%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV414+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 : n020.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 10:57:37 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 53 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 143 ( 21 ~; 0 |; 0 &; 122 @)
% ( 0 <=>; 0 =>; 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 : 50 ( 47 usr; 8 con; 0-3 aty)
% Number of variables : 49 ( 0 ^; 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_pq,type,
contains_pq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_pq,type,
create_pq: $i ).
thf(tp_create_pqp,type,
create_pqp: $i ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pq_eff,type,
findmin_pq_eff: $i > $i > $i ).
thf(tp_findmin_pq_res,type,
findmin_pq_res: $i > $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pq,type,
insert_pq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_pq,type,
isnonempty_pq: $i > $o ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_issmallestelement_pq,type,
issmallestelement_pq: $i > $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_phi,type,
phi: $i > $o ).
thf(tp_pi_find_min,type,
pi_find_min: $i > $o ).
thf(tp_pi_remove,type,
pi_remove: $i > $i > $o ).
thf(tp_pi_removemin,type,
pi_removemin: $i > $o ).
thf(tp_pi_sharp_find_min,type,
pi_sharp_find_min: $i > $i > $o ).
thf(tp_pi_sharp_remove,type,
pi_sharp_remove: $i > $i > $o ).
thf(tp_pi_sharp_removemin,type,
pi_sharp_removemin: $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pq,type,
remove_pq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_removemin_pq_eff,type,
removemin_pq_eff: $i > $i > $i ).
thf(tp_removemin_pq_res,type,
removemin_pq_res: $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_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(9,axiom,
! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
thf(27,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(35,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(41,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(43,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(45,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(55,axiom,
! [U: $i] :
~ ( contains_pq @ create_pq @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(57,axiom,
~ ( isnonempty_pq @ create_pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(63,conjecture,
! [U: $i] :
( ( i @ ( triple @ create_pqp @ create_slb @ U ) )
= create_pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(64,negated_conjecture,
( ( ! [U: $i] :
( ( i @ ( triple @ create_pqp @ create_slb @ U ) )
= create_pq ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [U: $i] :
( ( i @ ( triple @ create_pqp @ create_slb @ U ) )
= create_pq ) )
= $false ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(67,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(68,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(69,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(70,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(71,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(72,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(73,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(74,plain,
( ( ( i @ ( triple @ create_pqp @ create_slb @ sK1_U ) )
= create_pq )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(75,plain,
( ( ( i @ ( triple @ create_pqp @ create_slb @ sK1_U ) )
!= create_pq )
= $true ),
inference(polarity_switch,[status(thm)],[74]) ).
thf(76,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(78,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(79,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(81,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(82,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(83,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(84,plain,
( ( ( i @ ( triple @ create_pqp @ create_slb @ sK1_U ) )
!= create_pq )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(85,plain,
( ( isnonempty_pq @ create_pq )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV1: $i] :
( ( ~ ( contains_pq @ create_pq @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV2: $i] :
( ( ~ ( contains_slb @ create_slb @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV3: $i] :
( ( ! [SY10: $i] :
~ ( pair_in_list @ create_slb @ SV3 @ SY10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV4: $i] :
( ( ( update_slb @ create_slb @ SV4 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV5: $i] :
( ( ! [SY11: $i] : ( check_cpq @ ( triple @ SV5 @ create_slb @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV6: $i] :
( ( ! [SY12: $i] :
( ( i @ ( triple @ SV6 @ create_slb @ SY12 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
( ( ( i @ ( triple @ create_pqp @ create_slb @ sK1_U ) )
= create_pq )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV1: $i] :
( ( contains_pq @ create_pq @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV2: $i] :
( ( contains_slb @ create_slb @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV8: $i,SV5: $i] :
( ( check_cpq @ ( triple @ SV5 @ create_slb @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV9: $i,SV6: $i] :
( ( ( i @ ( triple @ SV6 @ create_slb @ SV9 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV7: $i,SV3: $i] :
( ( pair_in_list @ create_slb @ SV3 @ SV7 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(100,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[85,99,98,97,95,94,93,90,87]) ).
thf(101,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV414+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % 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 : n020.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 16:28:51 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
% 0.08/0.26
% 0.08/0.26 No.of.Axioms: 8
% 0.08/0.26
% 0.08/0.26 Length.of.Defs: 0
% 0.08/0.26
% 0.08/0.26 Contains.Choice.Funs: false
% 0.08/0.26 .
% 0.08/0.26
% 0.08/0.26 ********************************
% 0.08/0.26 * All subproblems solved! *
% 0.08/0.26 ********************************
% 0.08/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:100,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.26
% 0.08/0.26 %**** Beginning of derivation protocol ****
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26
% 0.08/0.26 %**** End of derivation protocol ****
% 0.08/0.26 %**** no. of clauses in derivation: 47 ****
% 0.08/0.26 %**** clause counter: 100 ****
% 0.08/0.26
% 0.08/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:100,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------