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iProver-SAT---3.9.4.CSA-Mod.s

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%------------------------------------------------------------------------------
% File     : iProver-SAT---3.9.4
% Problem  : SYN427+1 : TPTP v9.3.1. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT

% 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 : Fri Sep 25 03:46:30 PM UTC 2026

% Result   : CounterSatisfiable 3.73s 1.18s
% Output   : Model 3.73s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
%------ Positive definition of ndr1_0 
fof(lit_def,axiom,
    ( ndr1_0
  <=> $true ) ).

%------ Positive definition of sP76 
fof(lit_def_001,axiom,
    ( sP76
  <=> $false ) ).

%------ Positive definition of c2_1 
fof(lit_def_002,axiom,
    ! [X0] :
      ( c2_1(X0)
    <=> ( X0 = a1739
        | X0 = a1655
        | X0 = a1651
        | X0 = a1733
        | X0 = a1692
        | X0 = a1662
        | X0 = a1650
        | X0 = a1593
        | X0 = a1587 ) ) ).

%------ Positive definition of ndr1_1 
fof(lit_def_003,axiom,
    ! [X0] :
      ( ndr1_1(X0)
    <=> ( X0 = a1824
        | X0 = a1820
        | X0 = a1767
        | X0 = a1743
        | X0 = a1739
        | X0 = a1708
        | X0 = a1685
        | X0 = a1683
        | X0 = a1681
        | X0 = a1655
        | X0 = a1651
        | X0 = a1647
        | X0 = a1629
        | X0 = a1618
        | X0 = a1610
        | X0 = a1817
        | X0 = a1822
        | X0 = a1795
        | X0 = a1745
        | X0 = a1733
        | X0 = a1721
        | X0 = a1695
        | X0 = a1677
        | X0 = a1662
        | X0 = a1659
        | X0 = a1650
        | X0 = a1645
        | X0 = a1631
        | X0 = a1626
        | X0 = a1620
        | X0 = a1593
        | X0 = a1587
        | ( X0 != a1767
          & X0 != a1739
          & X0 != a1708
          & X0 != a1681
          & X0 != a1647
          & X0 != a1610
          & X0 != a1811
          & X0 != a1802
          & X0 != a1729
          & X0 != a1692
          & X0 != a1650
          & X0 != a1626
          & X0 != a1609 ) ) ) ).

%------ Positive definition of c10_2 
fof(lit_def_004,axiom,
    ! [X0,X1] :
      ( c10_2(X0,X1)
    <=> ( ( X1 = a1797
          & X0 = a1795 )
        | ( X1 = a1796
          & X0 = a1795 )
        | ( X1 = a1693
          & X0 = a1692 )
        | ( X1 = a1676
          & X0 = a1650 ) ) ) ).

%------ Positive definition of c3_2 
fof(lit_def_005,axiom,
    ! [X0,X1] :
      ( c3_2(X0,X1)
    <=> ( ( X1 = a1768
          & X0 = a1739 )
        | ( X1 = a1801
          & X0 = a1739 )
        | ( X1 = a1768
          & X0 = a1651 )
        | ( X1 = a1801
          & X0 = a1651 )
        | ( X1 = a1768
          & X0 = a1692 )
        | ( X1 = a1664
          & X0 = a1662 )
        | ( X1 = a1660
          & X0 = a1659 )
        | ( X1 = a1768
          & X0 = a1650 ) ) ) ).

%------ Positive definition of c4_2 
fof(lit_def_006,axiom,
    ! [X0,X1] :
      ( c4_2(X0,X1)
    <=> ( X1 = a1614
        | ( X1 = a1792
          & X0 = a1767 )
        | ( X1 = a1753
          & X0 = a1647 )
        | ( X1 != a1753
          & X1 != a1602
          & X1 != a1801
          & X0 = a1647 )
        | ( X1 = a1818
          & X0 = a1817 )
        | ( X1 = a1803
          & X0 = a1802 )
        | ( X1 = a1693
          & X0 = a1692 )
        | ( X1 = a1661
          & X0 = a1659 )
        | ( X1 = a1660
          & X0 = a1659 )
        | ( X1 = a1633
          & X0 = a1631 ) ) ) ).

%------ Positive definition of c1_1 
fof(lit_def_007,axiom,
    ! [X0] :
      ( c1_1(X0)
    <=> $false ) ).

%------ Positive definition of sP75 
fof(lit_def_008,axiom,
    ( sP75
  <=> $false ) ).

