%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV416+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 : n012.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 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 137 ( 108 unt; 0 typ; 0 def)
% Number of atoms : 587 ( 205 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1492 ( 134 ~; 106 |; 8 &;1214 @)
% ( 8 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 10 con; 0-3 aty)
% Number of variables : 336 ( 0 ^; 336 !; 0 ?; 336 :)
% 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_SY22,type,
sK2_SY22: $i ).
thf(tp_sK3_SY25,type,
sK3_SY25: $i ).
thf(tp_sK4_SY27,type,
sK4_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(6,axiom,
! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
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(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(52,axiom,
! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(63,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X )
=> ( ( i @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
= ( remove_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main3_li34) ).
thf(64,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ W @ X ) )
= ( i @ ( triple @ V @ W @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main3_li12) ).
thf(65,conjecture,
! [U: $i,V: $i,W: $i,X: $i] :
( ( pi_remove @ ( triple @ U @ V @ W ) @ X )
=> ( ( phi @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ U @ V @ W ) ) @ X )
& ( ( i @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
= ( remove_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co3) ).
thf(66,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( pi_remove @ ( triple @ U @ V @ W ) @ X )
=> ( ( phi @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ U @ V @ W ) ) @ X )
& ( ( i @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
= ( remove_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[65]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( pi_remove @ ( triple @ U @ V @ W ) @ X )
=> ( ( phi @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ U @ V @ W ) ) @ X )
& ( ( i @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
= ( remove_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(69,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(70,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(71,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X )
=> ( ( i @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
= ( remove_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(73,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ W @ X ) )
= ( i @ ( triple @ V @ W @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(74,plain,
( ( ! [SY22: $i,SY23: $i,SY24: $i] :
( ( pi_remove @ ( triple @ sK1_U @ SY22 @ SY23 ) @ SY24 )
=> ( ( phi @ ( remove_cpq @ ( triple @ sK1_U @ SY22 @ SY23 ) @ SY24 ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ SY22 @ SY23 ) ) @ SY24 )
& ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ SY22 @ SY23 ) @ SY24 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ SY22 @ SY23 ) ) @ SY24 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(75,plain,
( ( ! [SY25: $i,SY26: $i] :
( ( pi_remove @ ( triple @ sK1_U @ sK2_SY22 @ SY25 ) @ SY26 )
=> ( ( phi @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ SY25 ) @ SY26 ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ SY25 ) ) @ SY26 )
& ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ SY25 ) @ SY26 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ SY25 ) ) @ SY26 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(76,plain,
( ( ! [SY27: $i] :
( ( pi_remove @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ SY27 )
=> ( ( phi @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ SY27 ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ SY27 )
& ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ SY27 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(77,plain,
( ( ( pi_remove @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 )
=> ( ( phi @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
=> ( ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 )
& ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(78,plain,
( ( pi_remove @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 )
= $true ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(79,plain,
( ( phi @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
= $true ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(80,plain,
( ( ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 )
& ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[77]) ).
thf(81,plain,
( ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[80]) ).
thf(82,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[80]) ).
thf(83,plain,
( ( ~ ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) )
= $true ),
inference(polarity_switch,[status(thm)],[81]) ).
thf(84,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
!= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) )
= $true ),
inference(polarity_switch,[status(thm)],[82]) ).
thf(85,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ W @ X ) )
= ( i @ ( triple @ V @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(86,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X )
=> ( ( i @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
= ( remove_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(87,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(88,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(89,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(90,plain,
( ( ! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(91,plain,
( ( phi @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(92,plain,
( ( pi_remove @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(93,plain,
( ( ~ ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SX0 @ SX1 @ SX2 ) ) @ SX3 )
| ( ( i @ ( remove_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) )
= ( remove_pq @ ( i @ ( triple @ SX0 @ SX1 @ SX2 ) ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(95,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( remove_cpq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(97,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)],[89]) ).
