%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX200+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 11:02:32 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 134 ( 102 unt; 0 typ; 0 def)
% Number of atoms : 577 ( 207 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1303 ( 233 ~; 118 |; 3 &; 927 @)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 298 ( 0 ^; 288 !; 10 ?; 298 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_head,type,
head: $i > $i ).
thf(tp_leqNat,type,
leqNat: $i > $i > $o ).
thf(tp_merge,type,
merge: $i > $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_ord,type,
ord: $i > $o ).
thf(tp_proj1S,type,
proj1S: $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_tail,type,
tail: $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [Y: $i,Y2: $i,Xs: $i] :
( ( ord @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
<=> ( ( leqNat @ Y @ Y2 )
& ( ord @ ( cons @ Y2 @ Xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(2,axiom,
! [Y: $i] : ( ord @ ( cons @ Y @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(3,axiom,
ord @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(4,axiom,
! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ~ ( leqNat @ Z @ Y2 )
=> ( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(5,axiom,
! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( leqNat @ Z @ Y2 )
=> ( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(6,axiom,
! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(7,axiom,
! [Y: $i] :
( ( merge @ nil @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(8,axiom,
! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(9,axiom,
! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(10,axiom,
! [Y: $i] : ( leqNat @ z @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(11,axiom,
! [X: $i] :
( z
!= ( s @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(12,axiom,
! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(13,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(14,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(15,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(16,conjecture,
? [Xs: $i,Ys: $i] :
~ ( ( ord @ Xs )
=> ( ~ ( ord @ Ys )
=> ( ord @ ( merge @ Xs @ Ys ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_016) ).
thf(17,negated_conjecture,
( ( ? [Xs: $i,Ys: $i] :
~ ( ( ord @ Xs )
=> ( ~ ( ord @ Ys )
=> ( ord @ ( merge @ Xs @ Ys ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,plain,
( ( ? [Xs: $i,Ys: $i] :
~ ( ( ord @ Xs )
=> ( ~ ( ord @ Ys )
=> ( ord @ ( merge @ Xs @ Ys ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( ord @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
<=> ( ( leqNat @ Y @ Y2 )
& ( ord @ ( cons @ Y2 @ Xs ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [Y: $i] : ( ord @ ( cons @ Y @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ord @ nil )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ~ ( leqNat @ Z @ Y2 )
=> ( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( leqNat @ Z @ Y2 )
=> ( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [Y: $i] :
( ( merge @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,plain,
( ( ! [Y: $i] : ( leqNat @ z @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(29,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(31,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(32,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(33,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(34,plain,
( ( ~ ? [Xs: $i,Ys: $i] :
~ ( ( ord @ Xs )
=> ( ~ ( ord @ Ys )
=> ( ord @ ( merge @ Xs @ Ys ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(35,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(36,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(37,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ! [Y: $i] : ( leqNat @ z @ Y ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(41,plain,
( ( ! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(42,plain,
( ( ! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(43,plain,
( ( ! [Y: $i] :
( ( merge @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(44,plain,
( ( ! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(45,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( leqNat @ Z @ Y2 )
=> ( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(46,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ~ ( leqNat @ Z @ Y2 )
=> ( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(47,plain,
( ( ord @ nil )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [Y: $i] : ( ord @ ( cons @ Y @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( ord @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
<=> ( ( leqNat @ Y @ Y2 )
& ( ord @ ( cons @ Y2 @ Xs ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(50,plain,
( ( ~ ? [Xs: $i,Ys: $i] :
