%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ136^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n013.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 10:37:00 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 178 ( 100 ~; 17 |; 5 &; 56 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 0 ^; 52 !; 15 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_horus,type,
horus: $i ).
thf(tp_kronus,type,
kronus: $i ).
thf(tp_parent,type,
parent: $i > $i > $o ).
thf(tp_sutekh,type,
sutekh: $i ).
thf(tp_zeus,type,
zeus: $i ).
thf(1,axiom,
~ ( parent @ sutekh @ horus ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(2,axiom,
parent @ kronus @ zeus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(3,conjecture,
? [P: $i > $o,X: $i,Y: $i] :
( ( P @ X )
& ~ ( P @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hotwo) ).
thf(4,negated_conjecture,
( ( ? [P: $i > $o,X: $i,Y: $i] :
( ( P @ X )
& ~ ( P @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ? [P: $i > $o,X: $i,Y: $i] :
( ( P @ X )
& ~ ( P @ Y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ( parent @ sutekh @ horus ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( parent @ kronus @ zeus )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ? [P: $i > $o,X: $i,Y: $i] :
( ( P @ X )
& ~ ( P @ Y ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( parent @ kronus @ zeus )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( parent @ sutekh @ horus ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ? [P: $i > $o,X: $i,Y: $i] :
( ( P @ X )
& ~ ( P @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ~ ! [SX0: $i > $o] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ~ ( SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( parent @ sutekh @ horus )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [SX0: $i > $o] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ~ ( SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SX0: $i > $o] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ~ ( SX0 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(16,plain,
! [SV1: $i > $o] :
( ( ~ ~ ! [SY3: $i] :
~ ~ ! [SY4: $i] :
~ ~ ( ~ ( SV1 @ SY3 )
| ~ ~ ( SV1 @ SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: $i > $o] :
( ( ~ ! [SY3: $i] :
~ ~ ! [SY4: $i] :
~ ~ ( ~ ( SV1 @ SY3 )
| ~ ~ ( SV1 @ SY4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ! [SY3: $i] :
~ ~ ! [SY4: $i] :
~ ~ ( ~ ( SV1 @ SY3 )
| ~ ~ ( SV1 @ SY4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(19,plain,
! [SV2: $i,SV1: $i > $o] :
( ( ~ ~ ! [SY5: $i] :
~ ~ ( ~ ( SV1 @ SV2 )
| ~ ~ ( SV1 @ SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV2: $i,SV1: $i > $o] :
( ( ~ ! [SY5: $i] :
~ ~ ( ~ ( SV1 @ SV2 )
| ~ ~ ( SV1 @ SY5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV2: $i,SV1: $i > $o] :
( ( ! [SY5: $i] :
~ ~ ( ~ ( SV1 @ SV2 )
| ~ ~ ( SV1 @ SY5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(22,plain,
! [SV3: $i,SV2: $i,SV1: $i > $o] :
( ( ~ ~ ( ~ ( SV1 @ SV2 )
| ~ ~ ( SV1 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(23,plain,
! [SV3: $i,SV2: $i,SV1: $i > $o] :
( ( ~ ( ~ ( SV1 @ SV2 )
| ~ ~ ( SV1 @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
! [SV3: $i,SV2: $i,SV1: $i > $o] :
( ( ~ ( SV1 @ SV2 )
| ~ ~ ( SV1 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(25,plain,
! [SV3: $i,SV2: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV2 ) )
= $true )
| ( ( ~ ~ ( SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV3: $i,SV2: $i,SV1: $i > $o] :
( ( ( SV1 @ SV2 )
= $false )
| ( ( ~ ~ ( SV1 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV2: $i,SV3: $i,SV1: $i > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $false )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV2: $i,SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(29,plain,
! [SV2: $i,SV3: $i] :
( ( ( SV3 = SV2 )
= $true )
| ( ( SV2 = SV2 )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[28:[bind(SV1,$thf( ^ [SV4: $i] : ( SV4 = SV2 ) ))]]) ).
thf(30,plain,
! [SV2: $i,SV3: $i] :
( ( SV3 = SV2 )
= $true ),
inference(sim,[status(thm)],[29]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9,30,13]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ136^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 13:59:51 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.27
% 0.21/0.27 No.of.Axioms: 2
% 0.21/0.27
% 0.21/0.27 Length.of.Defs: 0
% 0.21/0.27
% 0.21/0.27 Contains.Choice.Funs: false
% 0.21/0.27
% 0.21/0.27 ********************************
% 0.21/0.27 * All subproblems solved! *
% 0.21/0.27 ********************************
% 0.21/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:31,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.21/0.27
% 0.21/0.27 %**** Beginning of derivation protocol ****
% 0.21/0.27 % SZS output start CNFRefutation
% See solution above
% 0.21/0.27
% 0.21/0.27 %**** End of derivation protocol ****
% 0.21/0.27 %**** no. of clauses in derivation: 32 ****
% 0.21/0.27 %**** clause counter: 31 ****
% 0.21/0.27
% 0.21/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:31,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------