%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX199+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 : n019.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 2.87s 0.74s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 366 ( 193 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 810 ( 66 ~; 55 |; 2 &; 673 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 226 ( 0 ^; 214 !; 12 ?; 226 :)
% 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_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,
! [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(2,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(3,axiom,
! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(4,axiom,
! [Y: $i] :
( ( merge @ nil @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(5,axiom,
! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(6,axiom,
! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(7,axiom,
! [Y: $i] : ( leqNat @ z @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(8,axiom,
! [X: $i] :
( z
!= ( s @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(9,axiom,
! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(10,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(11,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(12,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(13,conjecture,
? [Xs: $i,Ys: $i,Zs: $i] :
~ ( ( ( merge @ Xs @ Ys )
= ( merge @ Ys @ Xs ) )
=> ( ( ( merge @ Xs @ Zs )
= ( merge @ Zs @ Xs ) )
=> ( ( merge @ Ys @ Zs )
= ( merge @ Zs @ Ys ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_013) ).
thf(14,negated_conjecture,
( ( ? [Xs: $i,Ys: $i,Zs: $i] :
~ ( ( ( merge @ Xs @ Ys )
= ( merge @ Ys @ Xs ) )
=> ( ( ( merge @ Xs @ Zs )
= ( merge @ Zs @ Xs ) )
=> ( ( merge @ Ys @ Zs )
= ( merge @ Zs @ Ys ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ? [Xs: $i,Ys: $i,Zs: $i] :
~ ( ( ( merge @ Xs @ Ys )
= ( merge @ Ys @ Xs ) )
=> ( ( ( merge @ Xs @ Zs )
= ( merge @ Zs @ Xs ) )
=> ( ( merge @ Ys @ Zs )
= ( merge @ Zs @ Ys ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,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)],[1]) ).
thf(17,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)],[2]) ).
thf(18,plain,
( ( ! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [Y: $i] :
( ( merge @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [Y: $i] : ( leqNat @ z @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( ~ ? [Xs: $i,Ys: $i,Zs: $i] :
~ ( ( ( merge @ Xs @ Ys )
= ( merge @ Ys @ Xs ) )
=> ( ( ( merge @ Xs @ Zs )
= ( merge @ Zs @ Xs ) )
=> ( ( merge @ Ys @ Zs )
= ( merge @ Zs @ Ys ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ! [Xs: $i,Ys: $i] :
( ( ( merge @ Xs @ Ys )
!= ( merge @ Ys @ Xs ) )
| ! [Zs: $i] :
( ( ( merge @ Xs @ Zs )
!= ( merge @ Zs @ Xs ) )
| ( ( merge @ Ys @ Zs )
= ( merge @ Zs @ Ys ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(30,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i] :
( ( leqNat @ Z @ Y2 )
| ! [Ys: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(31,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i] :
( ~ ( leqNat @ Z @ Y2 )
| ! [Ys: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(32,plain,
( ( ! [Z: $i,M: $i] :
( ~ ( leqNat @ ( s @ Z ) @ ( s @ M ) )
| ( leqNat @ Z @ M ) )
& ! [Z: $i,M: $i] :
( ~ ( leqNat @ Z @ M )
| ( leqNat @ ( s @ Z ) @ ( s @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(33,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(34,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(35,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(36,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(37,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(39,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(40,plain,
( ( ! [Y: $i] : ( leqNat @ z @ Y ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(41,plain,
( ( ! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(42,plain,
( ( ! [Z: $i,M: $i] :
( ~ ( leqNat @ ( s @ Z ) @ ( s @ M ) )
| ( leqNat @ Z @ M ) )
& ! [Z: $i,M: $i] :
( ~ ( leqNat @ Z @ M )
| ( leqNat @ ( s @ Z ) @ ( s @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(43,plain,
( ( ! [Y: $i] :
( ( merge @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i] :
( ~ ( leqNat @ Z @ Y2 )
| ! [Ys: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(46,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i] :
( ( leqNat @ Z @ Y2 )
| ! [Ys: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(47,plain,
( ( ! [Xs: $i,Ys: $i] :
