%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : MGT070+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : 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 10:31:47 AM UTC 2026
% Result : Theorem 0.64s 0.37s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 165 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 1076 ( 305 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1891 ( 447 ~; 303 |; 37 &;1077 @)
% ( 6 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 421 ( 0 ^; 416 !; 5 ?; 421 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_axis_compatible,type,
axis_compatible: $i > $i > $i > $i > $o ).
thf(tp_axis_conflict,type,
axis_conflict: $i > $i > $i > $i > $o ).
thf(tp_axis_subsumes,type,
axis_subsumes: $i > $i > $i > $i > $o ).
thf(tp_box_verdict,type,
box_verdict: $i > $i > $i ).
thf(tp_compatible,type,
compatible: $i ).
thf(tp_completion_compatible,type,
completion_compatible: $i > $i > $i > $o ).
thf(tp_completion_conflict,type,
completion_conflict: $i > $i > $i > $i > $o ).
thf(tp_conflict,type,
conflict: $i ).
thf(tp_in_closed,type,
in_closed: $i > $i > $i > $o ).
thf(tp_in_lopen,type,
in_lopen: $i > $i > $i > $o ).
thf(tp_in_open,type,
in_open: $i > $i > $i > $o ).
thf(tp_in_ropen,type,
in_ropen: $i > $i > $i > $o ).
thf(tp_is_verdict,type,
is_verdict: $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_n0,type,
n0: $i ).
thf(tp_ninf,type,
ninf: $i ).
thf(tp_nsup,type,
nsup: $i ).
thf(tp_unknown,type,
unknown: $i ).
thf(4,axiom,
! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ( ( leq @ InfD @ U )
& ( leq @ U @ SupD )
& ( less @ U @ V )
& ( leq @ V @ SupD ) )
=> ( completion_compatible @ U @ InfD @ SupD ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sharpness_compat) ).
thf(6,axiom,
! [V: $i,InfD: $i,SupD: $i] :
( ( ( leq @ InfD @ V )
& ( leq @ V @ SupD ) )
=> ( completion_compatible @ V @ InfD @ SupD ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',completion_compat) ).
thf(24,axiom,
! [X: $i,A: $i,B: $i] :
( ( in_closed @ X @ A @ B )
<=> ( ( leq @ A @ X )
& ( leq @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_closed) ).
thf(26,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_trans) ).
thf(27,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( less @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( less @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_leq_trans) ).
thf(28,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( less @ Y @ Z ) )
=> ( less @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_less_trans) ).
thf(29,axiom,
! [X: $i,Y: $i] :
( ( less @ X @ Y )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_implies_leq) ).
thf(30,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ X ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_antisym) ).
thf(31,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_def) ).
thf(36,axiom,
! [X: $i] : ( leq @ X @ nsup ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_sup_ub) ).
thf(37,axiom,
! [X: $i] : ( leq @ ninf @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_inf_lb) ).
thf(40,conjecture,
? [V: $i] :
( ( leq @ ninf @ V )
& ( leq @ V @ nsup )
& ( completion_compatible @ V @ ninf @ nsup ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown_sound_compatible) ).
thf(41,negated_conjecture,
( ( ? [V: $i] :
( ( leq @ ninf @ V )
& ( leq @ V @ nsup )
& ( completion_compatible @ V @ ninf @ nsup ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[40]) ).
