%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM690^1 : 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 : 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 10:34:56 AM UTC 2026
% Result : Theorem 1.42s 0.53s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 249 ( 61 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 416 ( 21 ~; 35 |; 0 &; 354 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 11 con; 0-6 aty)
% Number of variables : 124 ( 42 ^; 82 !; 0 ?; 124 :)
% 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_pl,type,
pl: nat > nat > nat ).
thf(tp_sK10_E,type,
sK10_E: nat > nat > nat ).
thf(tp_sK11_E,type,
sK11_E: nat > nat > 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 > nat ).
thf(tp_sK5_E,type,
sK5_E: nat > nat > nat > nat > nat ).
thf(tp_sK6_E,type,
sK6_E: nat > nat > nat > nat > nat ).
thf(tp_sK7_E,type,
sK7_E: nat > 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_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] :
( ( some
@ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
=> ( ( moreis @ Xz @ Xu )
=> ( some
@ ^ [Xu_0: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) @ Xu_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).
thf(3,axiom,
lessis @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(4,axiom,
( some
@ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(5,conjecture,
( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22d) ).
thf(6,negated_conjecture,
( ( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( lessis @ Xx @ Xy )
=> ( moreis @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( some
@ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
=> ( ( moreis @ Xz @ Xu )
=> ( some
@ ^ [Xu_0: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) @ Xu_0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( lessis @ z @ u )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( some
@ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( lessis @ Xx @ Xy )
| ( moreis @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( some
@ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
| ! [Xz: nat,Xu: nat] :
( ~ ( moreis @ Xz @ Xu )
| ( some
@ ^ [Xu_0: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) @ Xu_0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( some
@ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( lessis @ z @ u )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( some
@ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
| ! [Xz: nat,Xu: nat] :
( ~ ( moreis @ Xz @ Xu )
| ( some
@ ^ [Xu_0: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) @ Xu_0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( lessis @ Xx @ Xy )
| ( moreis @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ~ ( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(20,plain,
! [SV1: nat] :
( ( ! [SY10: nat] :
( ~ ( some
@ ^ [SY11: nat] : ( diffprop @ SV1 @ SY10 @ SY11 ) )
| ! [SY12: nat,SY13: nat] :
( ~ ( moreis @ SY12 @ SY13 )
| ( some
@ ^ [SY14: nat] : ( diffprop @ ( pl @ SV1 @ SY12 ) @ ( pl @ SY10 @ SY13 ) @ SY14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: nat] :
( ( ! [SY15: nat] :
( ~ ( lessis @ SV2 @ SY15 )
| ( moreis @ SY15 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV3: nat,SV1: nat] :
( ( ~ ( some
@ ^ [SY16: nat] : ( diffprop @ SV1 @ SV3 @ SY16 ) )
| ! [SY17: nat,SY18: nat] :
( ~ ( moreis @ SY17 @ SY18 )
| ( some
@ ^ [SY19: nat] : ( diffprop @ ( pl @ SV1 @ SY17 ) @ ( pl @ SV3 @ SY18 ) @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: nat,SV2: nat] :
( ( ~ ( lessis @ SV2 @ SV4 )
| ( moreis @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: nat,SV1: nat] :
( ( ( ~ ( some
@ ^ [SY16: nat] : ( diffprop @ SV1 @ SV3 @ SY16 ) ) )
= $true )
| ( ( ! [SY17: nat,SY18: nat] :
( ~ ( moreis @ SY17 @ SY18 )
| ( some
@ ^ [SY19: nat] : ( diffprop @ ( pl @ SV1 @ SY17 ) @ ( pl @ SV3 @ SY18 ) @ SY19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV4: nat,SV2: nat] :
( ( ( ~ ( lessis @ SV2 @ SV4 ) )
= $true )
| ( ( moreis @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV3: nat,SV1: nat] :
( ( ( some
@ ^ [SY16: nat] : ( diffprop @ SV1 @ SV3 @ SY16 ) )
= $false )
| ( ( ! [SY17: nat,SY18: nat] :
( ~ ( moreis @ SY17 @ SY18 )
| ( some
@ ^ [SY19: nat] : ( diffprop @ ( pl @ SV1 @ SY17 ) @ ( pl @ SV3 @ SY18 ) @ SY19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV4: nat,SV2: nat] :
( ( ( lessis @ SV2 @ SV4 )
= $false )
| ( ( moreis @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV3: nat,SV1: nat,SV5: nat] :
( ( ( ! [SY20: nat] :
( ~ ( moreis @ SV5 @ SY20 )
| ( some
@ ^ [SY21: nat] : ( diffprop @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SY20 ) @ SY21 ) ) ) )
= $true )
| ( ( some
@ ^ [SY16: nat] : ( diffprop @ SV1 @ SV3 @ SY16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
( ( ( ~ ( moreis @ SV5 @ SV6 )
| ( some
@ ^ [SY22: nat] : ( diffprop @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) @ SY22 ) ) )
= $true )
| ( ( some
@ ^ [SY16: nat] : ( diffprop @ SV1 @ SV3 @ SY16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
( ( ( ~ ( moreis @ SV5 @ SV6 ) )
= $true )
| ( ( some
@ ^ [SY22: nat] : ( diffprop @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) @ SY22 ) )
= $true )
| ( ( some
@ ^ [SY16: nat] : ( diffprop @ SV1 @ SV3 @ SY16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(32,plain,
! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
( ( ( moreis @ SV5 @ SV6 )
= $false )
| ( ( some
@ ^ [SY22: nat] : ( diffprop @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) @ SY22 ) )
= $true )
| ( ( some
@ ^ [SY16: nat] : ( diffprop @ SV1 @ SV3 @ SY16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV7: nat,SV8: nat] :
( ( ( lessis @ SV8 @ SV7 )
= $false )
| ( ( moreis @ SV7 @ SV8 )
= $true ) ),
inference(rename,[status(thm)],[28]) ).
