%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV410+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n002.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 10:57:36 AM UTC 2026
% Result : Theorem 0.08s 0.22s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 33 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 113 ( 21 ~; 0 |; 0 &; 88 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 36 ( 0 ^; 29 !; 7 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bottom,type,
bottom: $i ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(3,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(9,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(11,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(13,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(19,conjecture,
! [U: $i] :
( ( contains_slb @ create_slb @ U )
=> ? [V: $i] : ( pair_in_list @ create_slb @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_co) ).
thf(20,negated_conjecture,
( ( ! [U: $i] :
( ( contains_slb @ create_slb @ U )
=> ? [V: $i] : ( pair_in_list @ create_slb @ U @ V ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [U: $i] :
( ( contains_slb @ create_slb @ U )
=> ? [V: $i] : ( pair_in_list @ create_slb @ U @ V ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(25,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ( contains_slb @ create_slb @ sK1_U )
=> ? [SY6: $i] : ( pair_in_list @ create_slb @ sK1_U @ SY6 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(27,plain,
( ( contains_slb @ create_slb @ sK1_U )
= $true ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(28,plain,
( ( ? [SY6: $i] : ( pair_in_list @ create_slb @ sK1_U @ SY6 ) )
= $false ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ? [SY6: $i] : ( pair_in_list @ create_slb @ sK1_U @ SY6 ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(30,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(31,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(32,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(33,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(34,plain,
( ( contains_slb @ create_slb @ sK1_U )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(35,plain,
( ( ~ ? [SY6: $i] : ( pair_in_list @ create_slb @ sK1_U @ SY6 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( pair_in_list @ create_slb @ sK1_U @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV1: $i] :
( ( ~ ( contains_slb @ create_slb @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV2: $i] :
( ( ! [SY7: $i] :
~ ( pair_in_list @ create_slb @ SV2 @ SY7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV3: $i] :
( ( ( update_slb @ create_slb @ SV3 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
( ( ~ ! [SX0: $i] :
~ ( pair_in_list @ create_slb @ sK1_U @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV1: $i] :
( ( contains_slb @ create_slb @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ! [SX0: $i] :
~ ( pair_in_list @ create_slb @ sK1_U @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV4: $i,SV2: $i] :
( ( pair_in_list @ create_slb @ SV2 @ SV4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV5: $i] :
( ( ~ ( pair_in_list @ create_slb @ sK1_U @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV5: $i] :
( ( pair_in_list @ create_slb @ sK1_U @ SV5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,47,45,42,40,37]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV410+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n002.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 16:30:42 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
% 0.08/0.22
% 0.08/0.22 No.of.Axioms: 4
% 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 * All subproblems solved! *
% 0.08/0.22 ********************************
% 0.08/0.22 % SZS status Theorem 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:48,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: 35 ****
% 0.08/0.22 %**** clause counter: 48 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Theorem 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:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------