thf(98,plain,
! [SV1: $i] :
( ( ! [SY28: $i,SY29: $i,SY30: $i,SY31: $i] :
( ( i @ ( triple @ SV1 @ SY29 @ SY30 ) )
= ( i @ ( triple @ SY28 @ SY29 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ( remove_pq @ ( insert_pq @ SV2 @ SY32 ) @ SY32 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(100,plain,
( ( pi_sharp_remove @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV3: $i] :
( ( ! [SY33: $i,SY34: $i,SY35: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV3 @ SY33 @ SY34 ) ) @ SY35 )
| ( ( i @ ( remove_cpq @ ( triple @ SV3 @ SY33 @ SY34 ) @ SY35 ) )
= ( remove_pq @ ( i @ ( triple @ SV3 @ SY33 @ SY34 ) ) @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV4: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( succ_cpq @ SV4 @ SY36 )
| ( succ_cpq @ SV4 @ ( remove_cpq @ SY36 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV5: $i] :
( ( ! [SY38: $i] :
~ ( ~ ( ~ ( pi_remove @ SV5 @ SY38 )
| ( pi_sharp_remove @ ( i @ SV5 ) @ SY38 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV5 ) @ SY38 )
| ( pi_remove @ SV5 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV6: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ~ ( pi_sharp_remove @ SV6 @ SY39 )
| ( contains_pq @ SV6 @ SY39 ) )
| ~ ( ~ ( contains_pq @ SV6 @ SY39 )
| ( pi_sharp_remove @ SV6 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( i @ ( triple @ SV1 @ SY40 @ SY41 ) )
= ( i @ ( triple @ SV7 @ SY40 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV8: $i,SV2: $i] :
( ( ( remove_pq @ ( insert_pq @ SV2 @ SV8 ) @ SV8 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV3 @ SV9 @ SY43 ) ) @ SY44 )
| ( ( i @ ( remove_cpq @ ( triple @ SV3 @ SV9 @ SY43 ) @ SY44 ) )
= ( remove_pq @ ( i @ ( triple @ SV3 @ SV9 @ SY43 ) ) @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY45: $i] :
( ~ ( succ_cpq @ SV4 @ SV10 )
| ( succ_cpq @ SV4 @ ( remove_cpq @ SV10 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( pi_remove @ SV5 @ SV11 )
| ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 )
| ( pi_remove @ SV5 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( pi_sharp_remove @ SV6 @ SV12 )
| ( contains_pq @ SV6 @ SV12 ) )
| ~ ( ~ ( contains_pq @ SV6 @ SV12 )
| ( pi_sharp_remove @ SV6 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV7: $i,SV13: $i,SV1: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( i @ ( triple @ SV1 @ SV13 @ SY46 ) )
= ( i @ ( triple @ SV7 @ SV13 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV14: $i,SV9: $i,SV3: $i] :
( ( ! [SY48: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SY48 )
| ( ( i @ ( remove_cpq @ ( triple @ SV3 @ SV9 @ SV14 ) @ SY48 ) )
= ( remove_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ( succ_cpq @ SV4 @ SV10 )
| ( succ_cpq @ SV4 @ ( remove_cpq @ SV10 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( pi_remove @ SV5 @ SV11 )
| ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 )
| ( pi_remove @ SV5 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ SV6 @ SV12 )
| ( contains_pq @ SV6 @ SV12 ) )
| ~ ( ~ ( contains_pq @ SV6 @ SV12 )
| ( pi_sharp_remove @ SV6 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV7: $i,SV16: $i,SV13: $i,SV1: $i] :
( ( ! [SY49: $i] :
( ( i @ ( triple @ SV1 @ SV13 @ SV16 ) )
= ( i @ ( triple @ SV7 @ SV13 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV3: $i] :
( ( ~ ( contains_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SV17 )
| ( ( i @ ( remove_cpq @ ( triple @ SV3 @ SV9 @ SV14 ) @ SV17 ) )
= ( remove_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( succ_cpq @ SV4 @ SV10 ) )
= $true )
| ( ( succ_cpq @ SV4 @ ( remove_cpq @ SV10 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( pi_remove @ SV5 @ SV11 )
| ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(120,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 )
| ( pi_remove @ SV5 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(121,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ SV6 @ SV12 )
| ( contains_pq @ SV6 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(122,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( contains_pq @ SV6 @ SV12 )
| ( pi_sharp_remove @ SV6 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(123,plain,