%------ Positive definition of c8_2 
fof(lit_def_009,axiom,
    ! [X0,X1] :
      ( c8_2(X0,X1)
    <=> ( ( X1 = a1825
          & X0 = a1824 )
        | ( X1 = a1821
          & X0 = a1820 )
        | ( X1 = a1744
          & X0 = a1743 )
        | ( X1 = a1761
          & X0 = a1685 )
        | ( X1 = a1715
          & X0 = a1685 )
        | ( X1 = a1686
          & X0 = a1685 )
        | ( X1 = a1682
          & X0 = a1685 )
        | ( X1 = a1665
          & X0 = a1685 )
        | ( X1 = a1690
          & X0 = a1685 )
        | ( X1 = a1614
          & X0 = a1685 )
        | ( X1 = a1600
          & X0 = a1685 )
        | ( X1 != a1761
          & X1 != a1715
          & X1 != a1682
          & X1 != a1665
          & X1 != a1690
          & X1 != a1614
          & X1 != a1600
          & X0 = a1685 )
        | ( X1 = a1619
          & X0 = a1618 )
        | ( X1 = a1818
          & X0 = a1817 )
        | ( X1 = a1737
          & X0 = a1822 )
        | ( X1 = a1734
          & X0 = a1733 )
        | ( X1 = a1697
          & X0 = a1695 )
        | ( X1 = a1696
          & X0 = a1695 )
        | ( X1 = a1742
          & X0 = a1677 ) ) ) ).

%------ Positive definition of c2_2 
fof(lit_def_010,axiom,
    ! [X0,X1] :
      ( c2_2(X0,X1)
    <=> ( ( X1 = a1800
          & X0 = a1767 )
        | ( X1 = a1602
          & X0 = a1767 )
        | ( X1 = a1744
          & X0 = a1743 )
        | ( X1 = a1800
          & X0 = a1708 )
        | ( X1 = a1800
          & X0 = a1681 )
        | ( X1 = a1800
          & X0 = a1655 )
        | ( X1 = a1656
          & X0 = a1655 )
        | ( X1 = a1652
          & X0 = a1651 )
        | ( X1 = a1800
          & X0 = a1647 )
        | ( X1 = a1810
          & X0 = a1629 )
        | ( X1 = a1742
          & X0 = a1822 )
        | ( X1 = a1800
          & X0 = a1733 )
        | ( X1 = a1800
          & X0 = a1736 )
        | ( X1 = a1742
          & X0 = a1677 )
        | ( X1 = a1800
          & X0 = a1662 )
        | ( X1 = a1800
          & X0 = a1659 )
        | ( X1 = a1800
          & X0 = a1650 )
        | ( X1 = a1646
          & X0 = a1645 )
        | ( X1 = a1800
          & X0 = a1620 )
        | ( X1 = a1800
          & X0 = a1593 )
        | ( X1 = a1800
          & X0 = a1587 ) ) ) ).

%------ Positive definition of c3_1 
fof(lit_def_011,axiom,
    ! [X0] :
      ( c3_1(X0)
    <=> ( X0 = a1767
        | X0 = a1811
        | X0 = a1729
        | X0 = a1620
        | X0 = a1609 ) ) ).

%------ Positive definition of sP74 
fof(lit_def_012,axiom,
    ( sP74
  <=> $false ) ).

%------ Positive definition of c6_2 
fof(lit_def_013,axiom,
    ! [X0,X1] :
      ( c6_2(X0,X1)
    <=> ( ( X0 != a1739
          & X0 != a1681
          & X0 != a1655
          & X0 != a1651
          & X0 != a1647
          & X0 != a1811
          & X0 != a1802
          & X0 != a1733
          & X0 != a1736
          & X0 != a1692
          & X0 != a1662
          & X0 != a1659
          & X0 != a1650
          & X0 != a1620
          & X0 != a1593
          & X0 != a1587
          & X1 = a1801 )
        | ( X0 != a1739
          & X0 != a1681
          & X0 != a1668
          & X0 != a1655
          & X0 != a1651
          & X0 != a1647
          & X0 != a1629
          & X0 != a1618
          & X0 != a1811
          & X0 != a1802
          & X0 != a1733
          & X0 != a1736
          & X0 != a1729
          & X0 != a1692
          & X0 != a1662
          & X0 != a1659
          & X0 != a1650
          & X0 != a1626
          & X0 != a1620
          & X0 != a1593
          & X0 != a1587
          & X1 = a1690 )
        | ( X0 != a1739
          & X0 != a1681
          & X0 != a1655
          & X0 != a1651
          & X0 != a1647
          & X0 != a1811
          & X0 != a1802
          & X0 != a1733
          & X0 != a1736
          & X0 != a1692
          & X0 != a1662
          & X0 != a1659
          & X0 != a1650
          & X0 != a1620
          & X0 != a1593
          & X0 != a1587
          & X1 = a1625 )
        | ( X1 = a1801
          & X0 = a1739 )
        | ( X1 = a1801
          & X0 = a1651 )
        | ( X1 = a1812
          & X0 = a1811 )
        | ( X1 = a1804
          & X0 = a1802 )
        | ( X1 = a1796
          & X0 = a1795 )
        | ( X1 = a1801
          & X0 = a1650 ) ) ) ).

