%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL613^1 : 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 : n007.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 10:29:30 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 50 ( 45 unt; 0 typ; 15 def)
% Number of atoms : 211 ( 52 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 338 ( 80 ~; 43 |; 14 &; 188 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 5 con; 0-3 aty)
% Number of variables : 88 ( 28 ^; 56 !; 4 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_individuals,type,
individuals: $tType ).
thf(tp_current_world,type,
current_world: $i ).
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_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK2_SY36,type,
sK2_SY36: $i > $o ).
thf(tp_sK3_SY41,type,
sK3_SY41: $i > $o ).
thf(tp_sK4_SY45,type,
sK4_SY45: $i ).
thf(tp_sK5_SY49,type,
sK5_SY49: $i ).
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,conjecture,
! [R: $i > $i > $o,X: $i > $o,Y: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ ( mand @ X @ Y ) ) @ ( mbox @ R @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o,X: $i > $o,Y: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ ( mand @ X @ Y ) ) @ ( mbox @ R @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o,SY1: $i > $o,SY2: $i > $o,SY27: $i] :
( ~ ! [SY28: $i] :
( ( SY0 @ SY27 @ SY28 )
=> ( ( SY1 @ SY28 )
& ( SY2 @ SY28 ) ) )
| ! [SY29: $i] :
( ( SY0 @ SY27 @ SY29 )
=> ( SY1 @ SY29 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(4,plain,
( ( ! [SY36: $i > $o,SY37: $i > $o,SY38: $i] :
( ~ ! [SY39: $i] :
( ( sK1_SY0 @ SY38 @ SY39 )
=> ( ( SY36 @ SY39 )
& ( SY37 @ SY39 ) ) )
| ! [SY40: $i] :
( ( sK1_SY0 @ SY38 @ SY40 )
=> ( SY36 @ SY40 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY41: $i > $o,SY42: $i] :
( ~ ! [SY43: $i] :
( ( sK1_SY0 @ SY42 @ SY43 )
=> ( ( sK2_SY36 @ SY43 )
& ( SY41 @ SY43 ) ) )
| ! [SY44: $i] :
( ( sK1_SY0 @ SY42 @ SY44 )
=> ( sK2_SY36 @ SY44 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY45: $i] :
( ~ ! [SY46: $i] :
( ( sK1_SY0 @ SY45 @ SY46 )
=> ( ( sK2_SY36 @ SY46 )
& ( sK3_SY41 @ SY46 ) ) )
| ! [SY44: $i] :
( ( sK1_SY0 @ SY45 @ SY44 )
=> ( sK2_SY36 @ SY44 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ~ ! [SY48: $i] :
( ( sK1_SY0 @ sK4_SY45 @ SY48 )
=> ( ( sK2_SY36 @ SY48 )
& ( sK3_SY41 @ SY48 ) ) )
| ! [SY49: $i] :
( ( sK1_SY0 @ sK4_SY45 @ SY49 )
=> ( sK2_SY36 @ SY49 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ~ ( ~ ! [SY48: $i] :
( ( sK1_SY0 @ sK4_SY45 @ SY48 )
=> ( ( sK2_SY36 @ SY48 )
& ( sK3_SY41 @ SY48 ) ) )
| ! [SY49: $i] :
( ( sK1_SY0 @ sK4_SY45 @ SY49 )
=> ( sK2_SY36 @ SY49 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY48: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SY48 )
| ( sK2_SY36 @ SY48 ) )
& ! [SY48: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SY48 )
| ( sK3_SY41 @ SY48 ) )
& ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
& ~ ( sK2_SY36 @ sK5_SY49 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [SY48: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SY48 )
| ( sK2_SY36 @ SY48 ) )
& ! [SY48: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SY48 )
| ( sK3_SY41 @ SY48 ) )
& ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
& ~ ( sK2_SY36 @ sK5_SY49 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK2_SY36 @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK3_SY41 @ SX0 ) ) )
| ~ ~ ( ~ ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
| ~ ~ ( sK2_SY36 @ sK5_SY49 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mall,mand,mbox,mcountersatisfiable,mdia,mexists,mfalse,miff,mimpl,minvalid,mnot,mor,msatisfiable,mtrue,mvalid]) ).
thf(12,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK2_SY36 @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK3_SY41 @ SX0 ) ) )
| ~ ~ ( ~ ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
| ~ ~ ( sK2_SY36 @ sK5_SY49 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK2_SY36 @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK3_SY41 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
| ~ ~ ( sK2_SY36 @ sK5_SY49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK2_SY36 @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK3_SY41 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
| ~ ~ ( sK2_SY36 @ sK5_SY49 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK2_SY36 @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK3_SY41 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
| ~ ~ ( sK2_SY36 @ sK5_SY49 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK2_SY36 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK3_SY41 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ~ ( sK2_SY36 @ sK5_SY49 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK2_SY36 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SX0: $i] :
( ~ ( sK1_SY0 @ sK4_SY45 @ SX0 )
| ( sK3_SY41 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( sK1_SY0 @ sK4_SY45 @ sK5_SY49 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( sK2_SY36 @ sK5_SY49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i] :
( ( ~ ( sK1_SY0 @ sK4_SY45 @ SV1 )
| ( sK2_SY36 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i] :
( ( ~ ( sK1_SY0 @ sK4_SY45 @ SV2 )
| ( sK3_SY41 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( sK2_SY36 @ sK5_SY49 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_SY0 @ sK4_SY45 @ SV1 ) )
= $true )
| ( ( sK2_SY36 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i] :
( ( ( ~ ( sK1_SY0 @ sK4_SY45 @ SV2 ) )
= $true )
| ( ( sK3_SY41 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( sK1_SY0 @ sK4_SY45 @ SV1 )
= $false )
| ( ( sK2_SY36 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( sK1_SY0 @ sK4_SY45 @ SV2 )
= $false )
| ( ( sK3_SY41 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,33,32,29]) ).
thf(35,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL613^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 12:22:45 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 0
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 2230
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23 .
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:34,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % 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: 35 ****
% 0.07/0.23 %**** clause counter: 34 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:34,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------