%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM635^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:34:43 AM UTC 2026
% Result : Theorem 0.08s 0.12s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 50 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 58 ( 18 ~; 5 |; 0 &; 32 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
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] :
( ( ( suc @ Xx )
= ( suc @ Xy ) )
=> ( Xx = Xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(2,axiom,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(3,conjecture,
( ( suc @ x )
!= ( suc @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz1) ).
thf(4,negated_conjecture,
( ( ( suc @ x )
!= ( suc @ y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ( suc @ x )
!= ( suc @ y ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ( suc @ Xx )
= ( suc @ Xy ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( x != y )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ( ( ( suc @ x )
!= ( suc @ y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( x != y )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ( suc @ Xx )
= ( suc @ Xy ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(11,plain,
( ( ~ ( ( ( suc @ x )
!= ( suc @ y ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( x != y )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( ( ( suc @ x )
!= ( suc @ y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( suc @ SX0 )
!= ( suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(15,plain,
( ( x = y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ( suc @ x )
!= ( suc @ y ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: nat] :
( ( ! [SY2: nat] :
( ( ( suc @ SV1 )
!= ( suc @ SY2 ) )
| ( SV1 = SY2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ( suc @ x )
= ( suc @ y ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV2: nat,SV1: nat] :
( ( ( ( suc @ SV1 )
!= ( suc @ SV2 ) )
| ( SV1 = SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV2: nat,SV1: nat] :
( ( ( ( suc @ SV1 )
!= ( suc @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(21,plain,
! [SV2: nat,SV1: nat] :
( ( ( ( suc @ SV1 )
= ( suc @ SV2 ) )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,21,18]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM635^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 13:30:46 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.12
% 0.08/0.12 No.of.Axioms: 2
% 0.08/0.12
% 0.08/0.12 Length.of.Defs: 0
% 0.08/0.12
% 0.08/0.12 Contains.Choice.Funs: false
% 0.08/0.12
% 0.08/0.12 ********************************
% 0.08/0.12 * All subproblems solved! *
% 0.08/0.12 ********************************
% 0.08/0.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.12
% 0.08/0.12 %**** Beginning of derivation protocol ****
% 0.08/0.12 % SZS output start CNFRefutation
% See solution above
% 0.08/0.12
% 0.08/0.12 %**** End of derivation protocol ****
% 0.08/0.12 %**** no. of clauses in derivation: 23 ****
% 0.08/0.12 %**** clause counter: 22 ****
% 0.08/0.12
% 0.08/0.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:22,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------