%------ Positive definition of c9_2 
fof(lit_def_014,axiom,
    ! [X0,X1] :
      ( c9_2(X0,X1)
    <=> ( ( X0 != a1668
          & X0 != a1629
          & X0 != a1618
          & X0 != a1811
          & X0 != a1802
          & X0 != a1729
          & X0 != a1626
          & X0 != a1620
          & X1 = a1625 )
        | ( X1 = a1686
          & X0 = a1685 )
        | ( X1 = a1602
          & X0 = a1647 )
        | ( X1 = a1801
          & X0 = a1647 )
        | ( X1 = a1619
          & X0 = a1618 )
        | ( X1 = a1819
          & X0 = a1817 )
        | ( X1 = a1738
          & X0 = a1822 )
        | ( X1 = a1803
          & X0 = a1802 )
        | ( X1 = a1735
          & X0 = a1733 )
        | ( X1 = a1600
          & X0 = a1733 )
        | ( X1 = a1600
          & X0 = a1695 )
        | ( X1 = a1678
          & X0 = a1677 )
        | ( X1 = a1661
          & X0 = a1659 )
        | ( X1 = a1633
          & X0 = a1631 )
        | ( X1 = a1632
          & X0 = a1631 ) ) ) ).

%------ Positive definition of c5_1 
fof(lit_def_015,axiom,
    ! [X0] :
      ( c5_1(X0)
    <=> ( X0 = a1708
        | X0 = a1681
        | X0 = a1647
        | X0 = a1618
        | X0 = a1811
        | X0 = a1802
        | X0 = a1736
        | X0 = a1729
        | X0 = a1692
        | X0 = a1631
        | X0 = a1626
        | X0 = a1620
        | X0 = a1609 ) ) ).

%------ Positive definition of sP73 
fof(lit_def_016,axiom,
    ( sP73
  <=> $true ) ).

%------ Positive definition of c9_1 
fof(lit_def_017,axiom,
    ! [X0] :
      ( c9_1(X0)
    <=> ( X0 = a1650
        | X0 = a1593 ) ) ).

%------ Positive definition of c6_1 
fof(lit_def_018,axiom,
    ! [X0] :
      ( c6_1(X0)
    <=> ( X0 = a1739
        | X0 = a1655 ) ) ).

%------ Positive definition of sP72 
fof(lit_def_019,axiom,
    ! [X0] :
      ( sP72(X0)
    <=> $false ) ).

%------ Positive definition of sP71 
fof(lit_def_020,axiom,
    ( sP71
  <=> $false ) ).

%------ Positive definition of c1_2 
fof(lit_def_021,axiom,
    ! [X0,X1] :
      ( c1_2(X0,X1)
    <=> ( ( X1 = a1746
          & X0 = a1745 )
        | ( X1 = a1735
          & X0 = a1733 ) ) ) ).

%------ Positive definition of c5_2 
fof(lit_def_022,axiom,
    ! [X0,X1] :
      ( c5_2(X0,X1)
    <=> ( ( X1 = a1825
          & X0 = a1824 )
        | ( X1 = a1684
          & X0 = a1683 )
        | ( X1 = a1823
          & X0 = a1822 )
        | ( X1 = a1804
          & X0 = a1802 )
        | ( X1 = a1735
          & X0 = a1733 )
        | ( X1 = a1663
          & X0 = a1662 )
        | ( X1 = a1660
          & X0 = a1659 ) ) ) ).

%------ Positive definition of c7_2 
fof(lit_def_023,axiom,
    ! [X0,X1] :
      ( c7_2(X0,X1)
    <=> ( ( X1 = a1751
          & X0 = a1767 )
        | ( X1 = a1630
          & X0 = a1629 )
        | ( X1 = a1751
          & X0 = a1811 )
        | ( X1 = a1803
          & X0 = a1802 )
        | ( X1 = a1734
          & X0 = a1733 )
        | ( X1 = a1663
          & X0 = a1662 )
        | ( X1 = a1751
          & X0 = a1620 )
        | ( X1 = a1621
          & X0 = a1620 ) ) ) ).

%------ Positive definition of sP70 
fof(lit_def_024,axiom,
    ( sP70
  <=> $true ) ).

%------ Positive definition of sP69 
fof(lit_def_025,axiom,
    ( sP69
  <=> $false ) ).

