%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM656^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n026.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 10:34:48 AM UTC 2026
% Result : Theorem 0.09s 0.18s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 253 ( 102 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 347 ( 125 ~; 60 |; 4 &; 142 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 89 ( 0 ^; 89 !; 0 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_less,type,
less: nat > nat > $o ).
thf(tp_more,type,
more: nat > nat > $o ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat] :
~ ( ( ( Xx = Xy )
=> ~ ( more @ Xx @ Xy ) )
=> ~ ~ ( ( ( more @ Xx @ Xy )
=> ~ ( less @ Xx @ Xy ) )
=> ~ ( ( less @ Xx @ Xy )
=> ( Xx != Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10b) ).
thf(2,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',et) ).
thf(3,axiom,
more @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(4,conjecture,
~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10g) ).
thf(5,negated_conjecture,
( ( ~ ( ~ ( less @ x @ y )
=> ( x = y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ~ ( ~ ( less @ x @ y )
=> ( x = y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: nat,Xy: nat] :
~ ( ( ( Xx = Xy )
=> ~ ( more @ Xx @ Xy ) )
=> ~ ~ ( ( ( more @ Xx @ Xy )
=> ~ ( less @ Xx @ Xy ) )
=> ~ ( ( less @ Xx @ Xy )
=> ( Xx != Xy ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( more @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ( less @ x @ y )
=> ( x = y ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ( less @ x @ y )
| ( x = y ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( Xx != Xy )
| ~ ( more @ Xx @ Xy ) )
& ! [Xx: nat,Xy: nat] :
( ~ ( more @ Xx @ Xy )
| ~ ( less @ Xx @ Xy ) )
& ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xx @ Xy )
| ( Xx != Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(13,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( more @ x @ y )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( Xx != Xy )
| ~ ( more @ Xx @ Xy ) )
& ! [Xx: nat,Xy: nat] :
( ~ ( more @ Xx @ Xy )
| ~ ( less @ Xx @ Xy ) )
& ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xx @ Xy )
| ( Xx != Xy ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ( less @ x @ y )
| ( x = y ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ~ ( more @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX1 ) )
| ~ ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: $o] :
( ( ~ SV1
| SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[15]) ).
thf(21,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[15]) ).
thf(22,plain,
( ( ( less @ x @ y )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(23,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ~ ( more @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX1 ) )
| ~ ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(25,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(27,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ~ ( more @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ~ ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX1 ) )
| ~ ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(29,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ~ ( more @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(33,plain,
( ( ~ ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX1 ) )
| ~ ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV2: nat] :
( ( ! [SY3: nat] :
( ( SV2 != SY3 )
| ~ ( more @ SV2 @ SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX1 ) )
| ~ ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: nat,SV2: nat] :
( ( ( SV2 != SV3 )
| ~ ( more @ SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(38,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV3: nat,SV2: nat] :
( ( ( SV2 != SV3 )
= $true )
| ( ( ~ ( more @ SV2 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(41,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( less @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: nat,SV2: nat] :
( ( ( SV2 = SV3 )
= $false )
| ( ( ~ ( more @ SV2 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV4: nat] :
( ( ! [SY4: nat] :
( ~ ( more @ SV4 @ SY4 )
| ~ ( less @ SV4 @ SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV5: nat] :
( ( ! [SY5: nat] :
( ~ ( less @ SV5 @ SY5 )
| ( SV5 != SY5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: nat,SV2: nat] :
( ( ( more @ SV2 @ SV3 )
= $false )
| ( ( SV2 = SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV6: nat,SV4: nat] :
( ( ~ ( more @ SV4 @ SV6 )
| ~ ( less @ SV4 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV7: nat,SV5: nat] :
( ( ~ ( less @ SV5 @ SV7 )
| ( SV5 != SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV6: nat,SV4: nat] :
( ( ( ~ ( more @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ( less @ SV4 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV7: nat,SV5: nat] :
( ( ( ~ ( less @ SV5 @ SV7 ) )
= $true )
| ( ( SV5 != SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV6: nat,SV4: nat] :
( ( ( more @ SV4 @ SV6 )
= $false )
| ( ( ~ ( less @ SV4 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV7: nat,SV5: nat] :
( ( ( less @ SV5 @ SV7 )
= $false )
| ( ( SV5 != SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV6: nat,SV4: nat] :
( ( ( less @ SV4 @ SV6 )
= $false )
| ( ( more @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV7: nat,SV5: nat] :
( ( ( SV5 = SV7 )
= $false )
| ( ( less @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,53,52,45,31,30,29,22]) ).
thf(55,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM656^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.15 % Computer : n026.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 13:35:16 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18
% 0.09/0.18 No.of.Axioms: 3
% 0.09/0.18
% 0.09/0.18 Length.of.Defs: 0
% 0.09/0.18
% 0.09/0.18 Contains.Choice.Funs: false
% 0.09/0.18 .
% 0.09/0.18
% 0.09/0.18 ********************************
% 0.09/0.18 * All subproblems solved! *
% 0.09/0.18 ********************************
% 0.09/0.18 % 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:54,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.09/0.18
% 0.09/0.18 %**** Beginning of derivation protocol ****
% 0.09/0.18 % SZS output start CNFRefutation
% See solution above
% 0.09/0.18
% 0.09/0.18 %**** End of derivation protocol ****
% 0.09/0.18 %**** no. of clauses in derivation: 55 ****
% 0.09/0.18 %**** clause counter: 54 ****
% 0.09/0.18
% 0.09/0.18 % 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:54,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------