%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PHI045^6 : TPTP v9.3.1. Released v9.0.0.
% 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 : 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 10:36:16 AM UTC 2026
% Result : Theorem 0.07s 0.20s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 158 ( 54 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 222 ( 55 ~; 36 |; 4 &; 123 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 5 ^; 40 !; 4 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_entity,type,
entity: $tType ).
thf(tp_god_like,type,
god_like: entity > $o ).
thf(tp_positive_property,type,
positive_property: ( entity > $o ) > $o ).
thf(tp_sK1_Y,type,
sK1_Y: ( entity > $o ) > ( entity > $o ) > entity ).
thf(1,axiom,
positive_property @ god_like,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(2,axiom,
! [P1: entity > $o,P2: entity > $o] :
( ( ( positive_property @ P1 )
& ! [Y: entity] :
( ( P1 @ Y )
=> ( P2 @ Y ) ) )
=> ( positive_property @ P2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coro2) ).
thf(3,axiom,
~ ( positive_property
@ ^ [X: entity] : ( X != X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coro1) ).
thf(4,conjecture,
? [X: entity] : ( god_like @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(5,negated_conjecture,
( ( ? [X: entity] : ( god_like @ X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ? [X: entity] : ( god_like @ X ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( positive_property @ god_like )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [P1: entity > $o,P2: entity > $o] :
( ( ( positive_property @ P1 )
& ! [Y: entity] :
( ( P1 @ Y )
=> ( P2 @ Y ) ) )
=> ( positive_property @ P2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ~ ( positive_property
@ ^ [X: entity] : ( X != X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ? [X: entity] : ( god_like @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [X: entity] :
~ ( god_like @ X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [P1: entity > $o,P2: entity > $o] :
( ( ( P1 @ ( sK1_Y @ P2 @ P1 ) )
& ~ ( P2 @ ( sK1_Y @ P2 @ P1 ) ) )
| ~ ( positive_property @ P1 )
| ( positive_property @ P2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(13,plain,
( ( ~ ( positive_property
@ ^ [X: entity] : ( X != X ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ! [P1: entity > $o,P2: entity > $o] :
( ( ( P1 @ ( sK1_Y @ P2 @ P1 ) )
& ~ ( P2 @ ( sK1_Y @ P2 @ P1 ) ) )
| ~ ( positive_property @ P1 )
| ( positive_property @ P2 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(15,plain,
( ( positive_property @ god_like )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(16,plain,
( ( ! [X: entity] :
~ ( god_like @ X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SX0: entity > $o,SX1: entity > $o] :
( ~ ( ~ ( SX0 @ ( sK1_Y @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK1_Y @ SX1 @ SX0 ) ) )
| ~ ( positive_property @ SX0 )
| ( positive_property @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( positive_property
@ ^ [SX0: entity] : ( SX0 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(19,plain,
! [SV1: entity] :
( ( ~ ( god_like @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: entity > $o] :
( ( ! [SY5: entity > $o] :
( ~ ( ~ ( SV2 @ ( sK1_Y @ SY5 @ SV2 ) )
| ~ ~ ( SY5 @ ( sK1_Y @ SY5 @ SV2 ) ) )
| ~ ( positive_property @ SV2 )
| ( positive_property @ SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( positive_property
@ ^ [SX0: entity] : ( SX0 != SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: entity] :
( ( god_like @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ~ ( ~ ( SV2 @ ( sK1_Y @ SV3 @ SV2 ) )
| ~ ~ ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) ) )
| ~ ( positive_property @ SV2 )
| ( positive_property @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK1_Y @ SV3 @ SV2 ) )
| ~ ~ ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) ) )
| ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK1_Y @ SV3 @ SV2 ) )
| ~ ~ ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ( ~ ( SV2 @ ( sK1_Y @ SV3 @ SV2 ) )
| ~ ~ ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) ) )
= $false )
| ( ( ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ( ~ ( SV2 @ ( sK1_Y @ SV3 @ SV2 ) ) )
= $false )
| ( ( ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(28,plain,
! [SV2: entity > $o,SV3: entity > $o] :
( ( ( ~ ~ ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) ) )
= $false )
| ( ( ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ( SV2 @ ( sK1_Y @ SV3 @ SV2 ) )
= $true )
| ( ( ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV2: entity > $o,SV3: entity > $o] :
( ( ( ~ ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) ) )
= $true )
| ( ( ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ( positive_property @ SV2 )
= $false )
| ( ( SV2 @ ( sK1_Y @ SV3 @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV2: entity > $o,SV3: entity > $o] :
( ( ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) )
= $false )
| ( ( ~ ( positive_property @ SV2 ) )
= $true )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV3: entity > $o,SV2: entity > $o] :
( ( ( positive_property @ SV2 )
= $false )
| ( ( SV3 @ ( sK1_Y @ SV3 @ SV2 ) )
= $false )
| ( ( positive_property @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,33,31,22,21]) ).
thf(35,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI045^6 : TPTP v9.3.1. Released v9.0.0.
% 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
% 0.07/0.18 % Computer : n011.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 13:50:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20
% 0.07/0.20 No.of.Axioms: 3
% 0.07/0.20
% 0.07/0.20 Length.of.Defs: 0
% 0.07/0.20
% 0.07/0.20 Contains.Choice.Funs: false
% 0.07/0.20
% 0.07/0.20 ********************************
% 0.07/0.20 * All subproblems solved! *
% 0.07/0.20 ********************************
% 0.07/0.20 % 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: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_experiment)
% 0.07/0.20
% 0.07/0.20 %**** Beginning of derivation protocol ****
% 0.07/0.20 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 35 ****
% 0.07/0.21 %**** clause counter: 34 ****
% 0.07/0.21
% 0.07/0.21 % 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: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_experiment)
%------------------------------------------------------------------------------