%------ Positive definition of sP68 
fof(lit_def_026,axiom,
    ( sP68
  <=> $true ) ).

%------ Positive definition of sP67 
fof(lit_def_027,axiom,
    ( sP67
  <=> $true ) ).

%------ Positive definition of c10_1 
fof(lit_def_028,axiom,
    ! [X0] :
      ( c10_1(X0)
    <=> ( X0 = a1822
        | X0 = a1811
        | X0 = a1609 ) ) ).

%------ Positive definition of sP66 
fof(lit_def_029,axiom,
    ( sP66
  <=> $false ) ).

%------ Positive definition of sP65 
fof(lit_def_030,axiom,
    ! [X0] :
      ( sP65(X0)
    <=> ( X0 != a1767
        & X0 != a1708
        & X0 != a1647
        & X0 != a1610
        & X0 != a1811
        & X0 != a1802
        & X0 != a1729
        & X0 != a1692
        & X0 != a1609 ) ) ).

%------ Positive definition of sP64 
fof(lit_def_031,axiom,
    ( sP64
  <=> $true ) ).

%------ Positive definition of sP63 
fof(lit_def_032,axiom,
    ( sP63
  <=> $true ) ).

%------ Positive definition of sP62 
fof(lit_def_033,axiom,
    ( sP62
  <=> $false ) ).

%------ Positive definition of sP61 
fof(lit_def_034,axiom,
    ! [X0] :
      ( sP61(X0)
    <=> $false ) ).

%------ Positive definition of sP60 
fof(lit_def_035,axiom,
    ! [X0] :
      ( sP60(X0)
    <=> $false ) ).

%------ Positive definition of sP59 
fof(lit_def_036,axiom,
    ( sP59
  <=> $true ) ).

%------ Positive definition of sP58 
fof(lit_def_037,axiom,
    ( sP58
  <=> $false ) ).

%------ Positive definition of sP57 
fof(lit_def_038,axiom,
    ( sP57
  <=> $false ) ).

%------ Positive definition of sP56 
fof(lit_def_039,axiom,
    ( sP56
  <=> $true ) ).

%------ Positive definition of sP55 
fof(lit_def_040,axiom,
    ( sP55
  <=> $false ) ).

%------ Positive definition of sP52 
fof(lit_def_041,axiom,
    ! [X0] :
      ( sP52(X0)
    <=> $false ) ).

%------ Positive definition of sP54 
fof(lit_def_042,axiom,
    ( sP54
  <=> $false ) ).

%------ Positive definition of sP53 
fof(lit_def_043,axiom,
    ( sP53
  <=> $false ) ).

%------ Positive definition of sP51 
fof(lit_def_044,axiom,
    ( sP51
  <=> $true ) ).

%------ Positive definition of sP50 
fof(lit_def_045,axiom,
    ( sP50
  <=> $true ) ).

%------ Positive definition of sP49 
fof(lit_def_046,axiom,
    ( sP49
  <=> $true ) ).

%------ Positive definition of c4_1 
fof(lit_def_047,axiom,
    ! [X0] :
      ( c4_1(X0)
    <=> ( X0 = a1733
        | X0 = a1692
        | X0 = a1667 ) ) ).

%------ Positive definition of sP48 
fof(lit_def_048,axiom,
    ( sP48
  <=> $false ) ).

%------ Positive definition of sP47 
fof(lit_def_049,axiom,
    ( sP47
  <=> $false ) ).

%------ Positive definition of sP46 
fof(lit_def_050,axiom,
    ( sP46
  <=> $false ) ).

%------ Positive definition of sP45 
fof(lit_def_051,axiom,
    ! [X0] :
      ( sP45(X0)
    <=> $false ) ).

%------ Positive definition of sP44 
fof(lit_def_052,axiom,
    ( sP44
  <=> $false ) ).

%------ Positive definition of c8_1 
fof(lit_def_053,axiom,
    ! [X0] :
      ( c8_1(X0)
    <=> ( X0 = a1824
        | X0 = a1767
        | X0 = a1752
        | X0 = a1725
        | X0 = a1704
        | X0 = a1683
        | X0 = a1681
        | X0 = a1647
        | X0 = a1822
        | X0 = a1811
        | X0 = a1802
        | X0 = a1745
        | X0 = a1736
        | X0 = a1729
        | X0 = a1711
        | X0 = a1677
        | X0 = a1662
        | X0 = a1659
        | X0 = a1620
        | X0 = a1609
        | ( X0 != a1752
          & X0 != a1739
          & X0 != a1725
          & X0 != a1704
          & X0 != a1651
          & X0 != a1647
          & X0 != a1802
          & X0 != a1745
          & X0 != a1733
          & X0 != a1736
          & X0 != a1711
          & X0 != a1692
          & X0 != a1662
          & X0 != a1659
          & X0 != a1650
          & X0 != a1620 ) ) ) ).