~ ( ( ord @ Xs )
=> ( ~ ( ord @ Ys )
=> ( ord @ ( merge @ Xs @ Ys ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(51,plain,
( ( ! [SX0: $i] :
( z
!= ( s @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(52,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( leqNat @ SX0 @ SX2 )
| ( ( merge @ ( cons @ SX0 @ SX1 ) @ ( cons @ SX2 @ SX3 ) )
= ( cons @ SX2 @ ( merge @ ( cons @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) )
| ~ ( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i] :
( nil
!= ( cons @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( leqNat @ SX0 @ SX2 )
| ( ( merge @ ( cons @ SX0 @ SX1 ) @ ( cons @ SX2 @ SX3 ) )
= ( cons @ SX0 @ ( merge @ SX1 @ ( cons @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord @ ( cons @ SX0 @ ( cons @ SX1 @ SX2 ) ) )
| ~ ( ~ ( leqNat @ SX0 @ SX1 )
| ~ ( ord @ ( cons @ SX1 @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( leqNat @ SX0 @ SX1 )
| ~ ( ord @ ( cons @ SX1 @ SX2 ) ) )
| ( ord @ ( cons @ SX0 @ ( cons @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(57,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ord @ SX0 )
| ~ ~ ( ord @ SX1 )
| ( ord @ ( merge @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(58,plain,
! [SV1: $i] :
( ( ! [SY29: $i] :
( ( head @ ( cons @ SV1 @ SY29 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(59,plain,
! [SV2: $i] :
( ( ! [SY30: $i] :
( ( tail @ ( cons @ SV2 @ SY30 ) )
= SY30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(60,plain,
! [SV3: $i] :
( ( ( proj1S @ ( s @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(61,plain,
! [SV4: $i] :
( ( leqNat @ z @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(62,plain,
! [SV5: $i] :
( ( ~ ( leqNat @ ( s @ SV5 ) @ z ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(63,plain,
! [SV6: $i] :
( ( ( merge @ nil @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(64,plain,
! [SV7: $i] :
( ( ! [SY31: $i] :
( ( merge @ ( cons @ SV7 @ SY31 ) @ nil )
= ( cons @ SV7 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(65,plain,
! [SV8: $i] :
( ( ord @ ( cons @ SV8 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV9: $i] :
( ( z
!= ( s @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(67,plain,
! [SV10: $i] :
( ( ! [SY32: $i,SY33: $i,SY34: $i] :
( ~ ~ ( leqNat @ SV10 @ SY33 )
| ( ( merge @ ( cons @ SV10 @ SY32 ) @ ( cons @ SY33 @ SY34 ) )
= ( cons @ SY33 @ ( merge @ ( cons @ SV10 @ SY32 ) @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(68,plain,
! [SV11: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ~ ( leqNat @ ( s @ SV11 ) @ ( s @ SY35 ) )
| ( leqNat @ SV11 @ SY35 ) )
| ~ ( ~ ( leqNat @ SV11 @ SY35 )
| ( leqNat @ ( s @ SV11 ) @ ( s @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(69,plain,
! [SV12: $i] :
( ( ! [SY36: $i] :
( nil
!= ( cons @ SV12 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(70,plain,
! [SV13: $i] :
( ( ! [SY37: $i,SY38: $i,SY39: $i] :
( ~ ( leqNat @ SV13 @ SY38 )
| ( ( merge @ ( cons @ SV13 @ SY37 ) @ ( cons @ SY38 @ SY39 ) )
= ( cons @ SV13 @ ( merge @ SY37 @ ( cons @ SY38 @ SY39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(71,plain,
! [SV14: $i] :
( ( ! [SY40: $i,SY41: $i] :
~ ( ~ ( ~ ( ord @ ( cons @ SV14 @ ( cons @ SY40 @ SY41 ) ) )
| ~ ( ~ ( leqNat @ SV14 @ SY40 )
| ~ ( ord @ ( cons @ SY40 @ SY41 ) ) ) )
| ~ ( ~ ~ ( ~ ( leqNat @ SV14 @ SY40 )
| ~ ( ord @ ( cons @ SY40 @ SY41 ) ) )
| ( ord @ ( cons @ SV14 @ ( cons @ SY40 @ SY41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(72,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ord @ SX0 )
| ~ ~ ( ord @ SX1 )
| ( ord @ ( merge @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV15: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV15 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
! [SV16: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV16 ) )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(75,plain,
! [SV5: $i] :
( ( leqNat @ ( s @ SV5 ) @ z )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV17: $i,SV7: $i] :
( ( ( merge @ ( cons @ SV7 @ SV17 ) @ nil )
= ( cons @ SV7 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV9: $i] :
( ( z
= ( s @ SV9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(78,plain,
! [SV18: $i,SV10: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ~ ( leqNat @ SV10 @ SY42 )
| ( ( merge @ ( cons @ SV10 @ SV18 ) @ ( cons @ SY42 @ SY43 ) )
= ( cons @ SY42 @ ( merge @ ( cons @ SV10 @ SV18 ) @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(79,plain,
! [SV19: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) )
| ( leqNat @ SV11 @ SV19 ) )
| ~ ( ~ ( leqNat @ SV11 @ SV19 )
| ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV20: $i,SV12: $i] :
( ( nil
!= ( cons @ SV12 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV21: $i,SV13: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( leqNat @ SV13 @ SY44 )
