%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n016.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 10:09:34 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 44 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 186 ( 14 ~; 11 |; 0 &; 161 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_1,type,
c_1: $i ).
thf(tp_c_HOL_Oabs,type,
c_HOL_Oabs: $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_less,type,
c_less: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_minus,type,
c_minus: $i > $i > $i > $i ).
thf(tp_c_times,type,
c_times: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_c,type,
v_c: $i ).
thf(tp_v_f,type,
v_f: $i > $i ).
thf(tp_v_h,type,
v_h: $i > $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(1,axiom,
! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(2,axiom,
! [V_x: $i] :
( ~ ( c_less @ c_0 @ V_x @ tc_nat )
| ( V_x
= ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(6,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(7,negated_conjecture,
! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(9,plain,
( ( ! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [V_x: $i] :
( ~ ( c_less @ c_0 @ V_x @ tc_nat )
| ( V_x
= ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(12,plain,
( ( v_x != c_0 )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(13,plain,
( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( v_x != c_0 )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [V_x: $i] :
( ~ ( c_less @ c_0 @ V_x @ tc_nat )
| ( V_x
= ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( v_x != c_0 )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(22,plain,
! [SV1: $i] :
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ SV1 ) ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ SV1 ) ) @ t_a ) @ t_a ) @ t_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(23,plain,
( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ t_a ) @ t_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV2: $i] :
( ( ~ ( c_less @ c_0 @ SV2 @ tc_nat )
| ( SV2
= ( c_Suc @ ( c_minus @ SV2 @ c_1 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV3: $i] :
( ( ( c_less @ c_0 @ SV3 @ tc_nat )
| ( SV3 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(27,plain,
( ( v_x = c_0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV2: $i] :
( ( ( ~ ( c_less @ c_0 @ SV2 @ tc_nat ) )
= $true )
| ( ( SV2
= ( c_Suc @ ( c_minus @ SV2 @ c_1 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: $i] :
( ( ( c_less @ c_0 @ SV3 @ tc_nat )
= $true )
| ( ( SV3 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( c_less @ c_0 @ SV2 @ tc_nat )
= $false )
| ( ( SV2
= ( c_Suc @ ( c_minus @ SV2 @ c_1 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,30,29,27,26,23]) ).
thf(32,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 18:22:14 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 5
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 32 ****
% 0.07/0.22 %**** clause counter: 31 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------