%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV254-2 : 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 : n013.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 10:56:39 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 69 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 199 ( 25 ~; 22 |; 0 &; 152 @)
% ( 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 : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 69 ( 0 ^; 69 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_SetInterval_OatLeastLessThan,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_emptyset,type,
c_emptyset: $i ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_nat,type,
v_nat: $i ).
thf(tp_v_x,type,
v_x: $i > $i ).
thf(1,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(2,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( c_emptyset
!= ( c_insert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(3,axiom,
! [V_m: $i] :
( ( c_SetInterval_OatLeastLessThan @ V_m @ ( c_Suc @ V_m ) @ tc_nat )
= ( c_insert @ V_m @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
thf(4,axiom,
! [T_a: $i,V_n: $i,V_m: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_lessequals @ V_n @ V_m @ T_a )
| ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
! [V_U: $i] :
( ( v_x @ V_U )
= v_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,negated_conjecture,
! [V_U: $i] : ( c_lessequals @ V_U @ ( v_x @ V_U ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(10,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( c_emptyset
!= ( c_insert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [V_m: $i] :
( ( c_SetInterval_OatLeastLessThan @ V_m @ ( c_Suc @ V_m ) @ tc_nat )
= ( c_insert @ V_m @ c_emptyset @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [T_a: $i,V_n: $i,V_m: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_lessequals @ V_n @ V_m @ T_a )
| ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
= c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [V_U: $i] :
( ( v_x @ V_U )
= v_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(15,plain,
( ( ! [V_U: $i] : ( c_lessequals @ V_U @ ( v_x @ V_U ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( c_emptyset
!= ( c_insert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(18,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_n: $i,V_m: $i] :
( ~ ( c_lessequals @ V_n @ V_m @ T_a )
| ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
= c_emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(19,plain,
( ( ! [V_U: $i] : ( c_lessequals @ V_U @ ( v_x @ V_U ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(20,plain,
( ( ! [V_U: $i] :
( ( v_x @ V_U )
= v_nat ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_n: $i,V_m: $i] :
( ~ ( c_lessequals @ V_n @ V_m @ T_a )
| ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
= c_emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [V_m: $i] :
( ( c_SetInterval_OatLeastLessThan @ V_m @ ( c_Suc @ V_m ) @ tc_nat )
= ( c_insert @ V_m @ c_emptyset @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( c_emptyset
!= ( c_insert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
! [SV1: $i] :
( ( c_lessequals @ SV1 @ ( v_x @ SV1 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( v_x @ SV2 )
= v_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV3: $i] :
( ( ~ ( class_Orderings_Oorder @ SV3 )
| ! [SY9: $i,SY10: $i] :
( ~ ( c_lessequals @ SY9 @ SY10 @ SV3 )
| ( ( c_SetInterval_OatLeastLessThan @ SY10 @ SY9 @ SV3 )
= c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( c_SetInterval_OatLeastLessThan @ SV4 @ ( c_Suc @ SV4 ) @ tc_nat )
= ( c_insert @ SV4 @ c_emptyset @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV5: $i] :
( ( ! [SY11: $i,SY12: $i] :
( c_emptyset
!= ( c_insert @ SV5 @ SY11 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV3: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV3 ) )
= $true )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( c_lessequals @ SY9 @ SY10 @ SV3 )
| ( ( c_SetInterval_OatLeastLessThan @ SY10 @ SY9 @ SV3 )
= c_emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV6: $i,SV5: $i] :
( ( ! [SY13: $i] :
( c_emptyset
!= ( c_insert @ SV5 @ SV6 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: $i] :
( ( ( class_Orderings_Oorder @ SV3 )
= $false )
| ( ( ! [SY9: $i,SY10: $i] :
( ~ ( c_lessequals @ SY9 @ SY10 @ SV3 )
| ( ( c_SetInterval_OatLeastLessThan @ SY10 @ SY9 @ SV3 )
= c_emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV7: $i,SV6: $i,SV5: $i] :
( ( c_emptyset
!= ( c_insert @ SV5 @ SV6 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: $i,SV8: $i] :
( ( ( ! [SY14: $i] :
( ~ ( c_lessequals @ SV8 @ SY14 @ SV3 )
| ( ( c_SetInterval_OatLeastLessThan @ SY14 @ SV8 @ SV3 )
= c_emptyset ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV7: $i,SV6: $i,SV5: $i] :
( ( c_emptyset
= ( c_insert @ SV5 @ SV6 @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: $i,SV9: $i,SV8: $i] :
( ( ( ~ ( c_lessequals @ SV8 @ SV9 @ SV3 )
| ( ( c_SetInterval_OatLeastLessThan @ SV9 @ SV8 @ SV3 )
= c_emptyset ) )
= $true )
| ( ( class_Orderings_Oorder @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: $i,SV9: $i,SV8: $i] :
( ( ( ~ ( c_lessequals @ SV8 @ SV9 @ SV3 ) )
= $true )
| ( ( ( c_SetInterval_OatLeastLessThan @ SV9 @ SV8 @ SV3 )
= c_emptyset )
= $true )
| ( ( class_Orderings_Oorder @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV3: $i,SV9: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV9 @ SV3 )
= $false )
| ( ( ( c_SetInterval_OatLeastLessThan @ SV9 @ SV8 @ SV3 )
= c_emptyset )
= $true )
| ( ( class_Orderings_Oorder @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,40,37,31,29,27,26]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV254-2 : 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
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 16:20:36 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20
% 0.08/0.20 No.of.Axioms: 6
% 0.08/0.20
% 0.08/0.20 Length.of.Defs: 0
% 0.08/0.20
% 0.08/0.20 Contains.Choice.Funs: false
% 0.08/0.20 .
% 0.08/0.20
% 0.08/0.20 ********************************
% 0.08/0.20 * All subproblems solved! *
% 0.08/0.20 ********************************
% 0.08/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.20
% 0.08/0.20 %**** Beginning of derivation protocol ****
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20
% 0.08/0.20 %**** End of derivation protocol ****
% 0.08/0.20 %**** no. of clauses in derivation: 42 ****
% 0.08/0.20 %**** clause counter: 41 ****
% 0.08/0.20
% 0.08/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------