%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX217+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 : n026.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 11:02:35 AM UTC 2026
% Result : Theorem 11.70s 2.33s
% Output : CNFRefutation 11.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 134 ( 120 unt; 0 typ; 0 def)
% Number of atoms : 411 ( 233 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 667 ( 101 ~; 28 |; 0 &; 529 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 165 ( 0 ^; 155 !; 10 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addNat,type,
addNat: $i > $i > $i ).
thf(tp_append,type,
append: $i > $i > $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_double,type,
double: $i > $i ).
thf(tp_evenNat,type,
evenNat: $i > $o ).
thf(tp_half,type,
half: $i > $i ).
thf(tp_head,type,
head: $i > $i ).
thf(tp_i,type,
i: $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_o,type,
o: $i ).
thf(tp_proj1Suc,type,
proj1Suc: $i > $i ).
thf(tp_rd,type,
rd: $i > $i ).
thf(tp_shw,type,
shw: $i > $i ).
thf(tp_suc,type,
suc: $i > $i ).
thf(tp_tail,type,
tail: $i > $i ).
thf(tp_x,type,
x: $i > $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( x @ X @ Y )
= ( rd @ ( append @ ( shw @ X ) @ ( shw @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(2,axiom,
! [Xs: $i] :
( ( rd @ ( cons @ o @ Xs ) )
= ( double @ ( rd @ Xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(3,axiom,
! [Xs: $i] :
( ( rd @ ( cons @ i @ Xs ) )
= ( suc @ ( double @ ( rd @ Xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(4,axiom,
( ( rd @ nil )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(5,axiom,
! [X: $i] :
( ( double @ X )
= ( addNat @ X @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(6,axiom,
! [Y: $i,Z: $i] :
( ( addNat @ ( suc @ Z ) @ Y )
= ( suc @ ( addNat @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(7,axiom,
! [Y: $i] :
( ( addNat @ zero @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(8,axiom,
! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(9,axiom,
! [Y: $i] :
( ( append @ nil @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(10,axiom,
! [Y: $i] :
( ~ ( evenNat @ ( suc @ Y ) )
=> ( ( shw @ ( suc @ Y ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(11,axiom,
! [Y: $i] :
( ( evenNat @ ( suc @ Y ) )
=> ( ( shw @ ( suc @ Y ) )
= ( cons @ o @ ( shw @ ( half @ ( suc @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(12,axiom,
( ( shw @ zero )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(13,axiom,
! [N: $i] :
( ( evenNat @ ( suc @ N ) )
<=> ~ ( evenNat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(14,axiom,
evenNat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(15,axiom,
! [N: $i] :
( ( half @ ( suc @ ( suc @ N ) ) )
= ( suc @ ( half @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(16,axiom,
( ( half @ ( suc @ zero ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(17,axiom,
( ( half @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(18,axiom,
i != o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(19,axiom,
! [X: $i] :
( zero
!= ( suc @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(20,axiom,
! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(21,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(22,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(23,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(24,conjecture,
? [X: $i,Y: $i] :
( ( x @ X @ Y )
!= ( x @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_024) ).