( ( ( merge @ Xs @ Ys )
!= ( merge @ Ys @ Xs ) )
| ! [Zs: $i] :
( ( ( merge @ Xs @ Zs )
!= ( merge @ Zs @ Xs ) )
| ( ( merge @ Ys @ Zs )
= ( merge @ Zs @ Ys ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(48,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(49,plain,
! [SV1: $i] :
( ( ! [SY26: $i] :
( ( head @ ( cons @ SV1 @ SY26 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(50,plain,
! [SV2: $i] :
( ( ! [SY27: $i] :
( ( tail @ ( cons @ SV2 @ SY27 ) )
= SY27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV3: $i] :
( ( ! [SY28: $i] :
( nil
!= ( cons @ SV3 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( proj1S @ ( s @ SV4 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV5: $i] :
( ( z
!= ( s @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV6: $i] :
( ( leqNat @ z @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
! [SV7: $i] :
( ( ~ ( leqNat @ ( s @ SV7 ) @ z ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV8: $i] :
( ( ( merge @ nil @ SV8 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(57,plain,
! [SV9: $i] :
( ( ! [SY29: $i] :
( ( merge @ ( cons @ SV9 @ SY29 ) @ nil )
= ( cons @ SV9 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV10: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( leqNat @ SV10 @ SY31 )
| ! [SY32: $i] :
( ( merge @ ( cons @ SV10 @ SY30 ) @ ( cons @ SY31 @ SY32 ) )
= ( cons @ SV10 @ ( merge @ SY30 @ ( cons @ SY31 @ SY32 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
! [SV11: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( leqNat @ SV11 @ SY34 )
| ! [SY35: $i] :
( ( merge @ ( cons @ SV11 @ SY33 ) @ ( cons @ SY34 @ SY35 ) )
= ( cons @ SY34 @ ( merge @ ( cons @ SV11 @ SY33 ) @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV12: $i] :
( ( ! [SY36: $i] :
( ( ( merge @ SV12 @ SY36 )
!= ( merge @ SY36 @ SV12 ) )
| ! [SY37: $i] :
( ( ( merge @ SV12 @ SY37 )
!= ( merge @ SY37 @ SV12 ) )
| ( ( merge @ SY36 @ SY37 )
= ( merge @ SY37 @ SY36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(62,plain,
! [SV13: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV13 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(63,plain,
! [SV14: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV14 ) )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(64,plain,
! [SV15: $i,SV3: $i] :
( ( nil
!= ( cons @ SV3 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(65,plain,
! [SV5: $i] :
( ( z
= ( s @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(66,plain,
! [SV7: $i] :
( ( leqNat @ ( s @ SV7 ) @ z )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV16: $i,SV9: $i] :
( ( ( merge @ ( cons @ SV9 @ SV16 ) @ nil )
= ( cons @ SV9 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV17: $i,SV10: $i] :
( ( ! [SY38: $i] :
( ~ ( leqNat @ SV10 @ SY38 )
| ! [SY39: $i] :
( ( merge @ ( cons @ SV10 @ SV17 ) @ ( cons @ SY38 @ SY39 ) )
= ( cons @ SV10 @ ( merge @ SV17 @ ( cons @ SY38 @ SY39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV18: $i,SV11: $i] :
( ( ! [SY40: $i] :
( ( leqNat @ SV11 @ SY40 )
| ! [SY41: $i] :
( ( merge @ ( cons @ SV11 @ SV18 ) @ ( cons @ SY40 @ SY41 ) )
= ( cons @ SY40 @ ( merge @ ( cons @ SV11 @ SV18 ) @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV19: $i,SV12: $i] :
( ( ( ( merge @ SV12 @ SV19 )
!= ( merge @ SV19 @ SV12 ) )
| ! [SY42: $i] :
( ( ( merge @ SV12 @ SY42 )
!= ( merge @ SY42 @ SV12 ) )
| ( ( merge @ SV19 @ SY42 )
= ( merge @ SY42 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(72,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(73,plain,
! [SV15: $i,SV3: $i] :
( ( nil
= ( cons @ SV3 @ SV15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV17: $i,SV20: $i,SV10: $i] :
( ( ~ ( leqNat @ SV10 @ SV20 )
| ! [SY43: $i] :
( ( merge @ ( cons @ SV10 @ SV17 ) @ ( cons @ SV20 @ SY43 ) )
= ( cons @ SV10 @ ( merge @ SV17 @ ( cons @ SV20 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV18: $i,SV21: $i,SV11: $i] :
( ( ( leqNat @ SV11 @ SV21 )
| ! [SY44: $i] :
( ( merge @ ( cons @ SV11 @ SV18 ) @ ( cons @ SV21 @ SY44 ) )
= ( cons @ SV21 @ ( merge @ ( cons @ SV11 @ SV18 ) @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV19: $i,SV12: $i] :
( ( ( ( merge @ SV12 @ SV19 )
!= ( merge @ SV19 @ SV12 ) )
= $true )
| ( ( ! [SY42: $i] :
( ( ( merge @ SV12 @ SY42 )
!= ( merge @ SY42 @ SV12 ) )
| ( ( merge @ SV19 @ SY42 )
= ( merge @ SY42 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(79,plain,
! [SV17: $i,SV20: $i,SV10: $i] :
( ( ( ~ ( leqNat @ SV10 @ SV20 ) )
= $true )
| ( ( ! [SY43: $i] :