%------ Positive definition of sP43 
fof(lit_def_054,axiom,
    ( sP43
  <=> $true ) ).

%------ Positive definition of sP42 
fof(lit_def_055,axiom,
    ( sP42
  <=> $false ) ).

%------ Positive definition of sP41 
fof(lit_def_056,axiom,
    ( sP41
  <=> $false ) ).

%------ Positive definition of sP40 
fof(lit_def_057,axiom,
    ( sP40
  <=> $false ) ).

%------ Positive definition of sP39 
fof(lit_def_058,axiom,
    ( sP39
  <=> $false ) ).

%------ Positive definition of sP38 
fof(lit_def_059,axiom,
    ( sP38
  <=> $false ) ).

%------ Positive definition of c7_1 
fof(lit_def_060,axiom,
    ! [X0] :
      ( c7_1(X0)
    <=> ( X0 = a1820
        | X0 = a1739
        | X0 = a1610
        | X0 = a1822
        | X0 = a1802
        | ( X0 != a1820
          & X0 != a1767
          & X0 != a1704
          & X0 != a1685
          & X0 != a1733
          & X0 != a1711 ) ) ) ).

%------ Positive definition of sP37 
fof(lit_def_061,axiom,
    ( sP37
  <=> $false ) ).

%------ Positive definition of sP36 
fof(lit_def_062,axiom,
    ( sP36
  <=> $true ) ).

%------ Positive definition of sP35 
fof(lit_def_063,axiom,
    ( sP35
  <=> $false ) ).

%------ Positive definition of sP34 
fof(lit_def_064,axiom,
    ( sP34
  <=> $true ) ).

%------ Positive definition of sP33 
fof(lit_def_065,axiom,
    ( sP33
  <=> $false ) ).

%------ Positive definition of sP32 
fof(lit_def_066,axiom,
    ( sP32
  <=> $false ) ).

%------ Positive definition of sP31 
fof(lit_def_067,axiom,
    ( sP31
  <=> $true ) ).

%------ Positive definition of sP30 
fof(lit_def_068,axiom,
    ! [X0] :
      ( sP30(X0)
    <=> X0 = a1822 ) ).

%------ Positive definition of sP29 
fof(lit_def_069,axiom,
    ( sP29
  <=> $false ) ).

%------ Positive definition of sP28 
fof(lit_def_070,axiom,
    ( sP28
  <=> $false ) ).

%------ Positive definition of sP27 
fof(lit_def_071,axiom,
    ( sP27
  <=> $false ) ).

%------ Positive definition of sP25 
fof(lit_def_072,axiom,
    ! [X0] :
      ( sP25(X0)
    <=> $false ) ).

%------ Positive definition of sP26 
fof(lit_def_073,axiom,
    ( sP26
  <=> $false ) ).

%------ Positive definition of sP24 
fof(lit_def_074,axiom,
    ( sP24
  <=> $false ) ).

%------ Positive definition of sP22 
fof(lit_def_075,axiom,
    ! [X0] :
      ( sP22(X0)
    <=> $false ) ).

%------ Positive definition of sP23 
fof(lit_def_076,axiom,
    ( sP23
  <=> $false ) ).

%------ Positive definition of sP21 
fof(lit_def_077,axiom,
    ! [X0] :
      ( sP21(X0)
    <=> $false ) ).

%------ Positive definition of sP18 
fof(lit_def_078,axiom,
    ! [X0] :
      ( sP18(X0)
    <=> $false ) ).

%------ Positive definition of sP20 
fof(lit_def_079,axiom,
    ( sP20
  <=> $false ) ).

%------ Positive definition of sP17 
fof(lit_def_080,axiom,
    ! [X0] :
      ( sP17(X0)
    <=> $false ) ).

%------ Positive definition of sP19 
fof(lit_def_081,axiom,
    ( sP19
  <=> $false ) ).

%------ Positive definition of sP16 
fof(lit_def_082,axiom,
    ! [X0] :
      ( sP16(X0)
    <=> $false ) ).

%------ Positive definition of sP15 
fof(lit_def_083,axiom,
    ( sP15
  <=> $false ) ).

%------ Positive definition of sP14 
fof(lit_def_084,axiom,
    ( sP14
  <=> $false ) ).

%------ Positive definition of sP12 
fof(lit_def_085,axiom,
    ! [X0] :
      ( sP12(X0)
    <=> $false ) ).