thf(25,negated_conjecture,
( ( ? [X: $i,Y: $i] :
( ( x @ X @ Y )
!= ( x @ Y @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,plain,
( ( ? [X: $i,Y: $i] :
( ( x @ X @ Y )
!= ( x @ Y @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( x @ X @ Y )
= ( rd @ ( append @ ( shw @ X ) @ ( shw @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(28,plain,
( ( ! [Xs: $i] :
( ( rd @ ( cons @ o @ Xs ) )
= ( double @ ( rd @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(29,plain,
( ( ! [Xs: $i] :
( ( rd @ ( cons @ i @ Xs ) )
= ( suc @ ( double @ ( rd @ Xs ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(30,plain,
( ( ( rd @ nil )
= zero )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( double @ X )
= ( addNat @ X @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(32,plain,
( ( ! [Y: $i,Z: $i] :
( ( addNat @ ( suc @ Z ) @ Y )
= ( suc @ ( addNat @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(33,plain,
( ( ! [Y: $i] :
( ( addNat @ zero @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(34,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(36,plain,
( ( ! [Y: $i] :
( ~ ( evenNat @ ( suc @ Y ) )
=> ( ( shw @ ( suc @ Y ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ Y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(37,plain,
( ( ! [Y: $i] :
( ( evenNat @ ( suc @ Y ) )
=> ( ( shw @ ( suc @ Y ) )
= ( cons @ o @ ( shw @ ( half @ ( suc @ Y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(38,plain,
( ( ( shw @ zero )
= nil )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(39,plain,
( ( ! [N: $i] :
( ( evenNat @ ( suc @ N ) )
<=> ~ ( evenNat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(40,plain,
( ( evenNat @ zero )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(41,plain,
( ( ! [N: $i] :
( ( half @ ( suc @ ( suc @ N ) ) )
= ( suc @ ( half @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(42,plain,
( ( ( half @ ( suc @ zero ) )
= zero )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(43,plain,
( ( ( half @ zero )
= zero )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(44,plain,
( ( i != o )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(50,plain,
( ( ~ ? [X: $i,Y: $i] :
( ( x @ X @ Y )
!= ( x @ Y @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(51,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(52,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(53,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(55,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(56,plain,
( ( i != o )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(57,plain,
( ( ( half @ zero )
= zero )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(58,plain,
( ( ( half @ ( suc @ zero ) )
= zero )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(59,plain,
( ( ! [N: $i] :
( ( half @ ( suc @ ( suc @ N ) ) )
= ( suc @ ( half @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(60,plain,
( ( evenNat @ zero )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(61,plain,
( ( ! [N: $i] :
( ( evenNat @ ( suc @ N ) )
<=> ~ ( evenNat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(62,plain,
( ( ( shw @ zero )
= nil )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(63,plain,
( ( ! [Y: $i] :
( ( evenNat @ ( suc @ Y ) )
=> ( ( shw @ ( suc @ Y ) )
= ( cons @ o @ ( shw @ ( half @ ( suc @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(64,plain,
( ( ! [Y: $i] :
( ~ ( evenNat @ ( suc @ Y ) )
=> ( ( shw @ ( suc @ Y ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(65,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(66,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(67,plain,
( ( ! [Y: $i] :
( ( addNat @ zero @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(68,plain,
( ( ! [Y: $i,Z: $i] :
( ( addNat @ ( suc @ Z ) @ Y )
= ( suc @ ( addNat @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(69,plain,
( ( ! [X: $i] :
( ( double @ X )
= ( addNat @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(70,plain,
( ( ( rd @ nil )
= zero )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(71,plain,
( ( ! [Xs: $i] :
( ( rd @ ( cons @ i @ Xs ) )
= ( suc @ ( double @ ( rd @ Xs ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(72,plain,
( ( ! [Xs: $i] :
( ( rd @ ( cons @ o @ Xs ) )
= ( double @ ( rd @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( x @ X @ Y )
= ( rd @ ( append @ ( shw @ X ) @ ( shw @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(74,plain,
( ( ~ ? [X: $i,Y: $i] :
( ( x @ X @ Y )
!= ( x @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(75,plain,