thf(42,plain,
( ( ? [V: $i] :
( ( leq @ ninf @ V )
& ( leq @ V @ nsup )
& ( completion_compatible @ V @ ninf @ nsup ) ) )
= $false ),
inference(unfold_def,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ( ( leq @ InfD @ U )
& ( leq @ U @ SupD )
& ( less @ U @ V )
& ( leq @ V @ SupD ) )
=> ( completion_compatible @ U @ InfD @ SupD ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(44,plain,
( ( ! [V: $i,InfD: $i,SupD: $i] :
( ( ( leq @ InfD @ V )
& ( leq @ V @ SupD ) )
=> ( completion_compatible @ V @ InfD @ SupD ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(45,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( in_closed @ X @ A @ B )
<=> ( ( leq @ A @ X )
& ( leq @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( less @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( less @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] :
( ( less @ X @ Y )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ X ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(52,plain,
( ( ! [X: $i] : ( leq @ X @ nsup ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(53,plain,
( ( ! [X: $i] : ( leq @ ninf @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(54,plain,
( ( ~ ? [V: $i] :
( ( leq @ ninf @ V )
& ( leq @ V @ nsup )
& ( completion_compatible @ V @ ninf @ nsup ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [X: $i] : ( leq @ ninf @ X ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(56,plain,
( ( ! [X: $i] : ( leq @ X @ nsup ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ X ) )
=> ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( less @ X @ Y )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( less @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( less @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(63,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( in_closed @ X @ A @ B )
<=> ( ( leq @ A @ X )
& ( leq @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(64,plain,
( ( ! [V: $i,InfD: $i,SupD: $i] :
( ( ( leq @ InfD @ V )
& ( leq @ V @ SupD ) )
=> ( completion_compatible @ V @ InfD @ SupD ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,InfD: $i,SupD: $i] :
( ( ( leq @ InfD @ U )
& ( leq @ U @ SupD )
& ( less @ U @ V )
& ( leq @ V @ SupD ) )
=> ( completion_compatible @ U @ InfD @ SupD ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(66,plain,
( ( ~ ? [V: $i] :
( ( leq @ ninf @ V )
& ( leq @ V @ nsup )
& ( completion_compatible @ V @ ninf @ nsup ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(67,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( leq @ ninf @ SX0 )
| ~ ( leq @ SX0 @ nsup ) )
| ~ ( completion_compatible @ SX0 @ ninf @ nsup ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX1 @ SX0 )
| ~ ( leq @ SX0 @ SX2 ) )
| ( completion_compatible @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( leq @ SX2 @ SX0 )
| ~ ( leq @ SX0 @ SX3 ) )
| ~ ( less @ SX0 @ SX1 ) )
| ~ ( leq @ SX1 @ SX3 ) )
| ( completion_compatible @ SX0 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( less @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( less @ SX1 @ SX2 ) )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in_closed @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ~ ( leq @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SX1 @ SX0 )
| ~ ( leq @ SX0 @ SX2 ) )
| ( in_closed @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ SX1 )
| ( less @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ~ ( ~ ( ( less @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ( leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(77,plain,
! [SV1: $i] :
( ( leq @ ninf @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(78,plain,
! [SV2: $i] :
( ( leq @ SV2 @ nsup )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(79,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( leq @ ninf @ SX0 )
| ~ ( leq @ SX0 @ nsup ) )
| ~ ( completion_compatible @ SX0 @ ninf @ nsup ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(80,plain,
! [SV3: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ~ ( ~ ( leq @ SY28 @ SV3 )
| ~ ( leq @ SV3 @ SY29 ) )