( ( merge @ ( cons @ SV10 @ SV17 ) @ ( cons @ SV20 @ SY43 ) )
= ( cons @ SV10 @ ( merge @ SV17 @ ( cons @ SV20 @ SY43 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV18: $i,SV21: $i,SV11: $i] :
( ( ( leqNat @ SV11 @ SV21 )
= $true )
| ( ( ! [SY44: $i] :
( ( merge @ ( cons @ SV11 @ SV18 ) @ ( cons @ SV21 @ SY44 ) )
= ( cons @ SV21 @ ( merge @ ( cons @ SV11 @ SV18 ) @ SY44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV19: $i,SV12: $i] :
( ( ( ( merge @ SV12 @ SV19 )
= ( merge @ SV19 @ SV12 ) )
= $false )
| ( ( ! [SY42: $i] :
( ( ( merge @ SV12 @ SY42 )
!= ( merge @ SY42 @ SV12 ) )
| ( ( merge @ SV19 @ SY42 )
= ( merge @ SY42 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV22: $i] :
( ( ! [SY45: $i] :
( ~ ( leqNat @ ( s @ SV22 ) @ ( s @ SY45 ) )
| ( leqNat @ SV22 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV23: $i] :
( ( ! [SY46: $i] :
( ~ ( leqNat @ SV23 @ SY46 )
| ( leqNat @ ( s @ SV23 ) @ ( s @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV17: $i,SV20: $i,SV10: $i] :
( ( ( leqNat @ SV10 @ SV20 )
= $false )
| ( ( ! [SY43: $i] :
( ( merge @ ( cons @ SV10 @ SV17 ) @ ( cons @ SV20 @ SY43 ) )
= ( cons @ SV10 @ ( merge @ SV17 @ ( cons @ SV20 @ SY43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV24: $i,SV21: $i,SV18: $i,SV11: $i] :
( ( ( ( merge @ ( cons @ SV11 @ SV18 ) @ ( cons @ SV21 @ SV24 ) )
= ( cons @ SV21 @ ( merge @ ( cons @ SV11 @ SV18 ) @ SV24 ) ) )
= $true )
| ( ( leqNat @ SV11 @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV19: $i,SV25: $i,SV12: $i] :
( ( ( ( ( merge @ SV12 @ SV25 )
!= ( merge @ SV25 @ SV12 ) )
| ( ( merge @ SV19 @ SV25 )
= ( merge @ SV25 @ SV19 ) ) )
= $true )
| ( ( ( merge @ SV12 @ SV19 )
= ( merge @ SV19 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV26: $i,SV22: $i] :
( ( ~ ( leqNat @ ( s @ SV22 ) @ ( s @ SV26 ) )
| ( leqNat @ SV22 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV27: $i,SV23: $i] :
( ( ~ ( leqNat @ SV23 @ SV27 )
| ( leqNat @ ( s @ SV23 ) @ ( s @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV28: $i,SV20: $i,SV17: $i,SV10: $i] :
( ( ( ( merge @ ( cons @ SV10 @ SV17 ) @ ( cons @ SV20 @ SV28 ) )
= ( cons @ SV10 @ ( merge @ SV17 @ ( cons @ SV20 @ SV28 ) ) ) )
= $true )
| ( ( leqNat @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV19: $i,SV25: $i,SV12: $i] :
( ( ( ( merge @ SV12 @ SV25 )
!= ( merge @ SV25 @ SV12 ) )
= $true )
| ( ( ( merge @ SV19 @ SV25 )
= ( merge @ SV25 @ SV19 ) )
= $true )
| ( ( ( merge @ SV12 @ SV19 )
= ( merge @ SV19 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV26: $i,SV22: $i] :
( ( ( ~ ( leqNat @ ( s @ SV22 ) @ ( s @ SV26 ) ) )
= $true )
| ( ( leqNat @ SV22 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV27: $i,SV23: $i] :
( ( ( ~ ( leqNat @ SV23 @ SV27 ) )
= $true )
| ( ( leqNat @ ( s @ SV23 ) @ ( s @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV19: $i,SV25: $i,SV12: $i] :
( ( ( ( merge @ SV12 @ SV25 )
= ( merge @ SV25 @ SV12 ) )
= $false )
| ( ( ( merge @ SV19 @ SV25 )
= ( merge @ SV25 @ SV19 ) )
= $true )
| ( ( ( merge @ SV12 @ SV19 )
= ( merge @ SV19 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV26: $i,SV22: $i] :
( ( ( leqNat @ ( s @ SV22 ) @ ( s @ SV26 ) )
= $false )
| ( ( leqNat @ SV22 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV27: $i,SV23: $i] :
( ( ( leqNat @ SV23 @ SV27 )
= $false )
| ( ( leqNat @ ( s @ SV23 ) @ ( s @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(96,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,95,94,93,89,85,73,67,66,65,63,62,56,54]) ).
thf(97,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX199+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21 % Computer : n019.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 17:11:16 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.87/0.74
% 2.87/0.74 No.of.Axioms: 12
% 2.87/0.74
% 2.87/0.74 Length.of.Defs: 0
% 2.87/0.74
% 2.87/0.74 Contains.Choice.Funs: false
% 2.87/0.74 ...
% 2.87/0.74
% 2.87/0.74 ********************************
% 2.87/0.74 * All subproblems solved! *
% 2.87/0.74 ********************************
% 2.87/0.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 2.87/0.74
% 2.87/0.74 %**** Beginning of derivation protocol ****
% 2.87/0.74 % SZS output start CNFRefutation
% See solution above
% 2.87/0.74
% 2.87/0.74 %**** End of derivation protocol ****
% 2.87/0.74 %**** no. of clauses in derivation: 97 ****
% 2.87/0.74 %**** clause counter: 96 ****
% 2.87/0.74
% 2.87/0.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------