( ( ! [SX0: $i] :
( ~ ~ ( evenNat @ ( suc @ SX0 ) )
| ( ( shw @ ( suc @ SX0 ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i] :
( nil
!= ( cons @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(77,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ( ( ( x @ SX0 @ SX1 )
!= ( x @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(78,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( evenNat @ ( suc @ SX0 ) )
| ~ ( evenNat @ SX0 ) )
| ~ ( ~ ~ ( evenNat @ SX0 )
| ( evenNat @ ( suc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( zero
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( evenNat @ ( suc @ SX0 ) )
| ( ( shw @ ( suc @ SX0 ) )
= ( cons @ o @ ( shw @ ( half @ ( suc @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(81,plain,
( ( i != o )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(82,plain,
! [SV1: $i] :
( ( ! [SY26: $i] :
( ( head @ ( cons @ SV1 @ SY26 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(83,plain,
! [SV2: $i] :
( ( ! [SY27: $i] :
( ( tail @ ( cons @ SV2 @ SY27 ) )
= SY27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(84,plain,
! [SV3: $i] :
( ( ( proj1Suc @ ( suc @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(85,plain,
! [SV4: $i] :
( ( ( half @ ( suc @ ( suc @ SV4 ) ) )
= ( suc @ ( half @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(86,plain,
! [SV5: $i] :
( ( ( append @ nil @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV6: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( append @ ( cons @ SY28 @ SY29 ) @ SV6 )
= ( cons @ SY28 @ ( append @ SY29 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV7: $i] :
( ( ( addNat @ zero @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV8: $i] :
( ( ! [SY30: $i] :
( ( addNat @ ( suc @ SY30 ) @ SV8 )
= ( suc @ ( addNat @ SY30 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV9: $i] :
( ( ( double @ SV9 )
= ( addNat @ SV9 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV10: $i] :
( ( ( rd @ ( cons @ i @ SV10 ) )
= ( suc @ ( double @ ( rd @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(92,plain,
! [SV11: $i] :
( ( ( rd @ ( cons @ o @ SV11 ) )
= ( double @ ( rd @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(93,plain,
! [SV12: $i] :
( ( ! [SY31: $i] :
( ( x @ SV12 @ SY31 )
= ( rd @ ( append @ ( shw @ SV12 ) @ ( shw @ SY31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(94,plain,
! [SV13: $i] :
( ( ~ ~ ( evenNat @ ( suc @ SV13 ) )
| ( ( shw @ ( suc @ SV13 ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ SV13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(95,plain,
! [SV14: $i] :
( ( ! [SY32: $i] :
( nil
!= ( cons @ SV14 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(96,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ( ( ( x @ SX0 @ SX1 )
!= ( x @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(97,plain,
! [SV15: $i] :
( ( ~ ( ~ ( ~ ( evenNat @ ( suc @ SV15 ) )
| ~ ( evenNat @ SV15 ) )
| ~ ( ~ ~ ( evenNat @ SV15 )
| ( evenNat @ ( suc @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV16: $i] :
( ( zero
!= ( suc @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(99,plain,
! [SV17: $i] :
( ( ~ ( evenNat @ ( suc @ SV17 ) )
| ( ( shw @ ( suc @ SV17 ) )
= ( cons @ o @ ( shw @ ( half @ ( suc @ SV17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(100,plain,
( ( i = o )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(101,plain,
! [SV18: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV18 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(102,plain,
! [SV19: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(103,plain,
! [SV6: $i,SV20: $i] :
( ( ! [SY33: $i] :
( ( append @ ( cons @ SV20 @ SY33 ) @ SV6 )
= ( cons @ SV20 @ ( append @ SY33 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV8: $i,SV21: $i] :
( ( ( addNat @ ( suc @ SV21 ) @ SV8 )
= ( suc @ ( addNat @ SV21 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV22: $i,SV12: $i] :
( ( ( x @ SV12 @ SV22 )
= ( rd @ ( append @ ( shw @ SV12 ) @ ( shw @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV13: $i] :
( ( ( ~ ~ ( evenNat @ ( suc @ SV13 ) ) )
= $true )
| ( ( ( shw @ ( suc @ SV13 ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV23: $i,SV14: $i] :
( ( nil
!= ( cons @ SV14 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(108,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ( ( ( x @ SX0 @ SX1 )
!= ( x @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(109,plain,
! [SV15: $i] :
( ( ~ ( ~ ( evenNat @ ( suc @ SV15 ) )
| ~ ( evenNat @ SV15 ) )
| ~ ( ~ ~ ( evenNat @ SV15 )
