%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV367+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 : 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 10:57:30 AM UTC 2026
% Result : Theorem 0.57s 0.29s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 110 ( 85 unt; 0 typ; 0 def)
% Number of atoms : 469 ( 196 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 930 ( 123 ~; 96 |; 3 &; 690 @)
% ( 6 <=>; 12 =>; 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 : 51 ( 48 usr; 9 con; 0-3 aty)
% Number of variables : 224 ( 0 ^; 224 !; 0 ?; 224 :)
% 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_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_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_SY27,type,
sK3_SY27: $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(7,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
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(30,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
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(51,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( contains_pq @ U @ W )
& ( V != W ) )
=> ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
thf(52,axiom,
! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(54,axiom,
! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( insert_pq @ U @ V ) @ W )
<=> ( ( contains_pq @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(55,axiom,
! [U: $i] :
~ ( contains_pq @ create_pq @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(63,conjecture,
! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W )
=> ( ( i @ ( remove_cpq @ ( triple @ U @ create_slb @ V ) @ W ) )
= ( remove_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_co) ).
thf(64,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W )
=> ( ( i @ ( remove_cpq @ ( triple @ U @ create_slb @ V ) @ W ) )
= ( remove_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W )
=> ( ( i @ ( remove_cpq @ ( triple @ U @ create_slb @ V ) @ W ) )
= ( remove_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(67,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(68,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(69,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(70,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(71,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(72,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(73,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(74,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( contains_pq @ U @ W )
& ( V != W ) )
=> ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(75,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(76,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( insert_pq @ U @ V ) @ W )
<=> ( ( contains_pq @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(77,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(78,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ SY25 ) ) @ SY26 )
=> ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ create_slb @ SY25 ) @ SY26 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ create_slb @ SY25 ) ) @ SY26 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(79,plain,
( ( ! [SY27: $i] :
( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ SY27 )
=> ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) @ SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ SY27 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(80,plain,
( ( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 )
=> ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) @ sK3_SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(81,plain,
( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(82,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) @ sK3_SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 ) )
= $false ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(83,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) @ sK3_SY27 ) )
!= ( remove_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 ) )
= $true ),
inference(polarity_switch,[status(thm)],[82]) ).
thf(84,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(85,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( insert_pq @ U @ V ) @ W )
<=> ( ( contains_pq @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(86,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(87,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( contains_pq @ U @ W )
& ( V != W ) )
=> ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(88,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(89,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(90,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(91,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(92,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(93,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(94,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(95,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(96,plain,
( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(97,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) @ sK3_SY27 ) )
!= ( remove_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( remove_cpq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( contains_pq @ SX0 @ SX2 )
| ~ ( ( SX1 != SX2 ) ) )
| ( ( remove_pq @ ( insert_pq @ SX0 @ SX1 ) @ SX2 )
