%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 11:02:37 AM UTC 2026
% Result : Unsatisfiable 1.88s 0.54s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 137 ( 127 unt; 0 typ; 0 def)
% Number of atoms : 391 ( 266 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 716 ( 22 ~; 20 |; 0 &; 674 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 0-4 aty)
% Number of variables : 260 ( 0 ^; 260 !; 0 ?; 260 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aux,type,
aux: $i > $i > $i > $i > $i ).
thf(tp_barbar,type,
barbar: $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_elem,type,
elem: $i > $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_eq3,type,
eq3: $i > $i > $i ).
thf(tp_eqNat,type,
eqNat: $i > $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_prop_union_comm,type,
prop_union_comm: $i > $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(3,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(4,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(5,axiom,
! [X: $i] :
( ( eq3 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(6,axiom,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(7,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(8,axiom,
! [X: $i] :
( ( eq2 @ z @ ( s @ X ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(9,axiom,
! [X: $i] :
( ( eq2 @ ( s @ X ) @ z )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ ( s @ X ) @ ( s @ Y ) )
= ( eq2 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(11,axiom,
( ( eq3 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(12,axiom,
( ( eq3 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(13,axiom,
! [X: $i,Y: $i] :
( ( prop_union_comm @ X @ Y )
= ( eq @ ( union @ X @ Y ) @ ( union @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(14,axiom,
! [Z: $i,Xs: $i,Y: $i] :
( ( union @ ( cons @ Z @ Xs ) @ Y )
= ( aux @ Y @ Z @ Xs @ ( elem @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(15,axiom,
! [Y: $i] :
( ( union @ nil @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(16,axiom,
! [X: $i,Z: $i,Xs: $i] :
( ( elem @ X @ ( cons @ Z @ Xs ) )
= ( barbar @ ( eqNat @ X @ Z ) @ ( elem @ X @ Xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(17,axiom,
! [X: $i] :
( ( elem @ X @ nil )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(18,axiom,
( ( eqNat @ z @ z )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(19,axiom,
! [X2: $i] :
( ( eqNat @ z @ ( s @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(20,axiom,
! [Z: $i] :
( ( eqNat @ ( s @ Z ) @ z )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(21,axiom,
! [Z: $i,Y2: $i] :
( ( eqNat @ ( s @ Z ) @ ( s @ Y2 ) )
= ( eqNat @ Z @ Y2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(22,axiom,
! [Y: $i] :
( ( barbar @ bfalse @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(23,axiom,
! [Y: $i] :
( ( barbar @ btrue @ Y )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(24,axiom,
! [Y: $i,Z: $i,Xs: $i] :
( ( aux @ Y @ Z @ Xs @ bfalse )
= ( cons @ Z @ ( union @ Xs @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(25,axiom,
! [Y: $i,Z: $i,Xs: $i] :
( ( aux @ Y @ Z @ Xs @ btrue )
= ( union @ Xs @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(26,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(27,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[26]) ).
thf(28,negated_conjecture,
! [X: $i,Y: $i] :
( ( eq3 @ ( prop_union_comm @ X @ Y ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(29,plain,
$false = $false,
inference(unfold_def,[status(thm)],[27]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(32,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(33,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(34,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( eq2 @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( eq2 @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( s @ X ) @ ( s @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(40,plain,
( ( ( eq3 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(41,plain,
( ( ( eq3 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( prop_union_comm @ X @ Y )
= ( eq @ ( union @ X @ Y ) @ ( union @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(43,plain,
( ( ! [Z: $i,Xs: $i,Y: $i] :
( ( union @ ( cons @ Z @ Xs ) @ Y )
= ( aux @ Y @ Z @ Xs @ ( elem @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(44,plain,
( ( ! [Y: $i] :
( ( union @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(45,plain,