| ( completion_compatible @ SV3 @ SY28 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV4: $i] :
( ( ! [SY30: $i,SY31: $i,SY32: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( leq @ SY31 @ SV4 )
| ~ ( leq @ SV4 @ SY32 ) )
| ~ ( less @ SV4 @ SY30 ) )
| ~ ( leq @ SY30 @ SY32 ) )
| ( completion_compatible @ SV4 @ SY31 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV5: $i] :
( ( ! [SY33: $i] :
( ~ ~ ( ~ ( leq @ SV5 @ SY33 )
| ~ ( leq @ SY33 @ SV5 ) )
| ( SV5 = SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV6: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ~ ( ~ ( less @ SV6 @ SY34 )
| ~ ( leq @ SY34 @ SY35 ) )
| ( less @ SV6 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV7: $i] :
( ( ! [SY36: $i] :
( ~ ( less @ SV7 @ SY36 )
| ( leq @ SV7 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV8: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( leq @ SV8 @ SY37 )
| ~ ( less @ SY37 @ SY38 ) )
| ( less @ SV8 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV9: $i] :
( ( ! [SY39: $i,SY40: $i] :
~ ( ~ ( ~ ( in_closed @ SV9 @ SY39 @ SY40 )
| ~ ( ~ ( leq @ SY39 @ SV9 )
| ~ ( leq @ SV9 @ SY40 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SY39 @ SV9 )
| ~ ( leq @ SV9 @ SY40 ) )
| ( in_closed @ SV9 @ SY39 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV10: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( leq @ SV10 @ SY41 )
| ( less @ SV10 @ SY41 )
| ( SV10 = SY41 ) )
| ~ ( ~ ( ( less @ SV10 @ SY41 )
| ( SV10 = SY41 ) )
| ( leq @ SV10 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV11: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ( leq @ SV11 @ SY42 )
| ~ ( leq @ SY42 @ SY43 ) )
| ( leq @ SV11 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(89,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( leq @ ninf @ SX0 )
| ~ ( leq @ SX0 @ nsup ) )
| ~ ( completion_compatible @ SX0 @ ninf @ nsup ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(90,plain,
! [SV3: $i,SV12: $i] :
( ( ! [SY44: $i] :
( ~ ~ ( ~ ( leq @ SV12 @ SV3 )
| ~ ( leq @ SV3 @ SY44 ) )
| ( completion_compatible @ SV3 @ SV12 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV13: $i,SV4: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( leq @ SY45 @ SV4 )
| ~ ( leq @ SV4 @ SY46 ) )
| ~ ( less @ SV4 @ SV13 ) )
| ~ ( leq @ SV13 @ SY46 ) )
| ( completion_compatible @ SV4 @ SY45 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV14: $i,SV5: $i] :
( ( ~ ~ ( ~ ( leq @ SV5 @ SV14 )
| ~ ( leq @ SV14 @ SV5 ) )
| ( SV5 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV15: $i,SV6: $i] :
( ( ! [SY47: $i] :
( ~ ~ ( ~ ( less @ SV6 @ SV15 )
| ~ ( leq @ SV15 @ SY47 ) )
| ( less @ SV6 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV16: $i,SV7: $i] :
( ( ~ ( less @ SV7 @ SV16 )
| ( leq @ SV7 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(95,plain,
! [SV17: $i,SV8: $i] :
( ( ! [SY48: $i] :
( ~ ~ ( ~ ( leq @ SV8 @ SV17 )
| ~ ( less @ SV17 @ SY48 ) )
| ( less @ SV8 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(96,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY49: $i] :
~ ( ~ ( ~ ( in_closed @ SV9 @ SV18 @ SY49 )
| ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SY49 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SY49 ) )
| ( in_closed @ SV9 @ SV18 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV10 @ SV19 )
| ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
| ~ ( ~ ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
| ( leq @ SV10 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(98,plain,
! [SV20: $i,SV11: $i] :
( ( ! [SY50: $i] :
( ~ ~ ( ~ ( leq @ SV11 @ SV20 )
| ~ ( leq @ SV20 @ SY50 ) )
| ( leq @ SV11 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV21: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( leq @ ninf @ SV21 )
| ~ ( leq @ SV21 @ nsup ) )
| ~ ( completion_compatible @ SV21 @ ninf @ nsup ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV22: $i,SV3: $i,SV12: $i] :
( ( ~ ~ ( ~ ( leq @ SV12 @ SV3 )
| ~ ( leq @ SV3 @ SV22 ) )
| ( completion_compatible @ SV3 @ SV12 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV13: $i,SV4: $i,SV23: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SY51 ) )
