%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM668^1 : 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 : n005.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 10:34:51 AM UTC 2026
% Result : Theorem 0.11s 0.20s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 42 ( 10 ~; 0 |; 0 &; 32 @)
% ( 0 <=>; 0 =>; 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 : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(1,conjecture,
~ ! [Xx_0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ Xx_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz18) ).
thf(2,negated_conjecture,
( ( ~ ! [Xx_0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ Xx_0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ! [Xx_0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ Xx_0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx_0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx_0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Xx_0: nat] :
( ( pl @ x @ y )
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
! [SV1: nat] :
( ( ( pl @ x @ y )
!= ( pl @ x @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: nat] :
( ( ( pl @ x @ y )
= ( pl @ x @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8]) ).
thf(10,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM668^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n005.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 13:33:53 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.20
% 0.11/0.20 No.of.Axioms: 0
% 0.11/0.20
% 0.11/0.20 Length.of.Defs: 0
% 0.11/0.20
% 0.11/0.20 Contains.Choice.Funs: false
% 0.11/0.20
% 0.11/0.20 ********************************
% 0.11/0.20 * All subproblems solved! *
% 0.11/0.20 ********************************
% 0.11/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:9,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.20
% 0.11/0.20 %**** Beginning of derivation protocol ****
% 0.11/0.20 % SZS output start CNFRefutation
% See solution above
% 0.11/0.20
% 0.11/0.20 %**** End of derivation protocol ****
% 0.11/0.20 %**** no. of clauses in derivation: 10 ****
% 0.11/0.20 %**** clause counter: 9 ****
% 0.11/0.20
% 0.11/0.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:9,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------