%------------------------------------------------------------------------------
% 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 : n018.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 : Unsatisfiable 0.43s 0.32s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 123 ( 123 unt; 0 typ; 0 def)
% Number of atoms : 317 ( 212 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 699 ( 8 ~; 0 |; 0 &; 691 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 6 con; 0-5 aty)
% Number of variables : 232 ( 0 ^; 232 !; 0 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aux,type,
aux: $i > $i > $i > $i > $i > $i ).
thf(tp_aux2,type,
aux2: $i > $i > $i > $i > $i ).
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_impl,type,
impl: $i > $i > $i ).
thf(tp_leqNat,type,
leqNat: $i > $i > $i ).
thf(tp_merge,type,
merge: $i > $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_ord,type,
ord: $i > $i ).
thf(tp_prop_merge_ord_not3,type,
prop_merge_ord_not3: $i > $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(2,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(3,axiom,
! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(4,axiom,
! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(6,axiom,
( ( eq2 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(7,axiom,
( ( eq2 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( prop_merge_ord_not3 @ X @ Y )
= ( impl @ ( eq2 @ ( ord @ X ) @ btrue ) @ ( impl @ ( eq2 @ ( ord @ Y ) @ bfalse ) @ ( eq2 @ ( ord @ ( merge @ X @ Y ) ) @ btrue ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(9,axiom,
! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(10,axiom,
! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(11,axiom,
! [Y: $i,Y2: $i,Xs: $i] :
( ( ord @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
= ( aux2 @ Y @ Y2 @ Xs @ ( leqNat @ Y @ Y2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(12,axiom,
! [Y: $i] :
( ( ord @ ( cons @ Y @ nil ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(13,axiom,
( ( ord @ nil )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(14,axiom,
! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( aux @ Z @ Xs @ Y2 @ Ys @ ( leqNat @ Z @ Y2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(15,axiom,
! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(16,axiom,
! [Y: $i] :
( ( merge @ nil @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(17,axiom,
! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
= ( leqNat @ Z @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(18,axiom,
! [Z: $i] :
( ( leqNat @ ( s @ Z ) @ z )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(19,axiom,
! [Y: $i] :
( ( leqNat @ z @ Y )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(20,axiom,
! [Y: $i,Y2: $i,Xs: $i] :
( ( aux2 @ Y @ Y2 @ Xs @ bfalse )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(21,axiom,
! [Y: $i,Y2: $i,Xs: $i] :
( ( aux2 @ Y @ Y2 @ Xs @ btrue )
= ( ord @ ( cons @ Y2 @ Xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(22,axiom,
! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( aux @ Z @ Xs @ Y2 @ Ys @ bfalse )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(23,axiom,
! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( aux @ Z @ Xs @ Y2 @ Ys @ btrue )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
! [X: $i,Y: $i] :
( ( eq2 @ ( prop_merge_ord_not3 @ X @ Y ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(27,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(33,plain,
( ( ( eq2 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(34,plain,
( ( ( eq2 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( prop_merge_ord_not3 @ X @ Y )
= ( impl @ ( eq2 @ ( ord @ X ) @ btrue ) @ ( impl @ ( eq2 @ ( ord @ Y ) @ bfalse ) @ ( eq2 @ ( ord @ ( merge @ X @ Y ) ) @ btrue ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(36,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(37,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(38,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( ord @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
= ( aux2 @ Y @ Y2 @ Xs @ ( leqNat @ Y @ Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(39,plain,
( ( ! [Y: $i] :
( ( ord @ ( cons @ Y @ nil ) )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