( ( ! [X: $i,Z: $i,Xs: $i] :
( ( elem @ X @ ( cons @ Z @ Xs ) )
= ( barbar @ ( eqNat @ X @ Z ) @ ( elem @ X @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( elem @ X @ nil )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(47,plain,
( ( ( eqNat @ z @ z )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(48,plain,
( ( ! [X2: $i] :
( ( eqNat @ z @ ( s @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(49,plain,
( ( ! [Z: $i] :
( ( eqNat @ ( s @ Z ) @ z )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(50,plain,
( ( ! [Z: $i,Y2: $i] :
( ( eqNat @ ( s @ Z ) @ ( s @ Y2 ) )
= ( eqNat @ Z @ Y2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(51,plain,
( ( ! [Y: $i] :
( ( barbar @ bfalse @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [Y: $i] :
( ( barbar @ btrue @ Y )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(53,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( aux @ Y @ Z @ Xs @ bfalse )
= ( cons @ Z @ ( union @ Xs @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(54,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( aux @ Y @ Z @ Xs @ btrue )
= ( union @ Xs @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( prop_union_comm @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(56,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(57,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(58,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( prop_union_comm @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] :
( ( eq3 @ ( prop_union_comm @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( aux @ Y @ Z @ Xs @ btrue )
= ( union @ Xs @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(62,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( aux @ Y @ Z @ Xs @ bfalse )
= ( cons @ Z @ ( union @ Xs @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(63,plain,
( ( ! [Y: $i] :
( ( barbar @ btrue @ Y )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(64,plain,
( ( ! [Y: $i] :
( ( barbar @ bfalse @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(65,plain,
( ( ! [Z: $i,Y2: $i] :
( ( eqNat @ ( s @ Z ) @ ( s @ Y2 ) )
= ( eqNat @ Z @ Y2 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(66,plain,
( ( ! [Z: $i] :
( ( eqNat @ ( s @ Z ) @ z )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(67,plain,
( ( ! [X2: $i] :
( ( eqNat @ z @ ( s @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(68,plain,
( ( ( eqNat @ z @ z )
= btrue )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(69,plain,
( ( ! [X: $i] :
( ( elem @ X @ nil )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( ! [X: $i,Z: $i,Xs: $i] :
( ( elem @ X @ ( cons @ Z @ Xs ) )
= ( barbar @ ( eqNat @ X @ Z ) @ ( elem @ X @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(71,plain,
( ( ! [Y: $i] :
( ( union @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(72,plain,
( ( ! [Z: $i,Xs: $i,Y: $i] :
( ( union @ ( cons @ Z @ Xs ) @ Y )
= ( aux @ Y @ Z @ Xs @ ( elem @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( prop_union_comm @ X @ Y )
= ( eq @ ( union @ X @ Y ) @ ( union @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(74,plain,
( ( ( eq3 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(75,plain,
( ( ( eq3 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( s @ X ) @ ( s @ Y ) )
= ( eq2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(77,plain,
( ( ! [X: $i] :
( ( eq2 @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(78,plain,
( ( ! [X: $i] :
( ( eq2 @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(79,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(80,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(81,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(82,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(83,plain,
( ( ! [X: $i,Z: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ! [Y: $i,X2: $i] :
( ( eq @ ( cons @ X @ Y ) @ ( cons @ Z @ X2 ) )
= ( eq @ Y @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(84,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ nil @ ( cons @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( cons @ X @ Y ) @ nil )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(86,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[56]) ).
thf(87,plain,
! [SV1: $i] :
( ( ! [SY43: $i] :
( ( eq3 @ ( prop_union_comm @ SV1 @ SY43 ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(88,plain,
! [SV2: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( aux @ SV2 @ SY44 @ SY45 @ btrue )