thf(42,plain,
! [SV7: nat,SV8: nat] :
( ( ( ( lessis @ SV8 @ SV7 )
= ( lessis @ z @ u ) )
= $false )
| ( ( moreis @ SV7 @ SV8 )
= $true ) ),
inference(res,[status(thm)],[38,16]) ).
thf(44,plain,
( ( moreis @ u @ z )
= $true ),
inference(extuni,[status(esa)],[42:[bind(SV7,$thf( u )),bind(SV8,$thf( z ))]]) ).
thf(45,plain,
! [SV9: nat,SV10: nat,SV11: nat,SV12: nat] :
( ( ( moreis @ SV12 @ SV11 )
= $false )
| ( ( some
@ ^ [SX0: nat] : ( diffprop @ ( pl @ SV10 @ SV12 ) @ ( pl @ SV9 @ SV11 ) @ SX0 ) )
= $true )
| ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV10 @ SV9 @ SX0 ) )
= $false ) ),
inference(rename,[status(thm)],[32]) ).
thf(56,plain,
! [SV9: nat,SV10: nat,SV11: nat,SV12: nat] :
( ( ( ( some
@ ^ [SX0: nat] : ( diffprop @ SV10 @ SV9 @ SX0 ) )
= ( some
@ ^ [Xv: nat] : ( diffprop @ y @ x @ Xv ) ) )
= $false )
| ( ( moreis @ SV12 @ SV11 )
= $false )
| ( ( some
@ ^ [SX0: nat] : ( diffprop @ ( pl @ SV10 @ SV12 ) @ ( pl @ SV9 @ SV11 ) @ SX0 ) )
= $true ) ),
inference(res,[status(thm)],[45,15]) ).
thf(58,plain,
! [SV11: nat,SV12: nat] :
( ( ( some
@ ^ [SX0: nat] : ( diffprop @ ( pl @ y @ SV12 ) @ ( pl @ x @ SV11 ) @ SX0 ) )
= $true )
| ( ( moreis @ SV12 @ SV11 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV9,$thf( x )),bind(SV10,$thf( y ))]]) ).
thf(130,plain,
! [SV13: nat,SV14: nat] :
( ( ( some
@ ^ [SX0: nat] : ( diffprop @ ( pl @ y @ SV14 ) @ ( pl @ x @ SV13 ) @ SX0 ) )
= $true )
| ( ( moreis @ SV14 @ SV13 )
= $false ) ),
inference(rename,[status(thm)],[58]) ).
thf(145,plain,
! [SV13: nat,SV14: nat] :
( ( ( ( some
@ ^ [SX0: nat] : ( diffprop @ ( pl @ y @ SV14 ) @ ( pl @ x @ SV13 ) @ SX0 ) )
= ( some
@ ^ [Xv: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Xv ) ) )
= $false )
| ( ( moreis @ SV14 @ SV13 )
= $false ) ),
inference(res,[status(thm)],[130,22]) ).
thf(148,plain,
( ( moreis @ u @ z )
= $false ),
inference(extuni,[status(esa)],[145:[bind(SV13,$thf( z )),bind(SV14,$thf( u ))]]) ).
thf(161,plain,
( ( ( moreis @ u @ z )
= ( moreis @ u @ z ) )
= $false ),
inference(res,[status(thm)],[148,44]) ).
thf(168,plain,
$false = $true,
inference(extuni,[status(esa)],[161]) ).
thf(169,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM690^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n017.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 13:30:31 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.42/0.53
% 1.42/0.53 No.of.Axioms: 4
% 1.42/0.53
% 1.42/0.53 Length.of.Defs: 0
% 1.42/0.53
% 1.42/0.53 Contains.Choice.Funs: false
% 1.42/0.53 ...
% 1.42/0.53
% 1.42/0.53 ********************************
% 1.42/0.53 * All subproblems solved! *
% 1.42/0.53 ********************************
% 1.42/0.53 % 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:168,loop_count:11,foatp_calls:3,translation:fof_experiment)
% 1.42/0.53
% 1.42/0.53 %**** Beginning of derivation protocol ****
% 1.42/0.53 % SZS output start CNFRefutation
% See solution above
% 1.42/0.53
% 1.42/0.53 %**** End of derivation protocol ****
% 1.42/0.53 %**** no. of clauses in derivation: 44 ****
% 1.42/0.53 %**** clause counter: 168 ****
% 1.42/0.53
% 1.42/0.53 % 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:168,loop_count:11,foatp_calls:3,translation:fof_experiment)
%------------------------------------------------------------------------------