%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM672^1 : 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 : n020.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 10:34:52 AM UTC 2026
% Result : Theorem 0.06s 0.22s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 220 ( 17 ~; 19 |; 0 &; 178 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 ^; 59 !; 0 ?; 59 :)
% 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_pl,type,
pl: nat > nat > 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] :
( ( less @ Xx @ Xy )
=> ( more @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz12) ).
thf(2,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( more @ Xx @ Xy )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(3,axiom,
! [Xx: nat,Xy: nat] :
( ( more @ Xx @ Xy )
=> ( less @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz11) ).
thf(4,axiom,
less @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(5,conjecture,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19c) ).
thf(6,negated_conjecture,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( less @ Xx @ Xy )
=> ( more @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( more @ Xx @ Xy )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( more @ Xx @ Xy )
=> ( less @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( less @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xx @ Xy )
| ( more @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(14,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( more @ Xx @ Xy )
| ! [Xz: nat] : ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( more @ Xx @ Xy )
| ( less @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(16,plain,
( ( less @ x @ y )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( more @ Xx @ Xy )
| ( less @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( more @ Xx @ Xy )
| ! [Xz: nat] : ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xx @ Xy )
| ( more @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
! [SV1: nat] :
( ( ! [SY7: nat] :
( ~ ( more @ SV1 @ SY7 )
| ( less @ SY7 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: nat] :
( ( ! [SY8: nat] :
( ~ ( more @ SV2 @ SY8 )
| ! [SY9: nat] : ( more @ ( pl @ SV2 @ SY9 ) @ ( pl @ SY8 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: nat] :
( ( ! [SY10: nat] :
( ~ ( less @ SV3 @ SY10 )
| ( more @ SY10 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV4: nat,SV1: nat] :
( ( ~ ( more @ SV1 @ SV4 )
| ( less @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV5: nat,SV2: nat] :
( ( ~ ( more @ SV2 @ SV5 )
| ! [SY11: nat] : ( more @ ( pl @ SV2 @ SY11 ) @ ( pl @ SV5 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV6: nat,SV3: nat] :
( ( ~ ( less @ SV3 @ SV6 )
| ( more @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: nat,SV1: nat] :
( ( ( ~ ( more @ SV1 @ SV4 ) )
= $true )
| ( ( less @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV5: nat,SV2: nat] :
( ( ( ~ ( more @ SV2 @ SV5 ) )
= $true )
| ( ( ! [SY11: nat] : ( more @ ( pl @ SV2 @ SY11 ) @ ( pl @ SV5 @ SY11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV6: nat,SV3: nat] :
( ( ( ~ ( less @ SV3 @ SV6 ) )
= $true )
| ( ( more @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: nat,SV1: nat] :
( ( ( more @ SV1 @ SV4 )
= $false )
| ( ( less @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: nat,SV2: nat] :
( ( ( more @ SV2 @ SV5 )
= $false )
| ( ( ! [SY11: nat] : ( more @ ( pl @ SV2 @ SY11 ) @ ( pl @ SV5 @ SY11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV6: nat,SV3: nat] :
( ( ( less @ SV3 @ SV6 )
= $false )
| ( ( more @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV5: nat,SV7: nat,SV2: nat] :
( ( ( more @ ( pl @ SV2 @ SV7 ) @ ( pl @ SV5 @ SV7 ) )
= $true )
| ( ( more @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,34,33,31,24]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM672^1 : 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
% 0.06/0.19 % Computer : n020.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 13:34:59 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.22
% 0.06/0.22 No.of.Axioms: 4
% 0.06/0.22
% 0.06/0.22 Length.of.Defs: 0
% 0.06/0.22
% 0.06/0.22 Contains.Choice.Funs: false
% 0.06/0.22
% 0.06/0.22 ********************************
% 0.06/0.22 * All subproblems solved! *
% 0.06/0.22 ********************************
% 0.06/0.22 % 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:35,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.06/0.22
% 0.06/0.22 %**** Beginning of derivation protocol ****
% 0.06/0.22 % SZS output start CNFRefutation
% See solution above
% 0.06/0.22
% 0.06/0.22 %**** End of derivation protocol ****
% 0.06/0.22 %**** no. of clauses in derivation: 36 ****
% 0.06/0.22 %**** clause counter: 35 ****
% 0.06/0.22
% 0.06/0.22 % 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:35,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------