%------ Positive definition of sP13 
fof(lit_def_086,axiom,
    ( sP13
  <=> $false ) ).

%------ Positive definition of sP11 
fof(lit_def_087,axiom,
    ( sP11
  <=> $false ) ).

%------ Positive definition of sP10 
fof(lit_def_088,axiom,
    ( sP10
  <=> $false ) ).

%------ Positive definition of sP9 
fof(lit_def_089,axiom,
    ! [X0] :
      ( sP9(X0)
    <=> ( X0 = a1739
        | X0 = a1651
        | X0 = a1610
        | X0 = a1650
        | ( X0 != a1767
          & X0 != a1739
          & X0 != a1708
          & X0 != a1681
          & X0 != a1655
          & X0 != a1651
          & X0 != a1647
          & X0 != a1610
          & X0 != a1811
          & X0 != a1802
          & X0 != a1733
          & X0 != a1736
          & X0 != a1729
          & X0 != a1692
          & X0 != a1662
          & X0 != a1659
          & X0 != a1650
          & X0 != a1620
          & X0 != a1609
          & X0 != a1593
          & X0 != a1587 ) ) ) ).

%------ Positive definition of sP8 
fof(lit_def_090,axiom,
    ( sP8
  <=> $false ) ).

%------ Positive definition of sP7 
fof(lit_def_091,axiom,
    ( sP7
  <=> $false ) ).

%------ Positive definition of sP6 
fof(lit_def_092,axiom,
    ( sP6
  <=> $false ) ).

%------ Positive definition of sP5 
fof(lit_def_093,axiom,
    ( sP5
  <=> $true ) ).

%------ Positive definition of sP4 
fof(lit_def_094,axiom,
    ( sP4
  <=> $false ) ).

%------ Positive definition of sP3 
fof(lit_def_095,axiom,
    ( sP3
  <=> $false ) ).

%------ Positive definition of sP2 
fof(lit_def_096,axiom,
    ( sP2
  <=> $false ) ).

%------ Positive definition of sP1 
fof(lit_def_097,axiom,
    ! [X0] :
      ( sP1(X0)
    <=> $false ) ).

%------ Positive definition of sP0 
fof(lit_def_098,axiom,
    ! [X0] :
      ( sP0(X0)
    <=> $false ) ).

%------ Positive definition of c1_0 
fof(lit_def_099,axiom,
    ( c1_0
  <=> $true ) ).

%------ Positive definition of c10_0 
fof(lit_def_100,axiom,
    ( c10_0
  <=> $true ) ).

%------ Positive definition of c6_0 
fof(lit_def_101,axiom,
    ( c6_0
  <=> $false ) ).

%------ Positive definition of c8_0 
fof(lit_def_102,axiom,
    ( c8_0
  <=> $false ) ).

%------ Positive definition of c7_0 
fof(lit_def_103,axiom,
    ( c7_0
  <=> $true ) ).

%------ Positive definition of c4_0 
fof(lit_def_104,axiom,
    ( c4_0
  <=> $false ) ).

%------ Positive definition of c5_0 
fof(lit_def_105,axiom,
    ( c5_0
  <=> $true ) ).

%------ Positive definition of c9_0 
fof(lit_def_106,axiom,
    ( c9_0
  <=> $true ) ).

%------ Positive definition of c3_0 
fof(lit_def_107,axiom,
    ( c3_0
  <=> $false ) ).