! [SV18: $i,SV7: $i,SV16: $i,SV13: $i,SV1: $i] :
( ( ( i @ ( triple @ SV1 @ SV13 @ SV16 ) )
= ( i @ ( triple @ SV7 @ SV13 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( contains_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SV17 ) )
= $true )
| ( ( ( i @ ( remove_cpq @ ( triple @ SV3 @ SV9 @ SV14 ) @ SV17 ) )
= ( remove_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( succ_cpq @ SV4 @ SV10 )
= $false )
| ( ( succ_cpq @ SV4 @ ( remove_cpq @ SV10 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( pi_remove @ SV5 @ SV11 )
| ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(127,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 )
| ( pi_remove @ SV5 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(128,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( pi_sharp_remove @ SV6 @ SV12 )
| ( contains_pq @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( contains_pq @ SV6 @ SV12 )
| ( pi_sharp_remove @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(130,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV3: $i] :
( ( ( contains_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SV17 )
= $false )
| ( ( ( i @ ( remove_cpq @ ( triple @ SV3 @ SV9 @ SV14 ) @ SV17 ) )
= ( remove_pq @ ( i @ ( triple @ SV3 @ SV9 @ SV14 ) ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( pi_remove @ SV5 @ SV11 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(132,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 ) )
= $true )
| ( ( pi_remove @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( pi_sharp_remove @ SV6 @ SV12 ) )
= $true )
| ( ( contains_pq @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( contains_pq @ SV6 @ SV12 ) )
= $true )
| ( ( pi_sharp_remove @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV11: $i,SV5: $i] :
( ( ( pi_remove @ SV5 @ SV11 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV11: $i,SV5: $i] :
( ( ( pi_sharp_remove @ ( i @ SV5 ) @ SV11 )
= $false )
| ( ( pi_remove @ SV5 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV12: $i,SV6: $i] :
( ( ( pi_sharp_remove @ SV6 @ SV12 )
= $false )
| ( ( contains_pq @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV12: $i,SV6: $i] :
( ( ( contains_pq @ SV6 @ SV12 )
= $false )
| ( ( pi_sharp_remove @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[91,138,137,136,135,130,125,123,106,100,92]) ).
thf(140,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ W @ X ) )
= ( i @ ( triple @ V @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(141,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X )
=> ( ( i @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
= ( remove_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(142,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(143,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(144,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(145,plain,
( ( ! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(146,plain,
( ( phi @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(147,plain,
( ( pi_remove @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(148,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
!= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(149,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)],[144]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( remove_cpq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SX0 @ SX1 @ SX2 ) ) @ SX3 )
| ( ( i @ ( remove_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) )
= ( remove_pq @ ( i @ ( triple @ SX0 @ SX1 @ SX2 ) ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(153,plain,
! [SV19: $i] :
( ( ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i] :
( ( i @ ( triple @ SV19 @ SY51 @ SY52 ) )
= ( i @ ( triple @ SY50 @ SY51 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV20: $i] :
( ( ! [SY54: $i] :
( ( remove_pq @ ( insert_pq @ SV20 @ SY54 ) @ SY54 )
= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(155,plain,
( ( ( i @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) @ sK4_SY27 ) )
= ( remove_pq @ ( i @ ( triple @ sK1_U @ sK2_SY22 @ sK3_SY25 ) ) @ sK4_SY27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(156,plain,
! [SV21: $i] :
( ( ! [SY55: $i] :
~ ( ~ ( ~ ( pi_sharp_remove @ SV21 @ SY55 )
