%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n003.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 10:27:49 AM UTC 2026
% Result : Unsatisfiable 1.78s 0.50s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 50 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 353 ( 24 ~; 24 |; 0 &; 305 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_is_a_theorem,type,
is_a_theorem: $i > $o ).
thf(tp_necessary,type,
necessary: $i > $i ).
thf(tp_not,type,
not: $i > $i ).
thf(1,axiom,
! [X: $i] :
( ~ ( is_a_theorem @ X )
| ( is_a_theorem @ ( necessary @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_of_necessitation) ).
thf(2,axiom,
! [X: $i] : ( is_a_theorem @ ( implies @ ( necessary @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation2) ).
thf(3,axiom,
! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ X @ Y ) ) @ ( implies @ ( necessary @ X ) @ ( necessary @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation1) ).
thf(4,axiom,
! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_49) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ Y @ Z ) ) @ ( implies @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_35) ).
thf(6,axiom,
! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_18) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,negated_conjecture,
~ ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [X: $i] :
( ~ ( is_a_theorem @ X )
| ( is_a_theorem @ ( necessary @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessary @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ X @ Y ) ) @ ( implies @ ( necessary @ X ) @ ( necessary @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ Y @ Z ) ) @ ( implies @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ Y @ Z ) ) @ ( implies @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ X @ Y ) ) @ ( implies @ ( necessary @ X ) @ ( necessary @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessary @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(28,plain,
( ( ! [X: $i] :
( ~ ( is_a_theorem @ X )
| ( is_a_theorem @ ( necessary @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(29,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(31,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ~ ( is_a_theorem @ ( implies @ SV1 @ SY13 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(32,plain,
! [SV2: $i] :
( ( ! [SY14: $i] : ( is_a_theorem @ ( implies @ SV2 @ ( implies @ SY14 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV3 @ ( implies @ SY15 @ SY16 ) ) @ ( implies @ ( implies @ SV3 @ SY15 ) @ ( implies @ SV3 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(34,plain,
! [SV4: $i] :
( ( ! [SY17: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SY17 ) ) @ ( implies @ SY17 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(35,plain,
! [SV5: $i] :
( ( ! [SY18: $i] : ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ SV5 @ SY18 ) ) @ ( implies @ ( necessary @ SV5 ) @ ( necessary @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(36,plain,
! [SV6: $i] :
( ( is_a_theorem @ ( implies @ ( necessary @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(37,plain,
! [SV7: $i] :
( ( ~ ( is_a_theorem @ SV7 )
| ( is_a_theorem @ ( necessary @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(38,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(39,plain,
! [SV8: $i,SV1: $i] :
( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV8 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV9: $i,SV2: $i] :
( ( is_a_theorem @ ( implies @ SV2 @ ( implies @ SV9 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY19: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV3 @ ( implies @ SV10 @ SY19 ) ) @ ( implies @ ( implies @ SV3 @ SV10 ) @ ( implies @ SV3 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV11: $i,SV4: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SV11 ) ) @ ( implies @ SV11 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV12: $i,SV5: $i] :
( ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ SV5 @ SV12 ) ) @ ( implies @ ( necessary @ SV5 ) @ ( necessary @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV7: $i] :
( ( ( ~ ( is_a_theorem @ SV7 ) )
= $true )
| ( ( is_a_theorem @ ( necessary @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV8 ) ) )
= $true )
| ( ( ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV13: $i,SV10: $i,SV3: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ SV3 @ ( implies @ SV10 @ SV13 ) ) @ ( implies @ ( implies @ SV3 @ SV10 ) @ ( implies @ SV3 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV7: $i] :
( ( ( is_a_theorem @ SV7 )
= $false )
| ( ( is_a_theorem @ ( necessary @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV8: $i,SV1: $i] :
( ( ( is_a_theorem @ ( implies @ SV1 @ SV8 ) )
= $false )
| ( ( ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV8 )
= $true )
| ( ( is_a_theorem @ ( implies @ SV1 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV8: $i,SV1: $i] :
( ( ( is_a_theorem @ SV1 )
= $false )
| ( ( is_a_theorem @ SV8 )
= $true )
| ( ( is_a_theorem @ ( implies @ SV1 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,50,47,46,43,42,40,38,36]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n003.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 12:08:54 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.78/0.50
% 1.78/0.50 No.of.Axioms: 8
% 1.78/0.50
% 1.78/0.50 Length.of.Defs: 0
% 1.78/0.50
% 1.78/0.50 Contains.Choice.Funs: false
% 1.78/0.50 .
% 1.78/0.50
% 1.78/0.50 ********************************
% 1.78/0.50 * All subproblems solved! *
% 1.78/0.50 ********************************
% 1.78/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 1.78/0.50
% 1.78/0.50 %**** Beginning of derivation protocol ****
% 1.78/0.50 % SZS output start CNFRefutation
% See solution above
% 1.78/0.50
% 1.78/0.50 %**** End of derivation protocol ****
% 1.78/0.50 %**** no. of clauses in derivation: 52 ****
% 1.78/0.50 %**** clause counter: 51 ****
% 1.78/0.50
% 1.78/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------