= ( insert_pq @ ( remove_pq @ SX0 @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( contains_pq @ ( insert_pq @ SX0 @ SX1 ) @ SX2 )
| ( contains_pq @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ~ ( ~ ( ( contains_pq @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ( contains_pq @ ( insert_pq @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(102,plain,
! [SV1: $i] :
( ( ~ ( contains_pq @ create_pq @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(103,plain,
! [SV2: $i] :
( ( ! [SY28: $i] :
( ( remove_pq @ ( insert_pq @ SV2 @ SY28 ) @ SY28 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV3: $i] :
( ( ~ ( contains_slb @ create_slb @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV4: $i] :
( ( ! [SY29: $i] :
~ ( pair_in_list @ create_slb @ SV4 @ SY29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV5: $i] :
( ( ( update_slb @ create_slb @ SV5 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV6: $i] :
( ( ! [SY30: $i] : ( check_cpq @ ( triple @ SV6 @ create_slb @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV7: $i] :
( ( ! [SY31: $i] :
( ( i @ ( triple @ SV7 @ create_slb @ SY31 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) @ sK3_SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY25 ) ) @ sK3_SY27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV8: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ( succ_cpq @ SV8 @ SY32 )
| ( succ_cpq @ SV8 @ ( remove_cpq @ SY32 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV9: $i] :
( ( ! [SY34: $i] :
~ ( ~ ( ~ ( pi_sharp_remove @ SV9 @ SY34 )
| ( contains_pq @ SV9 @ SY34 ) )
| ~ ( ~ ( contains_pq @ SV9 @ SY34 )
| ( pi_sharp_remove @ SV9 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV10: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ~ ( ~ ( contains_pq @ SV10 @ SY36 )
| ~ ( ( SY35 != SY36 ) ) )
| ( ( remove_pq @ ( insert_pq @ SV10 @ SY35 ) @ SY36 )
= ( insert_pq @ ( remove_pq @ SV10 @ SY36 ) @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV11: $i] :
( ( ! [SY37: $i,SY38: $i] :
~ ( ~ ( ~ ( contains_pq @ ( insert_pq @ SV11 @ SY37 ) @ SY38 )
| ( contains_pq @ SV11 @ SY38 )
| ( SY37 = SY38 ) )
| ~ ( ~ ( ( contains_pq @ SV11 @ SY38 )
| ( SY37 = SY38 ) )
| ( contains_pq @ ( insert_pq @ SV11 @ SY37 ) @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV1: $i] :
( ( contains_pq @ create_pq @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV12: $i,SV2: $i] :
( ( ( remove_pq @ ( insert_pq @ SV2 @ SV12 ) @ SV12 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV3: $i] :
( ( contains_slb @ create_slb @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV13: $i,SV4: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV4 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV14: $i,SV6: $i] :
( ( check_cpq @ ( triple @ SV6 @ create_slb @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV15: $i,SV7: $i] :
( ( ( i @ ( triple @ SV7 @ create_slb @ SV15 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV16: $i,SV8: $i] :
( ( ! [SY39: $i] :
( ~ ( succ_cpq @ SV8 @ SV16 )
| ( succ_cpq @ SV8 @ ( remove_cpq @ SV16 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV17: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( pi_sharp_remove @ SV9 @ SV17 )
| ( contains_pq @ SV9 @ SV17 ) )
| ~ ( ~ ( contains_pq @ SV9 @ SV17 )
| ( pi_sharp_remove @ SV9 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV18: $i,SV10: $i] :
( ( ! [SY40: $i] :
( ~ ~ ( ~ ( contains_pq @ SV10 @ SY40 )
| ~ ( ( SV18 != SY40 ) ) )
| ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SY40 )
= ( insert_pq @ ( remove_pq @ SV10 @ SY40 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV19: $i,SV11: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SY41 )
| ( contains_pq @ SV11 @ SY41 )
| ( SV19 = SY41 ) )
| ~ ( ~ ( ( contains_pq @ SV11 @ SY41 )
| ( SV19 = SY41 ) )
| ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV13: $i,SV4: $i] :
( ( pair_in_list @ create_slb @ SV4 @ SV13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV20: $i,SV16: $i,SV8: $i] :
( ( ~ ( succ_cpq @ SV8 @ SV16 )
| ( succ_cpq @ SV8 @ ( remove_cpq @ SV16 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(127,plain,
! [SV17: $i,SV9: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ SV9 @ SV17 )
| ( contains_pq @ SV9 @ SV17 ) )
| ~ ( ~ ( contains_pq @ SV9 @ SV17 )
| ( pi_sharp_remove @ SV9 @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(128,plain,
! [SV18: $i,SV21: $i,SV10: $i] :
( ( ~ ~ ( ~ ( contains_pq @ SV10 @ SV21 )
| ~ ( ( SV18 != SV21 ) ) )
| ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(129,plain,
! [SV22: $i,SV19: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
| ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
| ~ ( ~ ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
| ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV20: $i,SV16: $i,SV8: $i] :
( ( ( ~ ( succ_cpq @ SV8 @ SV16 ) )
= $true )
| ( ( succ_cpq @ SV8 @ ( remove_cpq @ SV16 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(131,plain,
! [SV17: $i,SV9: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ SV9 @ SV17 )
| ( contains_pq @ SV9 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(132,plain,
! [SV17: $i,SV9: $i] :
( ( ~ ( ~ ( contains_pq @ SV9 @ SV17 )
| ( pi_sharp_remove @ SV9 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV18: $i,SV21: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( contains_pq @ SV10 @ SV21 )
| ~ ( ( SV18 != SV21 ) ) ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV22: $i,SV19: $i,SV11: $i] :
