%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM665^1 : 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 : n008.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 10:34:50 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 59 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 307 ( 20 ~; 33 |; 0 &; 248 @)
% ( 0 <=>; 6 =>; 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 : 21 ( 18 usr; 10 con; 0-4 aty)
% Number of variables : 102 ( 40 ^; 62 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_diffprop,type,
diffprop: nat > nat > nat > $o ).
thf(tp_lessis,type,
lessis: nat > nat > $o ).
thf(tp_moreis,type,
moreis: nat > nat > $o ).
thf(tp_sK10_E,type,
sK10_E: nat > nat ).
thf(tp_sK11_E,type,
sK11_E: nat > nat > nat > nat > nat ).
thf(tp_sK1_E,type,
sK1_E: nat ).
thf(tp_sK2_E,type,
sK2_E: nat ).
thf(tp_sK3_E,type,
sK3_E: nat ).
thf(tp_sK4_E,type,
sK4_E: nat > nat > nat > nat ).
thf(tp_sK5_E,type,
sK5_E: nat > nat > nat > nat ).
thf(tp_sK6_E,type,
sK6_E: nat > nat > nat > nat ).
thf(tp_sK7_E,type,
sK7_E: nat > nat > nat > nat ).
thf(tp_sK8_E,type,
sK8_E: nat ).
thf(tp_sK9_E,type,
sK9_E: nat ).
thf(tp_some,type,
some: ( nat > $o ) > $o ).
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] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(2,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( some
@ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
=> ( ( lessis @ Xy @ Xz )
=> ( some
@ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16b) ).
thf(3,axiom,
( some
@ ^ [Xu: nat] : ( diffprop @ y @ z @ Xu ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(4,axiom,
moreis @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(5,conjecture,
( some
@ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16c) ).
thf(6,negated_conjecture,
( ( some
@ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( some
@ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( moreis @ Xx @ Xy )
=> ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( some
@ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
=> ( ( lessis @ Xy @ Xz )
=> ( some
@ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( some
@ ^ [Xu: nat] : ( diffprop @ y @ z @ Xu ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( moreis @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ( some
@ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( moreis @ Xx @ Xy )
| ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( some
@ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
| ! [Xz: nat] :
( ~ ( lessis @ Xy @ Xz )
| ( some
@ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( moreis @ x @ y )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( some
@ ^ [Xu: nat] : ( diffprop @ y @ z @ Xu ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( some
@ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
| ! [Xz: nat] :
( ~ ( lessis @ Xy @ Xz )
| ( some
@ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( moreis @ Xx @ Xy )
| ( lessis @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ~ ( some
@ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
! [SV1: nat] :
( ( ! [SY9: nat] :
( ~ ( some
@ ^ [SY10: nat] : ( diffprop @ SY9 @ SV1 @ SY10 ) )
| ! [SY11: nat] :
( ~ ( lessis @ SY9 @ SY11 )
| ( some
@ ^ [SY12: nat] : ( diffprop @ SY11 @ SV1 @ SY12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: nat] :
( ( ! [SY13: nat] :
( ~ ( moreis @ SV2 @ SY13 )
| ( lessis @ SY13 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( some
@ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: nat,SV3: nat] :
( ( ~ ( some
@ ^ [SY14: nat] : ( diffprop @ SV3 @ SV1 @ SY14 ) )
| ! [SY15: nat] :
( ~ ( lessis @ SV3 @ SY15 )
| ( some
@ ^ [SY12: nat] : ( diffprop @ SY15 @ SV1 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: nat,SV2: nat] :
( ( ~ ( moreis @ SV2 @ SV4 )
| ( lessis @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: nat,SV3: nat] :
( ( ( ~ ( some
@ ^ [SY14: nat] : ( diffprop @ SV3 @ SV1 @ SY14 ) ) )
= $true )
| ( ( ! [SY15: nat] :
( ~ ( lessis @ SV3 @ SY15 )
| ( some
@ ^ [SY12: nat] : ( diffprop @ SY15 @ SV1 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV4: nat,SV2: nat] :
