ( SV1 @ SY172 ) )
| ! [SY173: $i] :
( ~ ( rel @ SV3 @ SY173 )
| ! [SY169: $i] :
( ~ ( rel @ SY173 @ SY169 )
| ( SV1 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel @ sK2_SY157 @ SX0 )
| ~ ( a @ SX0 )
| ( b @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ~ ( rel @ sK2_SY157 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ~ ( b @ SX1 )
| ( c @ SX1 ) )
| ! [SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ~ ( a @ SX1 )
| ( c @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ~ ! [SY175: $i] :
( ~ ( rel @ SV4 @ SY175 )
| ( SV2 @ SY175 ) )
| ( SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ! [SY172: $i] :
( ~ ( rel @ SV3 @ SY172 )
| ( SV1 @ SY172 ) ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( rel @ SV3 @ SY173 )
| ! [SY169: $i] :
( ~ ( rel @ SY173 @ SY169 )
| ( SV1 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [SX0: $i] :
( ~ ( rel @ sK2_SY157 @ SX0 )
| ~ ( a @ SX0 )
| ( b @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( rel @ sK2_SY157 @ sK3_SX0 )
| ~ ! [SY176: $i] :
( ~ ( rel @ sK3_SX0 @ SY176 )
| ~ ( b @ SY176 )
| ( c @ SY176 ) )
| ! [SY177: $i] :
( ~ ( rel @ sK3_SX0 @ SY177 )
| ~ ( a @ SY177 )
| ( c @ SY177 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(30,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ~ ! [SY175: $i] :
( ~ ( rel @ SV4 @ SY175 )
| ( SV2 @ SY175 ) ) )
= $true )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ! [SY172: $i] :
( ~ ( rel @ SV3 @ SY172 )
| ( SV1 @ SY172 ) ) )
= $false )
| ( ( ! [SY173: $i] :
( ~ ( rel @ SV3 @ SY173 )
| ! [SY169: $i] :
( ~ ( rel @ SY173 @ SY169 )
| ( SV1 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV5: $i] :
( ( ~ ( rel @ sK2_SY157 @ SV5 )
| ~ ( a @ SV5 )
| ( b @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( rel @ sK2_SY157 @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ! [SY176: $i] :
( ~ ( rel @ sK3_SX0 @ SY176 )
| ~ ( b @ SY176 )
| ( c @ SY176 ) )
| ! [SY177: $i] :
( ~ ( rel @ sK3_SX0 @ SY177 )
| ~ ( a @ SY177 )
| ( c @ SY177 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ! [SY175: $i] :
( ~ ( rel @ SV4 @ SY175 )
| ( SV2 @ SY175 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
| ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) ) )
= $false )
| ( ( ! [SY173: $i] :
( ~ ( rel @ SV3 @ SY173 )
| ! [SY169: $i] :
( ~ ( rel @ SY173 @ SY169 )
| ( SV1 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(37,plain,
! [SV5: $i] :
( ( ( ~ ( rel @ sK2_SY157 @ SV5 ) )
= $true )
| ( ( ~ ( a @ SV5 )
| ( b @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( rel @ sK2_SY157 @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ! [SY176: $i] :
( ~ ( rel @ sK3_SX0 @ SY176 )
| ~ ( b @ SY176 )
| ( c @ SY176 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [SY177: $i] :
( ~ ( rel @ sK3_SX0 @ SY177 )
| ~ ( a @ SY177 )
| ( c @ SY177 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ ( sK5_SY175 @ SV2 @ SV4 ) )
| ( SV2 @ ( sK5_SY175 @ SV2 @ SV4 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(42,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) ) )
= $false )
| ( ( ! [SY173: $i] :
( ~ ( rel @ SV3 @ SY173 )
| ! [SY169: $i] :
( ~ ( rel @ SY173 @ SY169 )
| ( SV1 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $false )
| ( ( ! [SY173: $i] :
( ~ ( rel @ SV3 @ SY173 )
| ! [SY169: $i] :
( ~ ( rel @ SY173 @ SY169 )
| ( SV1 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(44,plain,
! [SV5: $i] :
( ( ( rel @ sK2_SY157 @ SV5 )
= $false )
| ( ( ~ ( a @ SV5 )
| ( b @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(45,plain,
( ( ! [SY176: $i] :
( ~ ( rel @ sK3_SX0 @ SY176 )
| ~ ( b @ SY176 )
| ( c @ SY176 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ( rel @ sK3_SX0 @ sK6_SY177 )
| ~ ( a @ sK6_SY177 )
| ( c @ sK6_SY177 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(47,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ ( sK5_SY175 @ SV2 @ SV4 ) ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(48,plain,
! [SV4: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK5_SY175 @ SV2 @ SV4 ) )
= $false )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $true )
| ( ( ! [SY173: $i] :
( ~ ( rel @ SV3 @ SY173 )
| ! [SY169: $i] :
( ~ ( rel @ SY173 @ SY169 )
| ( SV1 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(50,plain,
! [SV1: $i > $o,SV6: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV6 )
| ! [SY178: $i] :
( ~ ( rel @ SV6 @ SY178 )
| ( SV1 @ SY178 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV5: $i] :
( ( ( ~ ( a @ SV5 ) )
= $true )
| ( ( b @ SV5 )
= $true )
| ( ( rel @ sK2_SY157 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV7: $i] :
( ( ~ ( rel @ sK3_SX0 @ SV7 )
| ~ ( b @ SV7 )
| ( c @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
( ( ~ ( rel @ sK3_SX0 @ sK6_SY177 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(54,plain,
