%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV282^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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 : n017.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 10:49:52 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 21 unt; 0 typ; 3 def)
% Number of atoms : 92 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 185 ( 69 ~; 14 |; 15 &; 80 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 35 ^; 19 !; 16 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cNAT,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(tp_cSUCC,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(tp_cZERO,type,
cZERO: ( $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: ( ( $i > $o ) > $o ) > $o ).
thf(cNAT,definition,
( cNAT
= ( ^ [Xn: ( $i > $o ) > $o] :
! [Xp: ( ( $i > $o ) > $o ) > $o] :
( ( ( Xp @ cZERO )
& ! [Xx: ( $i > $o ) > $o] :
( ( Xp @ Xx )
=> ( Xp @ ( cSUCC @ Xx ) ) ) )
=> ( Xp @ Xn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cNAT_def) ).
thf(cSUCC,definition,
( cSUCC
= ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
? [Xx: $i] :
( ( Xp @ Xx )
& ( Xn
@ ^ [Xt: $i] :
( ( Xt != Xx )
& ( Xp @ Xt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def) ).
thf(cZERO,definition,
( cZERO
= ( ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def) ).
thf(1,conjecture,
cNAT @ cZERO,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTTTP6100) ).
thf(2,negated_conjecture,
( ( cNAT @ cZERO )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY1: ( $i > $o ) > $o] :
( ( SY0 @ SY1 )
=> ( SY0
@ ^ [SY2: $i > $o] :
? [SY3: $i] :
( ( SY2 @ SY3 )
& ( SY1
@ ^ [Xt: $i] :
( ( Xt != SY3 )
& ( SY2 @ Xt ) ) ) ) ) ) )
=> ( SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cNAT,cSUCC,cZERO]) ).
thf(4,plain,
( ( ( ( sK1_SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY16: ( $i > $o ) > $o] :
( ( sK1_SY0 @ SY16 )
=> ( sK1_SY0
@ ^ [SY2: $i > $o] :
? [SY3: $i] :
( ( SY2 @ SY3 )
& ( SY16
@ ^ [Xt: $i] :
( ( Xt != SY3 )
& ( SY2 @ Xt ) ) ) ) ) ) )
=> ( sK1_SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( sK1_SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY16: ( $i > $o ) > $o] :
( ( sK1_SY0 @ SY16 )
=> ( sK1_SY0
@ ^ [SY2: $i > $o] :
? [SY3: $i] :
( ( SY2 @ SY3 )
& ( SY16
@ ^ [Xt: $i] :
( ( Xt != SY3 )
& ( SY2 @ Xt ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( sK1_SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ( sK1_SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY16: ( $i > $o ) > $o] :
( ~ ( sK1_SY0 @ SY16 )
| ( sK1_SY0
@ ^ [SY2: $i > $o] :
? [SY3: $i] :
( ( SY2 @ SY3 )
& ( SY16
@ ^ [Xt: $i] :
( ( Xt != SY3 )
& ( SY2 @ Xt ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(10,plain,
( ( ! [SY16: ( $i > $o ) > $o] :
( ~ ( sK1_SY0 @ SY16 )
| ( sK1_SY0
@ ^ [SY2: $i > $o] :
? [SY3: $i] :
( ( SY2 @ SY3 )
& ( SY16
@ ^ [Xt: $i] :
( ( Xt != SY3 )
& ( SY2 @ Xt ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( sK1_SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( ~ ( sK1_SY0
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ( sK1_SY0
@ ^ [SX0: $i > $o] :
~ ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,cNAT,cSUCC,cZERO]) ).
thf(14,plain,
( ( sK1_SY0
@ ^ [SX0: $i > $o] :
~ ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[11,cNAT,cSUCC,cZERO]) ).
thf(15,plain,
( ( ! [SX0: ( $i > $o ) > $o] :
( ~ ( sK1_SY0 @ SX0 )
| ( sK1_SY0
@ ^ [SX1: $i > $o] :
~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ( SX0
@ ^ [SX3: $i] :
~ ( ~ ( ( SX3 != SX2 ) )
| ~ ( SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,cNAT,cSUCC,cZERO]) ).
thf(16,plain,
( ( sK1_SY0
@ ^ [SX0: $i > $o] :
~ ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ~ ( sK1_SY0 @ SV1 )
| ( sK1_SY0
@ ^ [SY22: $i > $o] :
~ ! [SY23: $i] :
~ ~ ( ~ ( SY22 @ SY23 )
| ~ ( SV1
@ ^ [SX3: $i] :
~ ( ~ ( ( SX3 != SY23 ) )
| ~ ( SY22 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SY0 @ SV1 ) )
= $true )
| ( ( sK1_SY0
@ ^ [SY22: $i > $o] :
~ ! [SY23: $i] :
~ ~ ( ~ ( SY22 @ SY23 )
| ~ ( SV1
@ ^ [SX3: $i] :
~ ( ~ ( ( SX3 != SY23 ) )
| ~ ( SY22 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( sK1_SY0 @ SV1 )
= $false )
| ( ( sK1_SY0
@ ^ [SY22: $i > $o] :
~ ! [SY23: $i] :
~ ~ ( ~ ( SY22 @ SY23 )
| ~ ( SV1
@ ^ [SX3: $i] :
~ ( ~ ( ( SX3 != SY23 ) )
| ~ ( SY22 @ SX3 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,19,16]) ).
thf(21,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV282^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 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
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:40:30 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 569
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:20,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 21 ****
% 0.08/0.23 %**** clause counter: 20 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:20,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------