( ( ( ord @ nil )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(41,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( aux @ Z @ Xs @ Y2 @ Ys @ ( leqNat @ Z @ Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(42,plain,
( ( ! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [Y: $i] :
( ( merge @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(44,plain,
( ( ! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
= ( leqNat @ Z @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(45,plain,
( ( ! [Z: $i] :
( ( leqNat @ ( s @ Z ) @ z )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(46,plain,
( ( ! [Y: $i] :
( ( leqNat @ z @ Y )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( aux2 @ Y @ Y2 @ Xs @ bfalse )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( aux2 @ Y @ Y2 @ Xs @ btrue )
= ( ord @ ( cons @ Y2 @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(49,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( aux @ Z @ Xs @ Y2 @ Ys @ bfalse )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(50,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( aux @ Z @ Xs @ Y2 @ Ys @ btrue )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( prop_merge_ord_not3 @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(52,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( prop_merge_ord_not3 @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( prop_merge_ord_not3 @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(55,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( aux @ Z @ Xs @ Y2 @ Ys @ btrue )
= ( cons @ Z @ ( merge @ Xs @ ( cons @ Y2 @ Ys ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(56,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( aux @ Z @ Xs @ Y2 @ Ys @ bfalse )
= ( cons @ Y2 @ ( merge @ ( cons @ Z @ Xs ) @ Ys ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(57,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( aux2 @ Y @ Y2 @ Xs @ btrue )
= ( ord @ ( cons @ Y2 @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(58,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( aux2 @ Y @ Y2 @ Xs @ bfalse )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(59,plain,
( ( ! [Y: $i] :
( ( leqNat @ z @ Y )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(60,plain,
( ( ! [Z: $i] :
( ( leqNat @ ( s @ Z ) @ z )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(61,plain,
( ( ! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
= ( leqNat @ Z @ M ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(62,plain,
( ( ! [Y: $i] :
( ( merge @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(63,plain,
( ( ! [Z: $i,Xs: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ nil )
= ( cons @ Z @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(64,plain,
( ( ! [Z: $i,Xs: $i,Y2: $i,Ys: $i] :
( ( merge @ ( cons @ Z @ Xs ) @ ( cons @ Y2 @ Ys ) )
= ( aux @ Z @ Xs @ Y2 @ Ys @ ( leqNat @ Z @ Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(65,plain,
( ( ( ord @ nil )
= btrue )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(66,plain,
( ( ! [Y: $i] :
( ( ord @ ( cons @ Y @ nil ) )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(67,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( ord @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
= ( aux2 @ Y @ Y2 @ Xs @ ( leqNat @ Y @ Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(68,plain,
( ( ! [Q: $i] :
( ( impl @ btrue @ Q )
= Q ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(69,plain,
( ( ! [Q: $i] :
( ( impl @ bfalse @ Q )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( prop_merge_ord_not3 @ X @ Y )
= ( impl @ ( eq2 @ ( ord @ X ) @ btrue ) @ ( impl @ ( eq2 @ ( ord @ Y ) @ bfalse ) @ ( eq2 @ ( ord @ ( merge @ X @ Y ) ) @ btrue ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(71,plain,
( ( ( eq2 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(72,plain,
( ( ( eq2 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(74,plain,
( ( ! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(75,plain,
( ( ! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(76,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(77,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(78,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[52]) ).