| ~ ( less @ SV4 @ SV13 ) )
| ~ ( leq @ SV13 @ SY51 ) )
| ( completion_compatible @ SV4 @ SV23 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV5 @ SV14 )
| ~ ( leq @ SV14 @ SV5 ) ) )
= $true )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV24: $i,SV15: $i,SV6: $i] :
( ( ~ ~ ( ~ ( less @ SV6 @ SV15 )
| ~ ( leq @ SV15 @ SV24 ) )
| ( less @ SV6 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( less @ SV7 @ SV16 ) )
= $true )
| ( ( leq @ SV7 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV25: $i,SV17: $i,SV8: $i] :
( ( ~ ~ ( ~ ( leq @ SV8 @ SV17 )
| ~ ( less @ SV17 @ SV25 ) )
| ( less @ SV8 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV26: $i,SV18: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( in_closed @ SV9 @ SV18 @ SV26 )
| ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) )
| ( in_closed @ SV9 @ SV18 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( ~ ( leq @ SV10 @ SV19 )
| ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
| ~ ( ~ ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
| ( leq @ SV10 @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV27: $i,SV20: $i,SV11: $i] :
( ( ~ ~ ( ~ ( leq @ SV11 @ SV20 )
| ~ ( leq @ SV20 @ SV27 ) )
| ( leq @ SV11 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV21: $i] :
( ( ~ ( ~ ~ ( ~ ( leq @ ninf @ SV21 )
| ~ ( leq @ SV21 @ nsup ) )
| ~ ( completion_compatible @ SV21 @ ninf @ nsup ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV22: $i,SV3: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV12 @ SV3 )
| ~ ( leq @ SV3 @ SV22 ) ) )
= $true )
| ( ( completion_compatible @ SV3 @ SV12 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
| ~ ( less @ SV4 @ SV13 ) )
| ~ ( leq @ SV13 @ SV28 ) )
| ( completion_compatible @ SV4 @ SV23 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ( leq @ SV5 @ SV14 )
| ~ ( leq @ SV14 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV24: $i,SV15: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( less @ SV6 @ SV15 )
| ~ ( leq @ SV15 @ SV24 ) ) )
= $true )
| ( ( less @ SV6 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV16: $i,SV7: $i] :
( ( ( less @ SV7 @ SV16 )
= $false )
| ( ( leq @ SV7 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV25: $i,SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV8 @ SV17 )
| ~ ( less @ SV17 @ SV25 ) ) )
= $true )
| ( ( less @ SV8 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV26: $i,SV18: $i,SV9: $i] :
( ( ~ ( ~ ( in_closed @ SV9 @ SV18 @ SV26 )
| ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) )
| ( in_closed @ SV9 @ SV18 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( ~ ( leq @ SV10 @ SV19 )
| ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(118,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( ~ ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
| ( leq @ SV10 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV27: $i,SV20: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV11 @ SV20 )
| ~ ( leq @ SV20 @ SV27 ) ) )
= $true )
| ( ( leq @ SV11 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV21: $i] :
( ( ~ ~ ( ~ ( leq @ ninf @ SV21 )
| ~ ( leq @ SV21 @ nsup ) )
| ~ ( completion_compatible @ SV21 @ ninf @ nsup ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(121,plain,
! [SV22: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( ~ ( leq @ SV12 @ SV3 )
| ~ ( leq @ SV3 @ SV22 ) ) )
= $false )
| ( ( completion_compatible @ SV3 @ SV12 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
| ~ ( less @ SV4 @ SV13 ) )
| ~ ( leq @ SV13 @ SV28 ) ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( leq @ SV5 @ SV14 )
| ~ ( leq @ SV14 @ SV5 ) )
= $true )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(124,plain,
! [SV24: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( ~ ( less @ SV6 @ SV15 )
| ~ ( leq @ SV15 @ SV24 ) ) )
= $false )
| ( ( less @ SV6 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV25: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( leq @ SV8 @ SV17 )
| ~ ( less @ SV17 @ SV25 ) ) )
= $false )
| ( ( less @ SV8 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV26: $i,SV18: $i,SV9: $i] :