| ( ( merge @ ( cons @ SV13 @ SV21 ) @ ( cons @ SY44 @ SY45 ) )
= ( cons @ SV13 @ ( merge @ SV21 @ ( cons @ SY44 @ SY45 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV22: $i,SV14: $i] :
( ( ! [SY46: $i] :
~ ( ~ ( ~ ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SY46 ) ) )
| ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SY46 ) ) ) )
| ~ ( ~ ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SY46 ) ) )
| ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SY46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(83,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ( ord @ SX0 )
| ~ ~ ( ord @ SX1 )
| ( ord @ ( merge @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(84,plain,
! [SV18: $i,SV23: $i,SV10: $i] :
( ( ! [SY47: $i] :
( ~ ~ ( leqNat @ SV10 @ SV23 )
| ( ( merge @ ( cons @ SV10 @ SV18 ) @ ( cons @ SV23 @ SY47 ) )
= ( cons @ SV23 @ ( merge @ ( cons @ SV10 @ SV18 ) @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV19: $i,SV11: $i] :
( ( ~ ( ~ ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) )
| ( leqNat @ SV11 @ SV19 ) )
| ~ ( ~ ( leqNat @ SV11 @ SV19 )
| ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV20: $i,SV12: $i] :
( ( nil
= ( cons @ SV12 @ SV20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV21: $i,SV24: $i,SV13: $i] :
( ( ! [SY48: $i] :
( ~ ( leqNat @ SV13 @ SV24 )
| ( ( merge @ ( cons @ SV13 @ SV21 ) @ ( cons @ SV24 @ SY48 ) )
= ( cons @ SV13 @ ( merge @ SV21 @ ( cons @ SV24 @ SY48 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
| ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) )
| ~ ( ~ ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
| ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV26: $i] :
( ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ( ord @ SV26 )
| ~ ~ ( ord @ SY49 )
| ( ord @ ( merge @ SV26 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV27: $i,SV18: $i,SV23: $i,SV10: $i] :
( ( ~ ~ ( leqNat @ SV10 @ SV23 )
| ( ( merge @ ( cons @ SV10 @ SV18 ) @ ( cons @ SV23 @ SV27 ) )
= ( cons @ SV23 @ ( merge @ ( cons @ SV10 @ SV18 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV19: $i,SV11: $i] :
( ( ~ ( ~ ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) )
| ( leqNat @ SV11 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(92,plain,
! [SV19: $i,SV11: $i] :
( ( ~ ( ~ ( leqNat @ SV11 @ SV19 )
| ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(93,plain,
! [SV28: $i,SV21: $i,SV24: $i,SV13: $i] :
( ( ~ ( leqNat @ SV13 @ SV24 )
| ( ( merge @ ( cons @ SV13 @ SV21 ) @ ( cons @ SV24 @ SV28 ) )
= ( cons @ SV13 @ ( merge @ SV21 @ ( cons @ SV24 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ~ ( ~ ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
| ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) )
| ~ ( ~ ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
| ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV26: $i] :
( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( ord @ SV26 )
| ~ ~ ( ord @ SY49 )
| ( ord @ ( merge @ SV26 @ SY49 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV27: $i,SV18: $i,SV23: $i,SV10: $i] :
( ( ( ~ ~ ( leqNat @ SV10 @ SV23 ) )
= $true )
| ( ( ( merge @ ( cons @ SV10 @ SV18 ) @ ( cons @ SV23 @ SV27 ) )
= ( cons @ SV23 @ ( merge @ ( cons @ SV10 @ SV18 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV19: $i,SV11: $i] :
( ( ~ ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) )
| ( leqNat @ SV11 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(98,plain,
! [SV19: $i,SV11: $i] :
( ( ~ ( leqNat @ SV11 @ SV19 )
| ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV28: $i,SV21: $i,SV24: $i,SV13: $i] :
( ( ( ~ ( leqNat @ SV13 @ SV24 ) )
= $true )
| ( ( ( merge @ ( cons @ SV13 @ SV21 ) @ ( cons @ SV24 @ SV28 ) )
= ( cons @ SV13 @ ( merge @ SV21 @ ( cons @ SV24 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ~ ( ~ ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
| ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ~ ( ~ ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
| ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(102,plain,
! [SV26: $i] :
( ( ! [SY49: $i] :
~ ~ ( ~ ( ord @ SV26 )
| ~ ~ ( ord @ SY49 )
| ( ord @ ( merge @ SV26 @ SY49 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(103,plain,
! [SV27: $i,SV18: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( leqNat @ SV10 @ SV23 ) )
= $false )
| ( ( ( merge @ ( cons @ SV10 @ SV18 ) @ ( cons @ SV23 @ SV27 ) )
= ( cons @ SV23 @ ( merge @ ( cons @ SV10 @ SV18 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV19: $i,SV11: $i] :
( ( ( ~ ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) ) )
= $true )
| ( ( leqNat @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV19: $i,SV11: $i] :
( ( ( ~ ( leqNat @ SV11 @ SV19 ) )