| ( contains_pq @ SV21 @ SY55 ) )
| ~ ( ~ ( contains_pq @ SV21 @ SY55 )
| ( pi_sharp_remove @ SV21 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV22: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( succ_cpq @ SV22 @ SY56 )
| ( succ_cpq @ SV22 @ ( remove_cpq @ SY56 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(158,plain,
! [SV23: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV23 @ SY58 @ SY59 ) ) @ SY60 )
| ( ( i @ ( remove_cpq @ ( triple @ SV23 @ SY58 @ SY59 ) @ SY60 ) )
= ( remove_pq @ ( i @ ( triple @ SV23 @ SY58 @ SY59 ) ) @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV24: $i] :
( ( ! [SY61: $i] :
~ ( ~ ( ~ ( pi_remove @ SV24 @ SY61 )
| ( pi_sharp_remove @ ( i @ SV24 ) @ SY61 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV24 ) @ SY61 )
| ( pi_remove @ SV24 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV25: $i,SV19: $i] :
( ( ! [SY62: $i,SY63: $i,SY64: $i] :
( ( i @ ( triple @ SV19 @ SY62 @ SY63 ) )
= ( i @ ( triple @ SV25 @ SY62 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(161,plain,
! [SV26: $i,SV20: $i] :
( ( ( remove_pq @ ( insert_pq @ SV20 @ SV26 ) @ SV26 )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(162,plain,
! [SV27: $i,SV21: $i] :
( ( ~ ( ~ ( ~ ( pi_sharp_remove @ SV21 @ SV27 )
| ( contains_pq @ SV21 @ SV27 ) )
| ~ ( ~ ( contains_pq @ SV21 @ SV27 )
| ( pi_sharp_remove @ SV21 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(163,plain,
! [SV28: $i,SV22: $i] :
( ( ! [SY65: $i] :
( ~ ( succ_cpq @ SV22 @ SV28 )
| ( succ_cpq @ SV22 @ ( remove_cpq @ SV28 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(164,plain,
! [SV29: $i,SV23: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV23 @ SV29 @ SY66 ) ) @ SY67 )
| ( ( i @ ( remove_cpq @ ( triple @ SV23 @ SV29 @ SY66 ) @ SY67 ) )
= ( remove_pq @ ( i @ ( triple @ SV23 @ SV29 @ SY66 ) ) @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(165,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( pi_remove @ SV24 @ SV30 )
| ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 )
| ( pi_remove @ SV24 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(166,plain,
! [SV25: $i,SV31: $i,SV19: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( i @ ( triple @ SV19 @ SV31 @ SY68 ) )
= ( i @ ( triple @ SV25 @ SV31 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(167,plain,
! [SV27: $i,SV21: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ SV21 @ SV27 )
| ( contains_pq @ SV21 @ SV27 ) )
| ~ ( ~ ( contains_pq @ SV21 @ SV27 )
| ( pi_sharp_remove @ SV21 @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(168,plain,
! [SV32: $i,SV28: $i,SV22: $i] :
( ( ~ ( succ_cpq @ SV22 @ SV28 )
| ( succ_cpq @ SV22 @ ( remove_cpq @ SV28 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(169,plain,
! [SV33: $i,SV29: $i,SV23: $i] :
( ( ! [SY70: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SY70 )
| ( ( i @ ( remove_cpq @ ( triple @ SV23 @ SV29 @ SV33 ) @ SY70 ) )
= ( remove_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(170,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( ~ ( pi_remove @ SV24 @ SV30 )
| ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 ) )
| ~ ( ~ ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 )
| ( pi_remove @ SV24 @ SV30 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(171,plain,
! [SV25: $i,SV34: $i,SV31: $i,SV19: $i] :
( ( ! [SY71: $i] :
( ( i @ ( triple @ SV19 @ SV31 @ SV34 ) )
= ( i @ ( triple @ SV25 @ SV31 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(172,plain,
! [SV27: $i,SV21: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ SV21 @ SV27 )
| ( contains_pq @ SV21 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(173,plain,
! [SV27: $i,SV21: $i] :
( ( ~ ( ~ ( contains_pq @ SV21 @ SV27 )
| ( pi_sharp_remove @ SV21 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(174,plain,
! [SV32: $i,SV28: $i,SV22: $i] :
( ( ( ~ ( succ_cpq @ SV22 @ SV28 ) )
= $true )
| ( ( succ_cpq @ SV22 @ ( remove_cpq @ SV28 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(175,plain,
! [SV35: $i,SV33: $i,SV29: $i,SV23: $i] :
( ( ~ ( contains_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SV35 )
| ( ( i @ ( remove_cpq @ ( triple @ SV23 @ SV29 @ SV33 ) @ SV35 ) )