( ( ~ ( ~ ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
| ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
| ~ ( ~ ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
| ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV20: $i,SV16: $i,SV8: $i] :
( ( ( succ_cpq @ SV8 @ SV16 )
= $false )
| ( ( succ_cpq @ SV8 @ ( remove_cpq @ SV16 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV17: $i,SV9: $i] :
( ( ~ ( pi_sharp_remove @ SV9 @ SV17 )
| ( contains_pq @ SV9 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(137,plain,
! [SV17: $i,SV9: $i] :
( ( ~ ( contains_pq @ SV9 @ SV17 )
| ( pi_sharp_remove @ SV9 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(138,plain,
! [SV18: $i,SV21: $i,SV10: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV10 @ SV21 )
| ~ ( ( SV18 != SV21 ) ) ) )
= $false )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(139,plain,
! [SV22: $i,SV19: $i,SV11: $i] :
( ( ~ ( ~ ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
| ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(140,plain,
! [SV19: $i,SV22: $i,SV11: $i] :
( ( ~ ( ~ ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
| ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(141,plain,
! [SV17: $i,SV9: $i] :
( ( ( ~ ( pi_sharp_remove @ SV9 @ SV17 ) )
= $true )
| ( ( contains_pq @ SV9 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(142,plain,
! [SV17: $i,SV9: $i] :
( ( ( ~ ( contains_pq @ SV9 @ SV17 ) )
= $true )
| ( ( pi_sharp_remove @ SV9 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(143,plain,
! [SV18: $i,SV21: $i,SV10: $i] :
( ( ( ~ ( contains_pq @ SV10 @ SV21 )
| ~ ( ( SV18 != SV21 ) ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(144,plain,
! [SV22: $i,SV19: $i,SV11: $i] :
( ( ~ ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
| ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(145,plain,
! [SV19: $i,SV22: $i,SV11: $i] :
( ( ~ ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
| ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(146,plain,
! [SV17: $i,SV9: $i] :
( ( ( pi_sharp_remove @ SV9 @ SV17 )
= $false )
| ( ( contains_pq @ SV9 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(147,plain,
! [SV17: $i,SV9: $i] :
( ( ( contains_pq @ SV9 @ SV17 )
= $false )
| ( ( pi_sharp_remove @ SV9 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(148,plain,
! [SV18: $i,SV21: $i,SV10: $i] :
( ( ( ~ ( contains_pq @ SV10 @ SV21 ) )
= $true )
| ( ( ~ ( ( SV18 != SV21 ) ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV22: $i,SV19: $i,SV11: $i] :
( ( ( ~ ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 ) )
= $true )
| ( ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(150,plain,
! [SV19: $i,SV22: $i,SV11: $i] :
( ( ( ~ ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV18: $i,SV21: $i,SV10: $i] :
( ( ( contains_pq @ SV10 @ SV21 )
= $false )
| ( ( ~ ( ( SV18 != SV21 ) ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(152,plain,
! [SV22: $i,SV19: $i,SV11: $i] :
( ( ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
= $false )
| ( ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(153,plain,
! [SV19: $i,SV22: $i,SV11: $i] :
( ( ( ( contains_pq @ SV11 @ SV22 )
| ( SV19 = SV22 ) )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(154,plain,
! [SV10: $i,SV21: $i,SV18: $i] :
( ( ( SV18 != SV21 )
= $false )
| ( ( contains_pq @ SV10 @ SV21 )
= $false )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(155,plain,
! [SV19: $i,SV22: $i,SV11: $i] :
( ( ( contains_pq @ SV11 @ SV22 )
= $true )
| ( ( SV19 = SV22 )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(156,plain,
! [SV19: $i,SV22: $i,SV11: $i] :
( ( ( contains_pq @ SV11 @ SV22 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(157,plain,
! [SV11: $i,SV22: $i,SV19: $i] :
( ( ( SV19 = SV22 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV11 @ SV19 ) @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(158,plain,
! [SV10: $i,SV21: $i,SV18: $i] :
( ( ( SV18 = SV21 )
= $true )
| ( ( contains_pq @ SV10 @ SV21 )
= $false )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV18 ) @ SV21 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV21 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(159,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[96,158,157,156,155,147,146,135,125,120,119,117,116,115,110,107,104]) ).
thf(160,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV367+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
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 16:27:21 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.29
% 0.57/0.29 No.of.Axioms: 12
% 0.57/0.29
% 0.57/0.29 Length.of.Defs: 0
% 0.57/0.29
% 0.57/0.29 Contains.Choice.Funs: false
% 0.57/0.29 ...
% 0.57/0.29
% 0.57/0.29 ********************************
% 0.57/0.29 * All subproblems solved! *
% 0.57/0.29 ********************************
% 0.57/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:159,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.29
% 0.57/0.29 %**** Beginning of derivation protocol ****
% 0.57/0.29 % SZS output start CNFRefutation
% See solution above
% 0.57/0.29
% 0.57/0.29 %**** End of derivation protocol ****
% 0.57/0.29 %**** no. of clauses in derivation: 110 ****
% 0.57/0.29 %**** clause counter: 159 ****
% 0.57/0.29
% 0.57/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:159,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------