thf(79,plain,
! [SV1: $i] :
( ( ! [SY41: $i] :
( ( eq2 @ ( prop_merge_ord_not3 @ SV1 @ SY41 ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(80,plain,
! [SV2: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i] :
( ( aux @ SV2 @ SY42 @ SY43 @ SY44 @ btrue )
= ( cons @ SV2 @ ( merge @ SY42 @ ( cons @ SY43 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(81,plain,
! [SV3: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i] :
( ( aux @ SV3 @ SY45 @ SY46 @ SY47 @ bfalse )
= ( cons @ SY46 @ ( merge @ ( cons @ SV3 @ SY45 ) @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(82,plain,
! [SV4: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ( aux2 @ SV4 @ SY48 @ SY49 @ btrue )
= ( ord @ ( cons @ SY48 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(83,plain,
! [SV5: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ( aux2 @ SV5 @ SY50 @ SY51 @ bfalse )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(84,plain,
! [SV6: $i] :
( ( ( leqNat @ z @ SV6 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(85,plain,
! [SV7: $i] :
( ( ( leqNat @ ( s @ SV7 ) @ z )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(86,plain,
! [SV8: $i] :
( ( ! [SY52: $i] :
( ( leqNat @ ( s @ SV8 ) @ ( s @ SY52 ) )
= ( leqNat @ SV8 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(87,plain,
! [SV9: $i] :
( ( ( merge @ nil @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(88,plain,
! [SV10: $i] :
( ( ! [SY53: $i] :
( ( merge @ ( cons @ SV10 @ SY53 ) @ nil )
= ( cons @ SV10 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(89,plain,
! [SV11: $i] :
( ( ! [SY54: $i,SY55: $i,SY56: $i] :
( ( merge @ ( cons @ SV11 @ SY54 ) @ ( cons @ SY55 @ SY56 ) )
= ( aux @ SV11 @ SY54 @ SY55 @ SY56 @ ( leqNat @ SV11 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(90,plain,
! [SV12: $i] :
( ( ( ord @ ( cons @ SV12 @ nil ) )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(91,plain,
! [SV13: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ( ord @ ( cons @ SV13 @ ( cons @ SY57 @ SY58 ) ) )
= ( aux2 @ SV13 @ SY57 @ SY58 @ ( leqNat @ SV13 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(92,plain,
! [SV14: $i] :
( ( ( impl @ btrue @ SV14 )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(93,plain,
! [SV15: $i] :
( ( ( impl @ bfalse @ SV15 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(94,plain,
! [SV16: $i] :
( ( ! [SY59: $i] :
( ( prop_merge_ord_not3 @ SV16 @ SY59 )
= ( impl @ ( eq2 @ ( ord @ SV16 ) @ btrue ) @ ( impl @ ( eq2 @ ( ord @ SY59 ) @ bfalse ) @ ( eq2 @ ( ord @ ( merge @ SV16 @ SY59 ) ) @ btrue ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(95,plain,
! [SV17: $i] :
( ( ! [SY60: $i] :
( ( eq @ ( s @ SV17 ) @ ( s @ SY60 ) )
= ( eq @ SV17 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(96,plain,
! [SV18: $i] :
( ( ( eq @ z @ ( s @ SV18 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(97,plain,
! [SV19: $i] :
( ( ( eq @ ( s @ SV19 ) @ z )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(98,plain,
! [SV20: $i] :
( ( ( eq @ SV20 @ SV20 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV21: $i] :
( ( ( eq2 @ SV21 @ SV21 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(100,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(101,plain,
! [SV22: $i,SV1: $i] :
( ( ( eq2 @ ( prop_merge_ord_not3 @ SV1 @ SV22 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(102,plain,
! [SV23: $i,SV2: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ( aux @ SV2 @ SV23 @ SY61 @ SY62 @ btrue )
= ( cons @ SV2 @ ( merge @ SV23 @ ( cons @ SY61 @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(103,plain,
! [SV24: $i,SV3: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ( aux @ SV3 @ SV24 @ SY63 @ SY64 @ bfalse )
= ( cons @ SY63 @ ( merge @ ( cons @ SV3 @ SV24 ) @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(104,plain,
! [SV25: $i,SV4: $i] :
( ( ! [SY65: $i] :
( ( aux2 @ SV4 @ SV25 @ SY65 @ btrue )
= ( ord @ ( cons @ SV25 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(105,plain,
! [SV26: $i,SV5: $i] :
( ( ! [SY66: $i] :
( ( aux2 @ SV5 @ SV26 @ SY66 @ bfalse )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(106,plain,
! [SV27: $i,SV8: $i] :