( ( ( ~ ( moreis @ SV2 @ SV4 ) )
= $true )
| ( ( lessis @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: nat,SV3: nat] :
( ( ( some
@ ^ [SY14: nat] : ( diffprop @ SV3 @ SV1 @ SY14 ) )
= $false )
| ( ( ! [SY15: nat] :
( ~ ( lessis @ SV3 @ SY15 )
| ( some
@ ^ [SY12: nat] : ( diffprop @ SY15 @ SV1 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV4: nat,SV2: nat] :
( ( ( moreis @ SV2 @ SV4 )
= $false )
| ( ( lessis @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: nat,SV5: nat,SV3: nat] :
( ( ( ~ ( lessis @ SV3 @ SV5 )
| ( some
@ ^ [SY17: nat] : ( diffprop @ SV5 @ SV1 @ SY17 ) ) )
= $true )
| ( ( some
@ ^ [SY14: nat] : ( diffprop @ SV3 @ SV1 @ SY14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: nat,SV5: nat,SV3: nat] :
( ( ( ~ ( lessis @ SV3 @ SV5 ) )
= $true )
| ( ( some
@ ^ [SY17: nat] : ( diffprop @ SV5 @ SV1 @ SY17 ) )
= $true )
| ( ( some
@ ^ [SY14: nat] : ( diffprop @ SV3 @ SV1 @ SY14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV1: nat,SV5: nat,SV3: nat] :
( ( ( lessis @ SV3 @ SV5 )
= $false )
| ( ( some
@ ^ [SY17: nat] : ( diffprop @ SV5 @ SV1 @ SY17 ) )
= $true )
| ( ( some
@ ^ [SY14: nat] : ( diffprop @ SV3 @ SV1 @ SY14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV6: nat,SV7: nat] :
( ( ( moreis @ SV7 @ SV6 )
= $false )
| ( ( lessis @ SV6 @ SV7 )
= $true ) ),
inference(rename,[status(thm)],[28]) ).
thf(45,plain,
! [SV6: nat,SV7: nat] :
( ( ( ( moreis @ SV7 @ SV6 )
= ( moreis @ x @ y ) )
= $false )
| ( ( lessis @ SV6 @ SV7 )
= $true ) ),
inference(res,[status(thm)],[39,15]) ).
thf(46,plain,
( ( lessis @ y @ x )
= $true ),
inference(extuni,[status(esa)],[45:[bind(SV6,$thf( y )),bind(SV7,$thf( x ))]]) ).
thf(76,plain,
! [SV8: nat,SV9: nat,SV10: nat] :
( ( ( lessis @ SV10 @ SV9 )
= $false )
| ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV9 @ SV8 @ SX0 ) )
= $true )
| ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV10 @ SV8 @ SX0 ) )
= $false ) ),
inference(rename,[status(thm)],[31]) ).
thf(94,plain,
! [SV8: nat,SV9: nat,SV10: nat] :
( ( ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV10 @ SV8 @ SX0 ) )
= ( some
@ ^ [Xu: nat] : ( diffprop @ y @ z @ Xu ) ) )
= $false )
| ( ( lessis @ SV10 @ SV9 )
= $false )
| ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV9 @ SV8 @ SX0 ) )
= $true ) ),
inference(res,[status(thm)],[76,16]) ).
thf(98,plain,
! [SV9: nat] :
( ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV9 @ z @ SX0 ) )
= $true )
| ( ( lessis @ y @ SV9 )
= $false ) ),
inference(extuni,[status(esa)],[94:[bind(SV8,$thf( z )),bind(SV10,$thf( y ))]]) ).
thf(116,plain,
! [SV11: nat] :
( ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV11 @ z @ SX0 ) )
= $true )
| ( ( lessis @ y @ SV11 )
= $false ) ),
inference(rename,[status(thm)],[98]) ).
thf(130,plain,
! [SV11: nat] :
( ( ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV11 @ z @ SX0 ) )
= ( some
@ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) )
= $false )
| ( ( lessis @ y @ SV11 )
= $false ) ),
inference(res,[status(thm)],[116,22]) ).
thf(133,plain,
( ( lessis @ y @ x )
= $false ),
inference(extuni,[status(esa)],[130:[bind(SV11,$thf( x ))]]) ).
thf(143,plain,
( ( ( lessis @ y @ x )
= ( lessis @ y @ x ) )
= $false ),
inference(res,[status(thm)],[133,46]) ).
thf(150,plain,
$false = $true,
inference(extuni,[status(esa)],[143]) ).
thf(151,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM665^1 : 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
% 0.09/0.16 % Computer : n008.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 13:33:45 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 4
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 0
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 ...
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:150,loop_count:13,foatp_calls:3,translation:fof_experiment)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 43 ****
% 0.09/0.23 %**** clause counter: 150 ****
% 0.09/0.23
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:150,loop_count:13,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------