( ( ~ ( ~ ( in_closed @ SV9 @ SV18 @ SV26 )
| ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(127,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ~ ( ~ ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) )
| ( in_closed @ SV9 @ SV18 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(128,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( leq @ SV10 @ SV19 )
| ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(129,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
| ( leq @ SV10 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(130,plain,
! [SV27: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( ~ ( leq @ SV11 @ SV20 )
| ~ ( leq @ SV20 @ SV27 ) ) )
= $false )
| ( ( leq @ SV11 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV21: $i] :
( ( ( ~ ~ ( ~ ( leq @ ninf @ SV21 )
| ~ ( leq @ SV21 @ nsup ) ) )
= $true )
| ( ( ~ ( completion_compatible @ SV21 @ ninf @ nsup ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV22: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( leq @ SV12 @ SV3 )
| ~ ( leq @ SV3 @ SV22 ) )
= $true )
| ( ( completion_compatible @ SV3 @ SV12 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(133,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
| ~ ( less @ SV4 @ SV13 ) )
| ~ ( leq @ SV13 @ SV28 ) ) )
= $false )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( leq @ SV5 @ SV14 ) )
= $true )
| ( ( ~ ( leq @ SV14 @ SV5 ) )
= $true )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV24: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( less @ SV6 @ SV15 )
| ~ ( leq @ SV15 @ SV24 ) )
= $true )
| ( ( less @ SV6 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV25: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV17 )
| ~ ( less @ SV17 @ SV25 ) )
= $true )
| ( ( less @ SV8 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(137,plain,
! [SV26: $i,SV18: $i,SV9: $i] :
( ( ~ ( in_closed @ SV9 @ SV18 @ SV26 )
| ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(138,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ~ ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) )
| ( in_closed @ SV9 @ SV18 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(139,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( leq @ SV10 @ SV19 ) )
= $true )
| ( ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) ) )
= $true )
| ( ( leq @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV27: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( leq @ SV11 @ SV20 )
| ~ ( leq @ SV20 @ SV27 ) )
= $true )
| ( ( leq @ SV11 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(142,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( leq @ ninf @ SV21 )
| ~ ( leq @ SV21 @ nsup ) ) )
= $false )
| ( ( ~ ( completion_compatible @ SV21 @ ninf @ nsup ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV22: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( leq @ SV12 @ SV3 ) )
= $true )
| ( ( ~ ( leq @ SV3 @ SV22 ) )
= $true )
| ( ( completion_compatible @ SV3 @ SV12 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
| ~ ( less @ SV4 @ SV13 ) )
| ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(145,plain,
! [SV14: $i,SV5: $i] :
( ( ( leq @ SV5 @ SV14 )
= $false )
| ( ( ~ ( leq @ SV14 @ SV5 ) )
= $true )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(146,plain,
! [SV24: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( less @ SV6 @ SV15 ) )
= $true )
| ( ( ~ ( leq @ SV15 @ SV24 ) )
= $true )
| ( ( less @ SV6 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(147,plain,
! [SV25: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV17 ) )
= $true )
| ( ( ~ ( less @ SV17 @ SV25 ) )
= $true )
| ( ( less @ SV8 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV26: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( in_closed @ SV9 @ SV18 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(149,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) )
= $true )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV19: $i,SV10: $i] :
( ( ( leq @ SV10 @ SV19 )
= $false )
| ( ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV19: $i,SV10: $i] :