= $true )
| ( ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV28: $i,SV21: $i,SV24: $i,SV13: $i] :
( ( ( leqNat @ SV13 @ SV24 )
= $false )
| ( ( ( merge @ ( cons @ SV13 @ SV21 ) @ ( cons @ SV24 @ SV28 ) )
= ( cons @ SV13 @ ( merge @ SV21 @ ( cons @ SV24 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ~ ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
| ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ~ ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
| ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(109,plain,
! [SV29: $i,SV26: $i] :
( ( ~ ~ ( ~ ( ord @ SV26 )
| ~ ~ ( ord @ SV29 )
| ( ord @ ( merge @ SV26 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV27: $i,SV18: $i,SV23: $i,SV10: $i] :
( ( ( leqNat @ SV10 @ SV23 )
= $true )
| ( ( ( merge @ ( cons @ SV10 @ SV18 ) @ ( cons @ SV23 @ SV27 ) )
= ( cons @ SV23 @ ( merge @ ( cons @ SV10 @ SV18 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(111,plain,
! [SV19: $i,SV11: $i] :
( ( ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) )
= $false )
| ( ( leqNat @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV19: $i,SV11: $i] :
( ( ( leqNat @ SV11 @ SV19 )
= $false )
| ( ( leqNat @ ( s @ SV11 ) @ ( s @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) )
= $true )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(115,plain,
! [SV29: $i,SV26: $i] :
( ( ~ ( ~ ( ord @ SV26 )
| ~ ~ ( ord @ SV29 )
| ( ord @ ( merge @ SV26 @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(116,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) ) )
= $false )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(118,plain,
! [SV29: $i,SV26: $i] :
( ( ~ ( ord @ SV26 )
| ~ ~ ( ord @ SV29 )
| ( ord @ ( merge @ SV26 @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(119,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
= $false )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(120,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( leqNat @ SV14 @ SV22 )
| ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
= $true )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(121,plain,
! [SV29: $i,SV26: $i] :
( ( ( ~ ( ord @ SV26 ) )
= $true )
| ( ( ~ ~ ( ord @ SV29 )
| ( ord @ ( merge @ SV26 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(122,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( leqNat @ SV14 @ SV22 ) )
= $false )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(123,plain,
! [SV14: $i,SV25: $i,SV22: $i] :
( ( ( ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
= $false )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( ~ ( leqNat @ SV14 @ SV22 ) )
= $true )
| ( ( ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
= $true )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV29: $i,SV26: $i] :
( ( ( ord @ SV26 )
= $false )
| ( ( ~ ~ ( ord @ SV29 )
| ( ord @ ( merge @ SV26 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( leqNat @ SV14 @ SV22 )
= $true )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV14: $i,SV25: $i,SV22: $i] :
( ( ( ord @ ( cons @ SV22 @ SV25 ) )
= $true )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(128,plain,
! [SV25: $i,SV22: $i,SV14: $i] :
( ( ( leqNat @ SV14 @ SV22 )
= $false )
| ( ( ~ ( ord @ ( cons @ SV22 @ SV25 ) ) )
= $true )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV26: $i,SV29: $i] :
( ( ( ~ ~ ( ord @ SV29 ) )
= $true )
| ( ( ord @ ( merge @ SV26 @ SV29 ) )
= $true )
| ( ( ord @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV14: $i,SV25: $i,SV22: $i] :
( ( ( ord @ ( cons @ SV22 @ SV25 ) )
= $false )
| ( ( leqNat @ SV14 @ SV22 )
= $false )
| ( ( ord @ ( cons @ SV14 @ ( cons @ SV22 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV26: $i,SV29: $i] :
( ( ( ~ ( ord @ SV29 ) )
= $false )
| ( ( ord @ ( merge @ SV26 @ SV29 ) )
= $true )
| ( ( ord @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(132,plain,
! [SV26: $i,SV29: $i] :
( ( ( ord @ SV29 )
= $true )
| ( ( ord @ ( merge @ SV26 @ SV29 ) )
= $true )
| ( ( ord @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(133,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,132,130,127,126,112,111,110,106,86,77,76,75,74,73,65,63,61,60]) ).
thf(134,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n013.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 17:10:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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: 15
% 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:0,axioms:15,ps:3,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:133,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: 134 ****
% 0.08/0.25 %**** clause counter: 133 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,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:133,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------