%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX206+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n014.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 11:02:33 AM UTC 2026
% Result : Theorem 0.09s 0.22s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 50 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 77 ( 9 ~; 0 |; 0 &; 68 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 28 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_proj1S,type,
proj1S: $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_x2,type,
x2: $i > $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [Y: $i,N: $i] :
( ( x2 @ ( s @ N ) @ Y )
= ( s @ ( x2 @ N @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(2,axiom,
! [Y: $i] :
( ( x2 @ z @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(3,axiom,
! [X: $i] :
( z
!= ( s @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(4,axiom,
! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(5,conjecture,
? [X: $i] :
( ( x2 @ X @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_005) ).
thf(6,negated_conjecture,
( ( ? [X: $i] :
( ( x2 @ X @ X )
= X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ? [X: $i] :
( ( x2 @ X @ X )
= X ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Y: $i,N: $i] :
( ( x2 @ ( s @ N ) @ Y )
= ( s @ ( x2 @ N @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [Y: $i] :
( ( x2 @ z @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ? [X: $i] :
( ( x2 @ X @ X )
= X ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [X: $i] :
( ( x2 @ X @ X )
!= X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(14,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [Y: $i] :
( ( x2 @ z @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(18,plain,
( ( ! [Y: $i,N: $i] :
( ( x2 @ ( s @ N ) @ Y )
= ( s @ ( x2 @ N @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( x2 @ X @ X )
!= X ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( proj1S @ ( s @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV2: $i] :
( ( z
!= ( s @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV3: $i] :
( ( ( x2 @ z @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV4: $i] :
( ( ! [SY6: $i] :
( ( x2 @ ( s @ SY6 ) @ SV4 )
= ( s @ ( x2 @ SY6 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV5: $i] :
( ( ( x2 @ SV5 @ SV5 )
!= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV2: $i] :
( ( z
= ( s @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV4: $i,SV6: $i] :
( ( ( x2 @ ( s @ SV6 ) @ SV4 )
= ( s @ ( x2 @ SV6 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV5: $i] :
( ( ( x2 @ SV5 @ SV5 )
= SV5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,27,26,25,22]) ).
thf(29,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX206+1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 17:11:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.22
% 0.09/0.22 No.of.Axioms: 4
% 0.09/0.22
% 0.09/0.22 Length.of.Defs: 0
% 0.09/0.22
% 0.09/0.22 Contains.Choice.Funs: false
% 0.09/0.22
% 0.09/0.22 ********************************
% 0.09/0.22 * All subproblems solved! *
% 0.09/0.22 ********************************
% 0.09/0.22 % 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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.09/0.22
% 0.09/0.22 %**** Beginning of derivation protocol ****
% 0.09/0.22 % SZS output start CNFRefutation
% See solution above
% 0.09/0.22
% 0.09/0.22 %**** End of derivation protocol ****
% 0.09/0.22 %**** no. of clauses in derivation: 29 ****
% 0.09/0.22 %**** clause counter: 28 ****
% 0.09/0.22
% 0.09/0.22 % 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:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------