( ( ( ( less @ SV10 @ SV19 )
| ( SV10 = SV19 ) )
= $false )
| ( ( leq @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV27: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( leq @ SV11 @ SV20 ) )
= $true )
| ( ( ~ ( leq @ SV20 @ SV27 ) )
= $true )
| ( ( leq @ SV11 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV21: $i] :
( ( ( ~ ( leq @ ninf @ SV21 )
| ~ ( leq @ SV21 @ nsup ) )
= $true )
| ( ( ~ ( completion_compatible @ SV21 @ ninf @ nsup ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(154,plain,
! [SV22: $i,SV3: $i,SV12: $i] :
( ( ( leq @ SV12 @ SV3 )
= $false )
| ( ( ~ ( leq @ SV3 @ SV22 ) )
= $true )
| ( ( completion_compatible @ SV3 @ SV12 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
| ~ ( less @ SV4 @ SV13 ) ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV5: $i,SV14: $i] :
( ( ( leq @ SV14 @ SV5 )
= $false )
| ( ( leq @ SV5 @ SV14 )
= $false )
| ( ( SV5 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV24: $i,SV15: $i,SV6: $i] :
( ( ( less @ SV6 @ SV15 )
= $false )
| ( ( ~ ( leq @ SV15 @ SV24 ) )
= $true )
| ( ( less @ SV6 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV25: $i,SV17: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV17 )
= $false )
| ( ( ~ ( less @ SV17 @ SV25 ) )
= $true )
| ( ( less @ SV8 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV26: $i,SV18: $i,SV9: $i] :
( ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $false )
| ( ( ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( ~ ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) ) )
= $false )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(161,plain,
! [SV19: $i,SV10: $i] :
( ( ( less @ SV10 @ SV19 )
= $true )
| ( ( SV10 = SV19 )
= $true )
| ( ( leq @ SV10 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(162,plain,
! [SV19: $i,SV10: $i] :
( ( ( less @ SV10 @ SV19 )
= $false )
| ( ( leq @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(163,plain,
! [SV19: $i,SV10: $i] :
( ( ( SV10 = SV19 )
= $false )
| ( ( leq @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(164,plain,
! [SV27: $i,SV20: $i,SV11: $i] :
( ( ( leq @ SV11 @ SV20 )
= $false )
| ( ( ~ ( leq @ SV20 @ SV27 ) )
= $true )
| ( ( leq @ SV11 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(165,plain,
! [SV21: $i] :
( ( ( ~ ( leq @ ninf @ SV21 ) )
= $true )
| ( ( ~ ( leq @ SV21 @ nsup ) )
= $true )
| ( ( ~ ( completion_compatible @ SV21 @ ninf @ nsup ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(166,plain,
! [SV12: $i,SV22: $i,SV3: $i] :
( ( ( leq @ SV3 @ SV22 )
= $false )
| ( ( leq @ SV12 @ SV3 )
= $false )
| ( ( completion_compatible @ SV3 @ SV12 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(167,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
| ~ ( less @ SV4 @ SV13 ) ) )
= $false )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV6: $i,SV24: $i,SV15: $i] :
( ( ( leq @ SV15 @ SV24 )
= $false )
| ( ( less @ SV6 @ SV15 )
= $false )
| ( ( less @ SV6 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV8: $i,SV25: $i,SV17: $i] :
( ( ( less @ SV17 @ SV25 )
= $false )
| ( ( leq @ SV8 @ SV17 )
= $false )
| ( ( less @ SV8 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(170,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) )
= $false )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(171,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( ~ ( leq @ SV18 @ SV9 )
| ~ ( leq @ SV9 @ SV26 ) )
= $true )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(172,plain,
! [SV11: $i,SV27: $i,SV20: $i] :
( ( ( leq @ SV20 @ SV27 )
= $false )
| ( ( leq @ SV11 @ SV20 )
= $false )
| ( ( leq @ SV11 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV21: $i] :
( ( ( leq @ ninf @ SV21 )
= $false )
| ( ( ~ ( leq @ SV21 @ nsup ) )
= $true )
| ( ( ~ ( completion_compatible @ SV21 @ ninf @ nsup ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
| ~ ( less @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(175,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( ~ ( leq @ SV18 @ SV9 ) )
= $false )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(176,plain,
! [SV18: $i,SV26: $i,SV9: $i] :
