%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM640^1 : 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 : n013.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 10:34:44 AM UTC 2026
% Result : Theorem 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 21 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 68 ( 2 ~; 0 |; 0 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 1 ( 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 : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ ( suc @ Xy ) )
= ( suc @ ( pl @ Xx @ Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4b) ).
thf(2,conjecture,
( ( suc @ ( pl @ x @ y ) )
= ( pl @ x @ ( suc @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4f) ).
thf(3,negated_conjecture,
( ( ( suc @ ( pl @ x @ y ) )
= ( pl @ x @ ( suc @ y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ( suc @ ( pl @ x @ y ) )
= ( pl @ x @ ( suc @ y ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ ( suc @ Xy ) )
= ( suc @ ( pl @ Xx @ Xy ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(6,plain,
( ( ( suc @ ( pl @ x @ y ) )
!= ( pl @ x @ ( suc @ y ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ ( suc @ Xy ) )
= ( suc @ ( pl @ Xx @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(8,plain,
( ( ( suc @ ( pl @ x @ y ) )
!= ( pl @ x @ ( suc @ y ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
! [SV1: nat] :
( ( ! [SY2: nat] :
( ( pl @ SV1 @ ( suc @ SY2 ) )
= ( suc @ ( pl @ SV1 @ SY2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(10,plain,
( ( ( suc @ ( pl @ x @ y ) )
= ( pl @ x @ ( suc @ y ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(11,plain,
! [SV2: nat,SV1: nat] :
( ( ( pl @ SV1 @ ( suc @ SV2 ) )
= ( suc @ ( pl @ SV1 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(12,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,11]) ).
thf(13,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM640^1 : 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
% 0.10/0.18 % Computer : n013.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 13:30:36 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 1
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 0
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: false
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:12,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 13 ****
% 0.10/0.22 %**** clause counter: 12 ****
% 0.10/0.22
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:12,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------