%------------------------------------------------------------------------------
% 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 : n009.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 : Unsatisfiable 0.08s 0.22s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 101 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 197 ( 7 ~; 0 |; 0 &; 190 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_impl,type,
impl: $i > $i > $i ).
thf(tp_plus_not_idem,type,
plus_not_idem: $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,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(2,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(3,axiom,
! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(4,axiom,
! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(6,axiom,
( ( eq2 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(7,axiom,
( ( eq2 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(8,axiom,
! [X: $i] :
( ( plus_not_idem @ X )
= ( impl @ ( eq @ ( x2 @ X @ X ) @ X ) @ ( eq2 @ btrue @ bfalse ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(9,axiom,
! [N: $i,Y: $i] :
( ( x2 @ ( s @ N ) @ Y )
= ( s @ ( x2 @ N @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(10,axiom,
! [Y: $i] :
( ( x2 @ z @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(11,axiom,
! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(12,axiom,
! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
! [X: $i] :
( ( eq2 @ ( plus_not_idem @ X ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ( eq2 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ( eq2 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( plus_not_idem @ X )
= ( impl @ ( eq @ ( x2 @ X @ X ) @ X ) @ ( eq2 @ btrue @ bfalse ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [N: $i,Y: $i] :
( ( x2 @ ( s @ N ) @ Y )
= ( s @ ( x2 @ N @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [Y: $i] :
( ( x2 @ z @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( eq2 @ ( plus_not_idem @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( eq2 @ ( plus_not_idem @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( eq2 @ ( plus_not_idem @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(33,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(34,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(35,plain,
( ( ! [Y: $i] :
( ( x2 @ z @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(36,plain,
( ( ! [N: $i,Y: $i] :
( ( x2 @ ( s @ N ) @ Y )
= ( s @ ( x2 @ N @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( plus_not_idem @ X )
= ( impl @ ( eq @ ( x2 @ X @ X ) @ X ) @ ( eq2 @ btrue @ bfalse ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(38,plain,
( ( ( eq2 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(39,plain,
( ( ( eq2 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(42,plain,
( ( ! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(45,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[30]) ).
thf(46,plain,
! [SV1: $i] :
( ( ( eq2 @ ( plus_not_idem @ SV1 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(47,plain,
! [SV2: $i] :
( ( ( impl @ btrue @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(48,plain,
! [SV3: $i] :
( ( ( impl @ bfalse @ SV3 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(49,plain,
! [SV4: $i] :
( ( ( x2 @ z @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(50,plain,
! [SV5: $i] :
( ( ! [SY13: $i] :
( ( x2 @ ( s @ SV5 ) @ SY13 )
= ( s @ ( x2 @ SV5 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV6: $i] :
( ( ( plus_not_idem @ SV6 )
= ( impl @ ( eq @ ( x2 @ SV6 @ SV6 ) @ SV6 ) @ ( eq2 @ btrue @ bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV7: $i] :
( ( ! [SY14: $i] :
( ( eq @ ( s @ SV7 ) @ ( s @ SY14 ) )
= ( eq @ SV7 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(53,plain,
! [SV8: $i] :
( ( ( eq @ z @ ( s @ SV8 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(54,plain,
! [SV9: $i] :
( ( ( eq @ ( s @ SV9 ) @ z )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(55,plain,
! [SV10: $i] :
( ( ( eq @ SV10 @ SV10 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(56,plain,
! [SV11: $i] :
( ( ( eq2 @ SV11 @ SV11 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(57,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(58,plain,
! [SV1: $i] :
( ( ( eq2 @ ( plus_not_idem @ SV1 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(59,plain,
! [SV12: $i,SV5: $i] :
( ( ( x2 @ ( s @ SV5 ) @ SV12 )
= ( s @ ( x2 @ SV5 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV13: $i,SV7: $i] :
( ( ( eq @ ( s @ SV7 ) @ ( s @ SV13 ) )
= ( eq @ SV7 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,60,59,58,57,56,55,54,53,51,49,48,47,39]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----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
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 17:11:32 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.22
% 0.08/0.22 No.of.Axioms: 13
% 0.08/0.22
% 0.08/0.22 Length.of.Defs: 0
% 0.08/0.22
% 0.08/0.22 Contains.Choice.Funs: false
% 0.08/0.22 .
% 0.08/0.22
% 0.08/0.22 ********************************
% 0.08/0.22 * All subproblems solved! *
% 0.08/0.22 ********************************
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.22
% 0.08/0.22 %**** Beginning of derivation protocol ****
% 0.08/0.22 % SZS output start CNFRefutation
% See solution above
% 0.08/0.22
% 0.08/0.22 %**** End of derivation protocol ****
% 0.08/0.22 %**** no. of clauses in derivation: 62 ****
% 0.08/0.22 %**** clause counter: 61 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------