| ( evenNat @ ( suc @ SV15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV16: $i] :
( ( zero
= ( suc @ SV16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV17: $i] :
( ( ( ~ ( evenNat @ ( suc @ SV17 ) ) )
= $true )
| ( ( ( shw @ ( suc @ SV17 ) )
= ( cons @ o @ ( shw @ ( half @ ( suc @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV6: $i,SV24: $i,SV20: $i] :
( ( ( append @ ( cons @ SV20 @ SV24 ) @ SV6 )
= ( cons @ SV20 @ ( append @ SV24 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV13: $i] :
( ( ( ~ ( evenNat @ ( suc @ SV13 ) ) )
= $false )
| ( ( ( shw @ ( suc @ SV13 ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV23: $i,SV14: $i] :
( ( nil
= ( cons @ SV14 @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV25: $i] :
( ( ~ ~ ! [SY34: $i] :
~ ( ( ( x @ SV25 @ SY34 )
!= ( x @ SY34 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV15: $i] :
( ( ~ ( ~ ( evenNat @ ( suc @ SV15 ) )
| ~ ( evenNat @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(117,plain,
! [SV15: $i] :
( ( ~ ( ~ ~ ( evenNat @ SV15 )
| ( evenNat @ ( suc @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(118,plain,
! [SV17: $i] :
( ( ( evenNat @ ( suc @ SV17 ) )
= $false )
| ( ( ( shw @ ( suc @ SV17 ) )
= ( cons @ o @ ( shw @ ( half @ ( suc @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV13: $i] :
( ( ( evenNat @ ( suc @ SV13 ) )
= $true )
| ( ( ( shw @ ( suc @ SV13 ) )
= ( cons @ i @ ( shw @ ( half @ ( suc @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(120,plain,
! [SV25: $i] :
( ( ~ ! [SY34: $i] :
~ ( ( ( x @ SV25 @ SY34 )
!= ( x @ SY34 @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV15: $i] :
( ( ~ ( evenNat @ ( suc @ SV15 ) )
| ~ ( evenNat @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV15: $i] :
( ( ~ ~ ( evenNat @ SV15 )
| ( evenNat @ ( suc @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV25: $i] :
( ( ! [SY34: $i] :
~ ( ( ( x @ SV25 @ SY34 )
!= ( x @ SY34 @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(124,plain,
! [SV15: $i] :
( ( ( ~ ( evenNat @ ( suc @ SV15 ) ) )
= $true )
| ( ( ~ ( evenNat @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(125,plain,
! [SV15: $i] :
( ( ( ~ ~ ( evenNat @ SV15 ) )
= $true )
| ( ( evenNat @ ( suc @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(126,plain,
! [SV26: $i,SV25: $i] :
( ( ~ ( ( ( x @ SV25 @ SV26 )
!= ( x @ SV26 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(127,plain,
! [SV15: $i] :
( ( ( evenNat @ ( suc @ SV15 ) )
= $false )
| ( ( ~ ( evenNat @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(128,plain,
! [SV15: $i] :
( ( ( ~ ( evenNat @ SV15 ) )
= $false )
| ( ( evenNat @ ( suc @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV26: $i,SV25: $i] :
( ( ( x @ SV25 @ SV26 )
!= ( x @ SV26 @ SV25 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV15: $i] :
( ( ( evenNat @ SV15 )
= $false )
| ( ( evenNat @ ( suc @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV15: $i] :
( ( ( evenNat @ SV15 )
= $true )
| ( ( evenNat @ ( suc @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(132,plain,
! [SV26: $i,SV25: $i] :
( ( ( x @ SV25 @ SV26 )
= ( x @ SV26 @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(133,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[57,132,131,130,119,118,114,112,110,105,104,102,101,100,92,91,90,88,86,85,84,70,62,60,58]) ).
thf(134,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX217+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 : n026.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 17:14:46 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.70/2.33
% 11.70/2.33 No.of.Axioms: 23
% 11.70/2.33
% 11.70/2.33 Length.of.Defs: 0
% 11.70/2.33
% 11.70/2.33 Contains.Choice.Funs: false
% 11.70/2.33 ..
% 11.70/2.33
% 11.70/2.33 ********************************
% 11.70/2.33 * All subproblems solved! *
% 11.70/2.33 ********************************
% 11.70/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,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:133,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.70/2.33
% 11.70/2.33 %**** Beginning of derivation protocol ****
% 11.70/2.33 % SZS output start CNFRefutation
% See solution above
% 11.70/2.33
% 11.70/2.33 %**** End of derivation protocol ****
% 11.70/2.33 %**** no. of clauses in derivation: 134 ****
% 11.70/2.33 %**** clause counter: 133 ****
% 11.70/2.33
% 11.70/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,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:133,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------