= ( union @ SY45 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(89,plain,
! [SV3: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( aux @ SV3 @ SY46 @ SY47 @ bfalse )
= ( cons @ SY46 @ ( union @ SY47 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(90,plain,
! [SV4: $i] :
( ( ( barbar @ btrue @ SV4 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(91,plain,
! [SV5: $i] :
( ( ( barbar @ bfalse @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(92,plain,
! [SV6: $i] :
( ( ! [SY48: $i] :
( ( eqNat @ ( s @ SV6 ) @ ( s @ SY48 ) )
= ( eqNat @ SV6 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(93,plain,
! [SV7: $i] :
( ( ( eqNat @ ( s @ SV7 ) @ z )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(94,plain,
! [SV8: $i] :
( ( ( eqNat @ z @ ( s @ SV8 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(95,plain,
! [SV9: $i] :
( ( ( elem @ SV9 @ nil )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(96,plain,
! [SV10: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( elem @ SV10 @ ( cons @ SY49 @ SY50 ) )
= ( barbar @ ( eqNat @ SV10 @ SY49 ) @ ( elem @ SV10 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(97,plain,
! [SV11: $i] :
( ( ( union @ nil @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(98,plain,
! [SV12: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( union @ ( cons @ SV12 @ SY51 ) @ SY52 )
= ( aux @ SY52 @ SV12 @ SY51 @ ( elem @ SV12 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(99,plain,
! [SV13: $i] :
( ( ! [SY53: $i] :
( ( prop_union_comm @ SV13 @ SY53 )
= ( eq @ ( union @ SV13 @ SY53 ) @ ( union @ SY53 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(100,plain,
! [SV14: $i] :
( ( ! [SY54: $i] :
( ( eq2 @ ( s @ SV14 ) @ ( s @ SY54 ) )
= ( eq2 @ SV14 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(101,plain,
! [SV15: $i] :
( ( ( eq2 @ ( s @ SV15 ) @ z )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(102,plain,
! [SV16: $i] :
( ( ( eq2 @ z @ ( s @ SV16 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(103,plain,
! [SV17: $i] :
( ( ( eq @ SV17 @ SV17 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(104,plain,
! [SV18: $i] :
( ( ( eq2 @ SV18 @ SV18 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(105,plain,
! [SV19: $i] :
( ( ( eq3 @ SV19 @ SV19 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(106,plain,
! [SV20: $i] :
( ( ! [SY55: $i] :
( ( ( eq2 @ SV20 @ SY55 )
!= bfalse )
| ! [SY56: $i,SY57: $i] :
( ( eq @ ( cons @ SV20 @ SY56 ) @ ( cons @ SY55 @ SY57 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(107,plain,
! [SV21: $i] :
( ( ! [SY58: $i] :
( ( ( eq2 @ SV21 @ SY58 )
!= btrue )
| ! [SY59: $i,SY60: $i] :
( ( eq @ ( cons @ SV21 @ SY59 ) @ ( cons @ SY58 @ SY60 ) )
= ( eq @ SY59 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(108,plain,
! [SV22: $i] :
( ( ! [SY61: $i] :
( ( eq @ nil @ ( cons @ SV22 @ SY61 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(109,plain,
! [SV23: $i] :
( ( ! [SY62: $i] :
( ( eq @ ( cons @ SV23 @ SY62 ) @ nil )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(110,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(111,plain,
! [SV24: $i,SV1: $i] :
( ( ( eq3 @ ( prop_union_comm @ SV1 @ SV24 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(112,plain,
! [SV25: $i,SV2: $i] :
( ( ! [SY63: $i] :
( ( aux @ SV2 @ SV25 @ SY63 @ btrue )
= ( union @ SY63 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(113,plain,
! [SV26: $i,SV3: $i] :
( ( ! [SY64: $i] :
( ( aux @ SV3 @ SV26 @ SY64 @ bfalse )
= ( cons @ SV26 @ ( union @ SY64 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(114,plain,
! [SV27: $i,SV6: $i] :
( ( ( eqNat @ ( s @ SV6 ) @ ( s @ SV27 ) )
= ( eqNat @ SV6 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(115,plain,
! [SV28: $i,SV10: $i] :
( ( ! [SY65: $i] :
( ( elem @ SV10 @ ( cons @ SV28 @ SY65 ) )
= ( barbar @ ( eqNat @ SV10 @ SV28 ) @ ( elem @ SV10 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV29: $i,SV12: $i] :
( ( ! [SY66: $i] :
( ( union @ ( cons @ SV12 @ SV29 ) @ SY66 )
= ( aux @ SY66 @ SV12 @ SV29 @ ( elem @ SV12 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV30: $i,SV13: $i] :
( ( ( prop_union_comm @ SV13 @ SV30 )
= ( eq @ ( union @ SV13 @ SV30 ) @ ( union @ SV30 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV31: $i,SV14: $i] :
( ( ( eq2 @ ( s @ SV14 ) @ ( s @ SV31 ) )
= ( eq2 @ SV14 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV32: $i,SV20: $i] :
