%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM692^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:34:57 AM UTC 2026
% Result : Theorem 0.12s 0.23s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 172 ( 45 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 296 ( 24 ~; 28 |; 0 &; 232 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 0 ^; 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_lessis,type,
lessis: nat > nat > $o ).
thf(tp_moreis,type,
moreis: nat > nat > $o ).
thf(tp_ts,type,
ts: nat > nat > nat ).
thf(tp_u,type,
u: nat ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(tp_z,type,
z: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ( moreis @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz14) ).
thf(2,axiom,
! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( moreis @ Xx @ Xy )
=> ( ( moreis @ Xz @ Xu )
=> ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23) ).
thf(3,axiom,
! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(4,axiom,
lessis @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(5,axiom,
lessis @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(6,conjecture,
lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23a) ).
thf(7,negated_conjecture,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ( moreis @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( moreis @ Xx @ Xy )
=> ( ( moreis @ Xz @ Xu )
=> ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( lessis @ z @ u )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( lessis @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( lessis @ x @ y )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( lessis @ z @ u )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( moreis @ Xx @ Xy )
=> ( ( moreis @ Xz @ Xu )
=> ( moreis @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ( moreis @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( moreis @ SX0 @ SX1 )
| ( lessis @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( lessis @ SX0 @ SX1 )
| ( moreis @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( moreis @ SX0 @ SX1 )
| ~ ( moreis @ SX2 @ SX3 )
| ( moreis @ ( ts @ SX0 @ SX2 ) @ ( ts @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(24,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: nat] :
( ( ! [SY8: nat] :
( ~ ( moreis @ SV1 @ SY8 )
| ( lessis @ SY8 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: nat] :
( ( ! [SY9: nat] :
( ~ ( lessis @ SV2 @ SY9 )
| ( moreis @ SY9 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: nat] :
( ( ! [SY10: nat,SY11: nat,SY12: nat] :
( ~ ( moreis @ SV3 @ SY10 )
| ~ ( moreis @ SY11 @ SY12 )
| ( moreis @ ( ts @ SV3 @ SY11 ) @ ( ts @ SY10 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: nat,SV1: nat] :
( ( ~ ( moreis @ SV1 @ SV4 )
| ( lessis @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: nat,SV2: nat] :
( ( ~ ( lessis @ SV2 @ SV5 )
| ( moreis @ SV5 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV6: nat,SV3: nat] :
( ( ! [SY13: nat,SY14: nat] :
( ~ ( moreis @ SV3 @ SV6 )
| ~ ( moreis @ SY13 @ SY14 )
| ( moreis @ ( ts @ SV3 @ SY13 ) @ ( ts @ SV6 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: nat,SV1: nat] :
( ( ( ~ ( moreis @ SV1 @ SV4 ) )
= $true )
| ( ( lessis @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: nat,SV2: nat] :
( ( ( ~ ( lessis @ SV2 @ SV5 ) )
= $true )
| ( ( moreis @ SV5 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV7: nat,SV6: nat,SV3: nat] :
( ( ! [SY15: nat] :
( ~ ( moreis @ SV3 @ SV6 )
| ~ ( moreis @ SV7 @ SY15 )
| ( moreis @ ( ts @ SV3 @ SV7 ) @ ( ts @ SV6 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV4: nat,SV1: nat] :
( ( ( moreis @ SV1 @ SV4 )
= $false )
| ( ( lessis @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV5: nat,SV2: nat] :
( ( ( lessis @ SV2 @ SV5 )
= $false )
| ( ( moreis @ SV5 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV8: nat,SV7: nat,SV6: nat,SV3: nat] :
( ( ~ ( moreis @ SV3 @ SV6 )
| ~ ( moreis @ SV7 @ SV8 )
| ( moreis @ ( ts @ SV3 @ SV7 ) @ ( ts @ SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV8: nat,SV7: nat,SV6: nat,SV3: nat] :
( ( ( ~ ( moreis @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( moreis @ SV7 @ SV8 )
| ( moreis @ ( ts @ SV3 @ SV7 ) @ ( ts @ SV6 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV8: nat,SV7: nat,SV6: nat,SV3: nat] :
( ( ( moreis @ SV3 @ SV6 )
= $false )
| ( ( ~ ( moreis @ SV7 @ SV8 )
| ( moreis @ ( ts @ SV3 @ SV7 ) @ ( ts @ SV6 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV6: nat,SV3: nat,SV8: nat,SV7: nat] :
( ( ( ~ ( moreis @ SV7 @ SV8 ) )
= $true )
| ( ( moreis @ ( ts @ SV3 @ SV7 ) @ ( ts @ SV6 @ SV8 ) )
= $true )
| ( ( moreis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV6: nat,SV3: nat,SV8: nat,SV7: nat] :
( ( ( moreis @ SV7 @ SV8 )
= $false )
| ( ( moreis @ ( ts @ SV3 @ SV7 ) @ ( ts @ SV6 @ SV8 ) )
= $true )
| ( ( moreis @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,40,35,34,24,16]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM692^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.19 % Computer : n007.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Oct 6 13:33:15 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.23
% 0.12/0.23 No.of.Axioms: 5
% 0.12/0.23
% 0.12/0.23 Length.of.Defs: 0
% 0.12/0.23
% 0.12/0.23 Contains.Choice.Funs: false
% 0.12/0.23 .
% 0.12/0.23
% 0.12/0.23 ********************************
% 0.12/0.23 * All subproblems solved! *
% 0.12/0.23 ********************************
% 0.12/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.23
% 0.12/0.23 %**** Beginning of derivation protocol ****
% 0.12/0.23 % SZS output start CNFRefutation
% See solution above
% 0.12/0.23
% 0.12/0.23 %**** End of derivation protocol ****
% 0.12/0.23 %**** no. of clauses in derivation: 42 ****
% 0.12/0.23 %**** clause counter: 41 ****
% 0.12/0.23
% 0.12/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------