= ( remove_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( ~ ( pi_remove @ SV24 @ SV30 )
| ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(177,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( ~ ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 )
| ( pi_remove @ SV24 @ SV30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(178,plain,
! [SV36: $i,SV25: $i,SV34: $i,SV31: $i,SV19: $i] :
( ( ( i @ ( triple @ SV19 @ SV31 @ SV34 ) )
= ( i @ ( triple @ SV25 @ SV31 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(179,plain,
! [SV27: $i,SV21: $i] :
( ( ~ ( pi_sharp_remove @ SV21 @ SV27 )
| ( contains_pq @ SV21 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(180,plain,
! [SV27: $i,SV21: $i] :
( ( ~ ( contains_pq @ SV21 @ SV27 )
| ( pi_sharp_remove @ SV21 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(181,plain,
! [SV32: $i,SV28: $i,SV22: $i] :
( ( ( succ_cpq @ SV22 @ SV28 )
= $false )
| ( ( succ_cpq @ SV22 @ ( remove_cpq @ SV28 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(182,plain,
! [SV35: $i,SV33: $i,SV29: $i,SV23: $i] :
( ( ( ~ ( contains_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SV35 ) )
= $true )
| ( ( ( i @ ( remove_cpq @ ( triple @ SV23 @ SV29 @ SV33 ) @ SV35 ) )
= ( remove_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(183,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( pi_remove @ SV24 @ SV30 )
| ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(184,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 )
| ( pi_remove @ SV24 @ SV30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(185,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ( pi_sharp_remove @ SV21 @ SV27 ) )
= $true )
| ( ( contains_pq @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(186,plain,
! [SV27: $i,SV21: $i] :
( ( ( ~ ( contains_pq @ SV21 @ SV27 ) )
= $true )
| ( ( pi_sharp_remove @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(187,plain,
! [SV35: $i,SV33: $i,SV29: $i,SV23: $i] :
( ( ( contains_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SV35 )
= $false )
| ( ( ( i @ ( remove_cpq @ ( triple @ SV23 @ SV29 @ SV33 ) @ SV35 ) )
= ( remove_pq @ ( i @ ( triple @ SV23 @ SV29 @ SV33 ) ) @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(188,plain,
! [SV30: $i,SV24: $i] :
( ( ( ~ ( pi_remove @ SV24 @ SV30 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(189,plain,
! [SV30: $i,SV24: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 ) )
= $true )
| ( ( pi_remove @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(190,plain,
! [SV27: $i,SV21: $i] :
( ( ( pi_sharp_remove @ SV21 @ SV27 )
= $false )
| ( ( contains_pq @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(191,plain,
! [SV27: $i,SV21: $i] :
( ( ( contains_pq @ SV21 @ SV27 )
= $false )
| ( ( pi_sharp_remove @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV30: $i,SV24: $i] :
( ( ( pi_remove @ SV24 @ SV30 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(193,plain,
! [SV30: $i,SV24: $i] :
( ( ( pi_sharp_remove @ ( i @ SV24 ) @ SV30 )
= $false )
| ( ( pi_remove @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(194,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[146,193,192,191,190,187,181,178,161,155,147]) ).
thf(195,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[194,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV416+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
% 0.08/0.12 % Computer : n012.cluster.edu
% 0.08/0.12 % Model : x86_64 x86_64
% 0.08/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.12 % Memory : 8046.5625MB
% 0.08/0.12 % OS : Linux 6.8.0-71-generic
% 0.08/0.12 % CPULimit : 300
% 0.08/0.12 % WCLimit : 300
% 0.08/0.12 % DateTime : Tue Oct 6 16:27:46 UTC 2026
% 0.08/0.12 % CPUTime :
% 0.08/0.12 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 6
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 .....
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % 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:194,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 137 ****
% 0.08/0.25 %**** clause counter: 194 ****
% 0.08/0.25
% 0.08/0.25 % 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:194,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------