%------ Positive definition of c2_0 
fof(lit_def_108,axiom,
    ( c2_0
  <=> $true ) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SYN427+1 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT
% 0.09/0.36  % Computer : n026.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Fri Sep 25 01:11:55 UTC 2026
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT
% 0.13/0.39  Running model finding
% 0.13/0.39  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fnt_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40  
% 0.13/0.40  % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40  
% 0.13/0.40  % Detected problem language: tptp
% 0.13/0.41  % Proving...
% 3.73/1.18  % SZS status Started for theBenchmark.p
% 3.73/1.18  % SZS status CounterSatisfiable for theBenchmark.p
% 3.73/1.18  
% 3.73/1.18  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.73/1.18  
% 3.73/1.18  ------  iProver source info
% 3.73/1.18  
% 3.73/1.18  git: date: 2026-07-19 20:42:38 +0200
% 3.73/1.18  git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.73/1.18  git: non_committed_changes: false
% 3.73/1.18  
% 3.73/1.18  ------ Parsing...
% 3.73/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.73/1.18  ------ Proving...
% 3.73/1.18  ------ Problem Properties 
% 3.73/1.18  
% 3.73/1.18  
% 3.73/1.18  clauses                                 914
% 3.73/1.18  conjectures                             460
% 3.73/1.18  EPR                                     914
% 3.73/1.18  Horn                                    507
% 3.73/1.18  unary                                   4
% 3.73/1.18  binary                                  408
% 3.73/1.18  lits                                    3818
% 3.73/1.18  lits eq                                 0
% 3.73/1.18  fd_pure                                 0
% 3.73/1.18  fd_pseudo                               0
% 3.73/1.18  fd_cond                                 0
% 3.73/1.18  fd_pseudo_cond                          0
% 3.73/1.18  AC symbols                              0
% 3.73/1.18  
% 3.73/1.18  ------ Input Options Time Limit: Unbounded
% 3.73/1.18  
% 3.73/1.18  
% 3.73/1.18  ------ Finite Models:
% 3.73/1.18  
% 3.73/1.18  ------ lit_activity_flag true
% 3.73/1.18  
% 3.73/1.18  ------ 
% 3.73/1.18  Current options:
% 3.73/1.18  ------ 
% 3.73/1.18  
% 3.73/1.18  ------ Input Options
% 3.73/1.18  
% 3.73/1.18  --out_options                           all
% 3.73/1.18  --tptp_safe_out                         true
% 3.73/1.18  --problem_path                          ""
% 3.73/1.18  --include_path                          ""
% 3.73/1.18  --clausifier                            res/vclausify_rel
% 3.73/1.18  --clausifier_options                    --mode clausify -t 101.66 -updr off
% 3.73/1.18  --stdin                                 false
% 3.73/1.18  --proof_out                             true
% 3.73/1.18  --proof_dot_file                        ""
% 3.73/1.18  --proof_reduce_dot                      []
% 3.73/1.18  --suppress_sat_res                      false
% 3.73/1.18  --suppress_unsat_res                    true
% 3.73/1.18  --stats_out                             none
% 3.73/1.18  --stats_mem                             false
% 3.73/1.18  --theory_stats_out                      false
% 3.73/1.18  
% 3.73/1.18  ------ General Options
% 3.73/1.18  
% 3.73/1.18  --fof                                   false
% 3.73/1.18  --time_out_real                         304.99
% 3.73/1.18  --time_out_virtual                      -1.
% 3.73/1.18  --rnd_seed                              13
% 3.73/1.18  --symbol_type_check                     false
% 3.73/1.18  --clausify_out                          false
% 3.73/1.18  --sig_cnt_out                           false
% 3.73/1.18  --trig_cnt_out                          false
% 3.73/1.18  --trig_cnt_out_tolerance                1.
% 3.73/1.18  --trig_cnt_out_sk_spl                   false
% 3.73/1.18  --abstr_cl_out                          false
% 3.73/1.18  
% 3.73/1.18  ------ Interactive Mode
% 3.73/1.18  
% 3.73/1.18  --interactive_mode                      false
% 3.73/1.18  --external_ip_address                   ""
% 3.73/1.18  --external_port                         0
% 3.73/1.18  
% 3.73/1.18  ------ Global Options
% 3.73/1.18  
% 3.73/1.18  --schedule                              none
% 3.73/1.18  --add_important_lit                     false
% 3.73/1.18  --prop_solver_per_cl                    500
% 3.73/1.18  --subs_bck_mult                         8
% 3.73/1.18  --min_unsat_core                        false
% 3.73/1.18  --soft_assumptions                      false
% 3.73/1.18  --soft_lemma_size                       3
% 3.73/1.18  --prop_impl_unit_size                   0
% 3.73/1.18  --prop_impl_unit                        []
% 3.73/1.18  --share_sel_clauses                     true
% 3.73/1.18  --reset_solvers                         false
% 3.73/1.18  --bc_imp_inh                            [conj_cone]
% 3.73/1.18  --conj_cone_tolerance                   3.
% 3.73/1.18  --extra_neg_conj                        none
% 3.73/1.18  --large_theory_mode                     true