( ( ~ ( a @ sK6_SY177 )
| ( c @ sK6_SY177 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(55,plain,
! [SV2: $i > $o,SV4: $i] :
( ( ( rel @ SV4 @ ( sK5_SY175 @ SV2 @ SV4 ) )
= $true )
| ( ( SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(56,plain,
! [SV1: $i > $o,SV8: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV8 )
| ! [SY179: $i] :
( ~ ( rel @ SV8 @ SY179 )
| ( SV1 @ SY179 ) ) )
= $true )
| ( ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV1: $i > $o,SV6: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY178: $i] :
( ~ ( rel @ SV6 @ SY178 )
| ( SV1 @ SY178 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( a @ SV5 )
= $false )
| ( ( b @ SV5 )
= $true )
| ( ( rel @ sK2_SY157 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV7: $i] :
( ( ( ~ ( rel @ sK3_SX0 @ SV7 ) )
= $true )
| ( ( ~ ( b @ SV7 )
| ( c @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(60,plain,
( ( rel @ sK3_SX0 @ sK6_SY177 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(61,plain,
( ( ~ ( a @ sK6_SY177 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(62,plain,
( ( c @ sK6_SY177 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(63,plain,
! [SV1: $i > $o,SV8: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV8 ) )
= $true )
| ( ( ! [SY179: $i] :
( ~ ( rel @ SV8 @ SY179 )
| ( SV1 @ SY179 ) ) )
= $true )
| ( ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV1: $i > $o,SV6: $i,SV3: $i] :
( ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( ! [SY178: $i] :
( ~ ( rel @ SV6 @ SY178 )
| ( SV1 @ SY178 ) ) )
= $true )
| ( ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV7: $i] :
( ( ( rel @ sK3_SX0 @ SV7 )
= $false )
| ( ( ~ ( b @ SV7 )
| ( c @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(66,plain,
( ( a @ sK6_SY177 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(67,plain,
! [SV1: $i > $o,SV8: $i,SV3: $i] :
( ( ( rel @ SV3 @ SV8 )
= $false )
| ( ( ! [SY179: $i] :
( ~ ( rel @ SV8 @ SY179 )
| ( SV1 @ SY179 ) ) )
= $true )
| ( ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV3: $i,SV1: $i > $o,SV9: $i,SV6: $i] :
( ( ( ~ ( rel @ SV6 @ SV9 )
| ( SV1 @ SV9 ) )
= $true )
| ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV7: $i] :
( ( ( ~ ( b @ SV7 ) )
= $true )
| ( ( c @ SV7 )
= $true )
| ( ( rel @ sK3_SX0 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV3: $i,SV1: $i > $o,SV10: $i,SV8: $i] :
( ( ( ~ ( rel @ SV8 @ SV10 )
| ( SV1 @ SV10 ) )
= $true )
| ( ( rel @ SV3 @ SV8 )
= $false )
| ( ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV3: $i,SV1: $i > $o,SV9: $i,SV6: $i] :
( ( ( ~ ( rel @ SV6 @ SV9 ) )
= $true )
| ( ( SV1 @ SV9 )
= $true )
| ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV7: $i] :
( ( ( b @ SV7 )
= $false )
| ( ( c @ SV7 )
= $true )
| ( ( rel @ sK3_SX0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV3: $i,SV1: $i > $o,SV10: $i,SV8: $i] :
( ( ( ~ ( rel @ SV8 @ SV10 ) )
= $true )
| ( ( SV1 @ SV10 )
= $true )
| ( ( rel @ SV3 @ SV8 )
= $false )
| ( ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV3: $i,SV1: $i > $o,SV9: $i,SV6: $i] :
( ( ( rel @ SV6 @ SV9 )
= $false )
| ( ( SV1 @ SV9 )
= $true )
| ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( SV1 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV3: $i,SV1: $i > $o,SV10: $i,SV8: $i] :
( ( ( rel @ SV8 @ SV10 )
= $false )
| ( ( SV1 @ SV10 )
= $true )
| ( ( rel @ SV3 @ SV8 )
= $false )
| ( ( rel @ SV3 @ ( sK4_SY172 @ SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(76,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,75,74,72,66,62,60,58,55,48,38]) ).
thf(77,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV430^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.21 % Computer : n011.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Oct 6 16:30:36 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.29
% 0.10/0.29 No.of.Axioms: 2
% 0.10/0.29
% 0.10/0.29 Length.of.Defs: 3652
% 0.10/0.29
% 0.10/0.29 Contains.Choice.Funs: false
% 0.10/0.29 ...
% 0.10/0.29
% 0.10/0.29 ********************************
% 0.10/0.29 * All subproblems solved! *
% 0.10/0.29 ********************************
% 0.10/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,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:76,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.29
% 0.10/0.29 %**** Beginning of derivation protocol ****
% 0.10/0.29 % SZS output start CNFRefutation
% See solution above
% 0.10/0.29
% 0.10/0.29 %**** End of derivation protocol ****
% 0.10/0.29 %**** no. of clauses in derivation: 77 ****
% 0.10/0.29 %**** clause counter: 76 ****
% 0.10/0.29
% 0.10/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,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:76,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------