( ( ( ( eq2 @ SV20 @ SV32 )
!= bfalse )
| ! [SY67: $i,SY68: $i] :
( ( eq @ ( cons @ SV20 @ SY67 ) @ ( cons @ SV32 @ SY68 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV33: $i,SV21: $i] :
( ( ( ( eq2 @ SV21 @ SV33 )
!= btrue )
| ! [SY69: $i,SY70: $i] :
( ( eq @ ( cons @ SV21 @ SY69 ) @ ( cons @ SV33 @ SY70 ) )
= ( eq @ SY69 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV34: $i,SV22: $i] :
( ( ( eq @ nil @ ( cons @ SV22 @ SV34 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(122,plain,
! [SV35: $i,SV23: $i] :
( ( ( eq @ ( cons @ SV23 @ SV35 ) @ nil )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(123,plain,
! [SV24: $i,SV1: $i] :
( ( ( eq3 @ ( prop_union_comm @ SV1 @ SV24 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV36: $i,SV25: $i,SV2: $i] :
( ( ( aux @ SV2 @ SV25 @ SV36 @ btrue )
= ( union @ SV36 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV37: $i,SV26: $i,SV3: $i] :
( ( ( aux @ SV3 @ SV26 @ SV37 @ bfalse )
= ( cons @ SV26 @ ( union @ SV37 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV38: $i,SV28: $i,SV10: $i] :
( ( ( elem @ SV10 @ ( cons @ SV28 @ SV38 ) )
= ( barbar @ ( eqNat @ SV10 @ SV28 ) @ ( elem @ SV10 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV39: $i,SV29: $i,SV12: $i] :
( ( ( union @ ( cons @ SV12 @ SV29 ) @ SV39 )
= ( aux @ SV39 @ SV12 @ SV29 @ ( elem @ SV12 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV32: $i,SV20: $i] :
( ( ( ( eq2 @ SV20 @ SV32 )
!= bfalse )
= $true )
| ( ( ! [SY67: $i,SY68: $i] :
( ( eq @ ( cons @ SV20 @ SY67 ) @ ( cons @ SV32 @ SY68 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV33: $i,SV21: $i] :
( ( ( ( eq2 @ SV21 @ SV33 )
!= btrue )
= $true )
| ( ( ! [SY69: $i,SY70: $i] :
( ( eq @ ( cons @ SV21 @ SY69 ) @ ( cons @ SV33 @ SY70 ) )
= ( eq @ SY69 @ SY70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV32: $i,SV20: $i] :
( ( ( ( eq2 @ SV20 @ SV32 )
= bfalse )
= $false )
| ( ( ! [SY67: $i,SY68: $i] :
( ( eq @ ( cons @ SV20 @ SY67 ) @ ( cons @ SV32 @ SY68 ) )
= bfalse ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV33: $i,SV21: $i] :
( ( ( ( eq2 @ SV21 @ SV33 )
= btrue )
= $false )
| ( ( ! [SY69: $i,SY70: $i] :
( ( eq @ ( cons @ SV21 @ SY69 ) @ ( cons @ SV33 @ SY70 ) )
= ( eq @ SY69 @ SY70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(132,plain,
! [SV32: $i,SV40: $i,SV20: $i] :
( ( ( ! [SY71: $i] :
( ( eq @ ( cons @ SV20 @ SV40 ) @ ( cons @ SV32 @ SY71 ) )
= bfalse ) )
= $true )
| ( ( ( eq2 @ SV20 @ SV32 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(133,plain,
! [SV33: $i,SV41: $i,SV21: $i] :
( ( ( ! [SY72: $i] :
( ( eq @ ( cons @ SV21 @ SV41 ) @ ( cons @ SV33 @ SY72 ) )
= ( eq @ SV41 @ SY72 ) ) )
= $true )
| ( ( ( eq2 @ SV21 @ SV33 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(134,plain,
! [SV42: $i,SV32: $i,SV40: $i,SV20: $i] :
( ( ( ( eq @ ( cons @ SV20 @ SV40 ) @ ( cons @ SV32 @ SV42 ) )
= bfalse )
= $true )
| ( ( ( eq2 @ SV20 @ SV32 )
= bfalse )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(135,plain,
! [SV43: $i,SV33: $i,SV41: $i,SV21: $i] :
( ( ( ( eq @ ( cons @ SV21 @ SV41 ) @ ( cons @ SV33 @ SV43 ) )
= ( eq @ SV41 @ SV43 ) )
= $true )
| ( ( ( eq2 @ SV21 @ SV33 )
= btrue )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,135,134,127,126,125,124,123,122,121,118,117,114,110,105,104,103,102,101,97,95,94,93,91,90,75,74]) ).
thf(137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n015.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 17:17:14 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.88/0.54
% 1.88/0.54 No.of.Axioms: 26
% 1.88/0.54
% 1.88/0.54 Length.of.Defs: 0
% 1.88/0.54
% 1.88/0.54 Contains.Choice.Funs: false
% 1.88/0.54 ....
% 1.88/0.54
% 1.88/0.54 ********************************
% 1.88/0.54 * All subproblems solved! *
% 1.88/0.54 ********************************
% 1.88/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:26,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:136,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 1.88/0.54
% 1.88/0.54 %**** Beginning of derivation protocol ****
% 1.88/0.54 % SZS output start CNFRefutation
% See solution above
% 1.88/0.54
% 1.88/0.54 %**** End of derivation protocol ****
% 1.88/0.54 %**** no. of clauses in derivation: 137 ****
% 1.88/0.54 %**** clause counter: 136 ****
% 1.88/0.54
% 1.88/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:26,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:136,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------