%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV402+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 10:57:35 AM UTC 2026
% Result : Theorem 0.06s 0.30s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 283 ( 78 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 507 ( 124 ~; 53 |; 10 &; 310 @)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 91 ( 0 ^; 91 !; 0 ?; 91 :)
% 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_sK2_V,type,
sK2_V: $i ).
thf(tp_sK3_SY13,type,
sK3_SY13: $i ).
thf(tp_sK4_SY15,type,
sK4_SY15: $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/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(9,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(11,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(13,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(15,axiom,
! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(19,conjecture,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ create_slb @ V @ W )
& ( strictly_less_than @ W @ X ) )
=> ( pair_in_list @ ( update_slb @ create_slb @ X ) @ V @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l38_co) ).
thf(20,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ create_slb @ V @ W )
& ( strictly_less_than @ W @ X ) )
=> ( pair_in_list @ ( update_slb @ create_slb @ X ) @ V @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ create_slb @ V @ W )
& ( strictly_less_than @ W @ X ) )
=> ( pair_in_list @ ( update_slb @ create_slb @ X ) @ V @ X ) ) )
= $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,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(27,plain,
( ( ! [V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ create_slb @ V @ W )
& ( strictly_less_than @ W @ X ) )
=> ( pair_in_list @ ( update_slb @ create_slb @ X ) @ V @ X ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(28,plain,
( ( ! [SY13: $i,SY14: $i] :
( ( ( pair_in_list @ create_slb @ sK2_V @ SY13 )
& ( strictly_less_than @ SY13 @ SY14 ) )
=> ( pair_in_list @ ( update_slb @ create_slb @ SY14 ) @ sK2_V @ SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( ! [SY15: $i] :
( ( ( pair_in_list @ create_slb @ sK2_V @ sK3_SY13 )
& ( strictly_less_than @ sK3_SY13 @ SY15 ) )
=> ( pair_in_list @ ( update_slb @ create_slb @ SY15 ) @ sK2_V @ SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( ( ( pair_in_list @ create_slb @ sK2_V @ sK3_SY13 )
& ( strictly_less_than @ sK3_SY13 @ sK4_SY15 ) )
=> ( pair_in_list @ ( update_slb @ create_slb @ sK4_SY15 ) @ sK2_V @ sK4_SY15 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(31,plain,
( ( pair_in_list @ create_slb @ sK2_V @ sK3_SY13 )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(32,plain,
( ( strictly_less_than @ sK3_SY13 @ sK4_SY15 )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(33,plain,
( ( pair_in_list @ ( update_slb @ create_slb @ sK4_SY15 ) @ sK2_V @ sK4_SY15 )
= $false ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( pair_in_list @ ( update_slb @ create_slb @ sK4_SY15 ) @ sK2_V @ sK4_SY15 ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(36,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(37,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(38,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(39,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(40,plain,
( ( strictly_less_than @ sK3_SY13 @ sK4_SY15 )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(41,plain,
( ( pair_in_list @ create_slb @ sK2_V @ sK3_SY13 )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(42,plain,
( ( ~ ( pair_in_list @ ( update_slb @ create_slb @ sK4_SY15 ) @ sK2_V @ sK4_SY15 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(43,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) )
| ( strictly_less_than @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(44,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV1: $i] :
( ( ~ ( contains_slb @ create_slb @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY16: $i] :
~ ( pair_in_list @ create_slb @ SV2 @ SY16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV3: $i] :
( ( ( update_slb @ create_slb @ SV3 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
( ( pair_in_list @ ( update_slb @ create_slb @ sK4_SY15 ) @ sK2_V @ sK4_SY15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV4: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV4 @ SY17 )
| ~ ( ~ ( less_than @ SV4 @ SY17 )
| ~ ~ ( less_than @ SY17 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV4 @ SY17 )
| ~ ~ ( less_than @ SY17 @ SV4 ) )
| ( strictly_less_than @ SV4 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV1: $i] :
( ( contains_slb @ create_slb @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV4 @ SV6 )
| ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) )
| ( strictly_less_than @ SV4 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV5: $i,SV2: $i] :
( ( pair_in_list @ create_slb @ SV2 @ SV5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV4 @ SV6 )
| ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) )
| ( strictly_less_than @ SV4 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV4 @ SV6 )
| ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(56,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) )
| ( strictly_less_than @ SV4 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(57,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( strictly_less_than @ SV4 @ SV6 )
| ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(58,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) )
| ( strictly_less_than @ SV4 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( strictly_less_than @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) )
= $true )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV6: $i,SV4: $i] :
( ( ( strictly_less_than @ SV4 @ SV6 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) ) )
= $false )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) )
= $false )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( less_than @ SV4 @ SV6 )
| ~ ~ ( less_than @ SV6 @ SV4 ) )
= $true )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(65,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( less_than @ SV4 @ SV6 ) )
= $false )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(66,plain,
! [SV4: $i,SV6: $i] :
( ( ( ~ ~ ( less_than @ SV6 @ SV4 ) )
= $false )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(67,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( less_than @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV6 @ SV4 ) )
= $true )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV6: $i,SV4: $i] :
( ( ( less_than @ SV4 @ SV6 )
= $true )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV4: $i,SV6: $i] :
( ( ( ~ ( less_than @ SV6 @ SV4 ) )
= $true )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(70,plain,
! [SV6: $i,SV4: $i] :
( ( ( less_than @ SV4 @ SV6 )
= $false )
| ( ( ~ ~ ( less_than @ SV6 @ SV4 ) )
= $true )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV4: $i,SV6: $i] :
( ( ( less_than @ SV6 @ SV4 )
= $false )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV4: $i,SV6: $i] :
( ( ( ~ ( less_than @ SV6 @ SV4 ) )
= $false )
| ( ( less_than @ SV4 @ SV6 )
= $false )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(73,plain,
! [SV4: $i,SV6: $i] :
( ( ( less_than @ SV6 @ SV4 )
= $true )
| ( ( less_than @ SV4 @ SV6 )
= $false )
| ( ( strictly_less_than @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(74,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,73,71,68,53,50,48,47,44,41]) ).
thf(75,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV402+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.21 % Computer : n011.cluster.edu
% 0.06/0.21 % Model : x86_64 x86_64
% 0.06/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.21 % Memory : 8046.5625MB
% 0.06/0.21 % OS : Linux 6.8.0-71-generic
% 0.06/0.21 % CPULimit : 300
% 0.06/0.21 % WCLimit : 300
% 0.06/0.21 % DateTime : Tue Oct 6 16:27:36 UTC 2026
% 0.06/0.22 % CPUTime :
% 0.06/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.30
% 0.06/0.30 No.of.Axioms: 5
% 0.06/0.30
% 0.06/0.30 Length.of.Defs: 0
% 0.06/0.30
% 0.06/0.30 Contains.Choice.Funs: false
% 0.06/0.30 .
% 0.06/0.30
% 0.06/0.30 ********************************
% 0.06/0.30 * All subproblems solved! *
% 0.06/0.30 ********************************
% 0.06/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:74,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.30
% 0.06/0.30 %**** Beginning of derivation protocol ****
% 0.06/0.30 % SZS output start CNFRefutation
% See solution above
% 0.06/0.30
% 0.06/0.30 %**** End of derivation protocol ****
% 0.06/0.30 %**** no. of clauses in derivation: 62 ****
% 0.06/0.30 %**** clause counter: 74 ****
% 0.06/0.30
% 0.06/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:74,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------