( ( ( leqNat @ ( s @ SV8 ) @ ( s @ SV27 ) )
= ( leqNat @ SV8 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(107,plain,
! [SV28: $i,SV10: $i] :
( ( ( merge @ ( cons @ SV10 @ SV28 ) @ nil )
= ( cons @ SV10 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
! [SV29: $i,SV11: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ( merge @ ( cons @ SV11 @ SV29 ) @ ( cons @ SY67 @ SY68 ) )
= ( aux @ SV11 @ SV29 @ SY67 @ SY68 @ ( leqNat @ SV11 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(109,plain,
! [SV30: $i,SV13: $i] :
( ( ! [SY69: $i] :
( ( ord @ ( cons @ SV13 @ ( cons @ SV30 @ SY69 ) ) )
= ( aux2 @ SV13 @ SV30 @ SY69 @ ( leqNat @ SV13 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(110,plain,
! [SV31: $i,SV16: $i] :
( ( ( prop_merge_ord_not3 @ SV16 @ SV31 )
= ( impl @ ( eq2 @ ( ord @ SV16 ) @ btrue ) @ ( impl @ ( eq2 @ ( ord @ SV31 ) @ bfalse ) @ ( eq2 @ ( ord @ ( merge @ SV16 @ SV31 ) ) @ btrue ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(111,plain,
! [SV32: $i,SV17: $i] :
( ( ( eq @ ( s @ SV17 ) @ ( s @ SV32 ) )
= ( eq @ SV17 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV22: $i,SV1: $i] :
( ( ( eq2 @ ( prop_merge_ord_not3 @ SV1 @ SV22 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV33: $i,SV23: $i,SV2: $i] :
( ( ! [SY70: $i] :
( ( aux @ SV2 @ SV23 @ SV33 @ SY70 @ btrue )
= ( cons @ SV2 @ ( merge @ SV23 @ ( cons @ SV33 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV34: $i,SV24: $i,SV3: $i] :
( ( ! [SY71: $i] :
( ( aux @ SV3 @ SV24 @ SV34 @ SY71 @ bfalse )
= ( cons @ SV34 @ ( merge @ ( cons @ SV3 @ SV24 ) @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV35: $i,SV25: $i,SV4: $i] :
( ( ( aux2 @ SV4 @ SV25 @ SV35 @ btrue )
= ( ord @ ( cons @ SV25 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV36: $i,SV26: $i,SV5: $i] :
( ( ( aux2 @ SV5 @ SV26 @ SV36 @ bfalse )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV37: $i,SV29: $i,SV11: $i] :
( ( ! [SY72: $i] :
( ( merge @ ( cons @ SV11 @ SV29 ) @ ( cons @ SV37 @ SY72 ) )
= ( aux @ SV11 @ SV29 @ SV37 @ SY72 @ ( leqNat @ SV11 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(118,plain,
! [SV38: $i,SV30: $i,SV13: $i] :
( ( ( ord @ ( cons @ SV13 @ ( cons @ SV30 @ SV38 ) ) )
= ( aux2 @ SV13 @ SV30 @ SV38 @ ( leqNat @ SV13 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(119,plain,
! [SV39: $i,SV33: $i,SV23: $i,SV2: $i] :
( ( ( aux @ SV2 @ SV23 @ SV33 @ SV39 @ btrue )
= ( cons @ SV2 @ ( merge @ SV23 @ ( cons @ SV33 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV40: $i,SV34: $i,SV24: $i,SV3: $i] :
( ( ( aux @ SV3 @ SV24 @ SV34 @ SV40 @ bfalse )
= ( cons @ SV34 @ ( merge @ ( cons @ SV3 @ SV24 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV41: $i,SV37: $i,SV29: $i,SV11: $i] :
( ( ( merge @ ( cons @ SV11 @ SV29 ) @ ( cons @ SV37 @ SV41 ) )
= ( aux @ SV11 @ SV29 @ SV37 @ SV41 @ ( leqNat @ SV11 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(122,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,121,120,119,118,116,115,112,111,110,107,106,100,99,98,97,96,93,92,90,87,85,84,72,71]) ).
thf(123,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[122]) ).
%------------------------------------------------------------------------------
%----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
% 0.09/0.18 % Computer : n018.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 17:13:37 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/0.32
% 0.43/0.32 No.of.Axioms: 24
% 0.43/0.32
% 0.43/0.32 Length.of.Defs: 0
% 0.43/0.32
% 0.43/0.32 Contains.Choice.Funs: false
% 0.43/0.32 ...
% 0.43/0.32
% 0.43/0.32 ********************************
% 0.43/0.32 * All subproblems solved! *
% 0.43/0.32 ********************************
% 0.43/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:122,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.43/0.32
% 0.43/0.32 %**** Beginning of derivation protocol ****
% 0.43/0.32 % SZS output start CNFRefutation
% See solution above
% 0.43/0.32
% 0.43/0.32 %**** End of derivation protocol ****
% 0.43/0.32 %**** no. of clauses in derivation: 123 ****
% 0.43/0.32 %**** clause counter: 122 ****
% 0.43/0.32
% 0.43/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:122,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------