( ( ( ~ ( leq @ SV9 @ SV26 ) )
= $false )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(177,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( ~ ( leq @ SV18 @ SV9 ) )
= $true )
| ( ( ~ ( leq @ SV9 @ SV26 ) )
= $true )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV21: $i] :
( ( ( leq @ SV21 @ nsup )
= $false )
| ( ( leq @ ninf @ SV21 )
= $false )
| ( ( ~ ( completion_compatible @ SV21 @ ninf @ nsup ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(179,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) ) )
= $true )
| ( ( ~ ( less @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(180,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( leq @ SV18 @ SV9 )
= $true )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(181,plain,
! [SV18: $i,SV26: $i,SV9: $i] :
( ( ( leq @ SV9 @ SV26 )
= $true )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(182,plain,
! [SV26: $i,SV9: $i,SV18: $i] :
( ( ( leq @ SV18 @ SV9 )
= $false )
| ( ( ~ ( leq @ SV9 @ SV26 ) )
= $true )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV21: $i] :
( ( ( completion_compatible @ SV21 @ ninf @ nsup )
= $false )
| ( ( leq @ ninf @ SV21 )
= $false )
| ( ( leq @ SV21 @ nsup )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) ) )
= $false )
| ( ( ~ ( less @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(185,plain,
! [SV18: $i,SV26: $i,SV9: $i] :
( ( ( leq @ SV9 @ SV26 )
= $false )
| ( ( leq @ SV18 @ SV9 )
= $false )
| ( ( in_closed @ SV9 @ SV18 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( leq @ SV23 @ SV4 )
| ~ ( leq @ SV4 @ SV28 ) )
= $true )
| ( ( ~ ( less @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(187,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( leq @ SV23 @ SV4 ) )
= $true )
| ( ( ~ ( leq @ SV4 @ SV28 ) )
= $true )
| ( ( ~ ( less @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(188,plain,
! [SV13: $i,SV28: $i,SV4: $i,SV23: $i] :
( ( ( leq @ SV23 @ SV4 )
= $false )
| ( ( ~ ( leq @ SV4 @ SV28 ) )
= $true )
| ( ( ~ ( less @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(189,plain,
! [SV13: $i,SV23: $i,SV28: $i,SV4: $i] :
( ( ( leq @ SV4 @ SV28 )
= $false )
| ( ( leq @ SV23 @ SV4 )
= $false )
| ( ( ~ ( less @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(190,plain,
! [SV28: $i,SV23: $i,SV13: $i,SV4: $i] :
( ( ( less @ SV4 @ SV13 )
= $false )
| ( ( leq @ SV23 @ SV4 )
= $false )
| ( ( leq @ SV4 @ SV28 )
= $false )
| ( ( ~ ( leq @ SV13 @ SV28 ) )
= $true )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(191,plain,
! [SV23: $i,SV4: $i,SV28: $i,SV13: $i] :
( ( ( leq @ SV13 @ SV28 )
= $false )
| ( ( leq @ SV4 @ SV28 )
= $false )
| ( ( leq @ SV23 @ SV4 )
= $false )
| ( ( less @ SV4 @ SV13 )
= $false )
| ( ( completion_compatible @ SV4 @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(192,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[77,191,185,183,181,180,172,169,168,166,163,162,161,156,114,78]) ).
thf(193,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT070+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.22 % Computer : n020.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Oct 6 12:44:51 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.37
% 0.64/0.37 No.of.Axioms: 11
% 0.64/0.37
% 0.64/0.37 Length.of.Defs: 0
% 0.64/0.37
% 0.64/0.37 Contains.Choice.Funs: false
% 0.64/0.37 .....
% 0.64/0.37
% 0.64/0.37 ********************************
% 0.64/0.37 * All subproblems solved! *
% 0.64/0.37 ********************************
% 0.64/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,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:192,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.64/0.37
% 0.64/0.37 %**** Beginning of derivation protocol ****
% 0.64/0.37 % SZS output start CNFRefutation
% See solution above
% 0.64/0.37
% 0.64/0.37 %**** End of derivation protocol ****
% 0.64/0.37 %**** no. of clauses in derivation: 165 ****
% 0.64/0.37 %**** clause counter: 192 ****
% 0.64/0.37
% 0.64/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,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:192,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------