% 3.73/1.18  --prolific_symb_bound                   200
% 3.73/1.18  --lt_threshold                          2000
% 3.73/1.18  --clause_weak_htbl                      true
% 3.73/1.18  --gc_record_bc_elim                     false
% 3.73/1.18  
% 3.73/1.18  ------ Preprocessing Options
% 3.73/1.18  
% 3.73/1.18  --preprocessing_flag                    false
% 3.73/1.18  --time_out_prep_mult                    0.1
% 3.73/1.18  --splitting_mode                        input
% 3.73/1.18  --splitting_grd                         true
% 3.73/1.18  --splitting_cvd                         false
% 3.73/1.18  --splitting_cvd_svl                     false
% 3.73/1.18  --splitting_nvd                         32
% 3.73/1.18  --sub_typing                            false
% 3.73/1.18  --prep_eq_flat_conj                     false
% 3.73/1.18  --prep_ineq_split                       false
% 3.73/1.18  --prep_eq_flat_all_gr                   false
% 3.73/1.18  --prep_gs_sim                           true
% 3.73/1.18  --prep_unflatten                        true
% 3.73/1.18  --prep_res_sim                          true
% 3.73/1.18  --prep_sup_sim_all                      true
% 3.73/1.18  --prep_sup_sim_sup                      false
% 3.73/1.18  --prep_upred                            true
% 3.73/1.18  --prep_well_definedness                 true
% 3.73/1.18  --prep_sem_filter                       exhaustive
% 3.73/1.18  --prep_sem_filter_out                   false
% 3.73/1.18  --pred_elim                             true
% 3.73/1.18  --res_sim_input                         true
% 3.73/1.18  --eq_ax_congr_red                       true
% 3.73/1.18  --pure_diseq_elim                       true
% 3.73/1.18  --brand_transform                       false
% 3.73/1.18  --non_eq_to_eq                          false
% 3.73/1.18  --prep_eq_proxy                         false
% 3.73/1.18  --prep_def_merge                        true
% 3.73/1.18  --prep_def_merge_prop_impl              false
% 3.73/1.18  --prep_def_merge_mbd                    true
% 3.73/1.18  --prep_def_merge_tr_red                 false
% 3.73/1.18  --prep_def_merge_tr_cl                  false
% 3.73/1.18  --smt_preprocessing                     false
% 3.73/1.18  --smt_ac_axioms                         fast
% 3.73/1.18  --preprocessed_out                      false
% 3.73/1.18  --preprocessed_stats                    false
% 3.73/1.18  
% 3.73/1.18  ------ Abstraction refinement Options
% 3.73/1.18  
% 3.73/1.18  --abstr_ref                             []
% 3.73/1.18  --abstr_ref_prep                        false
% 3.73/1.18  --abstr_ref_until_sat                   false
% 3.73/1.18  --abstr_ref_sig_restrict                funpre
% 3.73/1.18  --abstr_ref_af_restrict_to_split_sk     false
% 3.73/1.18  --abstr_ref_under                       []
% 3.73/1.18  
% 3.73/1.18  ------ SAT Options
% 3.73/1.18  
% 3.73/1.18  --sat_mode                              true
% 3.73/1.18  --sat_fm_restart_options                ""
% 3.73/1.18  --sat_gr_def                            false
% 3.73/1.18  --sat_epr_types                         true
% 3.73/1.18  --sat_non_cyclic_types                  false
% 3.73/1.18  --sat_finite_models                     true
% 3.73/1.18  --sat_fm_lemmas                         false
% 3.73/1.18  --sat_fm_prep                           false
% 3.73/1.18  --sat_fm_uc_incr                        true
% 3.73/1.18  --sat_out_model                         pos
% 3.73/1.18  --sat_out_clauses                       false
% 3.73/1.18  
% 3.73/1.18  ------ QBF Options
% 3.73/1.18  
% 3.73/1.18  --qbf_mode                              false
% 3.73/1.18  --qbf_elim_univ                         false
% 3.73/1.18  --qbf_dom_inst                          none
% 3.73/1.18  --qbf_dom_pre_inst                      false
% 3.73/1.18  --qbf_sk_in                             false
% 3.73/1.18  --qbf_pred_elim                         true
% 3.73/1.18  --qbf_split                             512
% 3.73/1.18  
% 3.73/1.18  ------ BMC1 Options
% 3.73/1.18  
% 3.73/1.18  --bmc1_incremental                      false
% 3.73/1.18  --bmc1_axioms                           reachable_all
% 3.73/1.18  --bmc1_min_bound                        0
% 3.73/1.18  --bmc1_max_bound                        -1
% 3.73/1.18  --bmc1_max_bound_default                -1
% 3.73/1.18  --bmc1_symbol_reachability              true
% 3.73/1.18  --bmc1_property_lemmas                  false
% 3.73/1.18  --bmc1_k_induction                      false
% 3.73/1.18  --bmc1_non_equiv_states                 false
% 3.73/1.18  --bmc1_deadlock                         false
% 3.73/1.18  --bmc1_ucm                              false
% 3.73/1.18  --bmc1_add_unsat_core                   none
% 3.73/1.18  --bmc1_unsat_core_children              false
% 3.73/1.18  --bmc1_unsat_core_extrapolate_axioms    false
% 3.73/1.18  --bmc1_out_stat                         full
% 3.73/1.18  --bmc1_ground_init                      false
% 3.73/1.18  --bmc1_pre_inst_next_state              false
% 3.73/1.18  --bmc1_pre_inst_state                   false
% 3.73/1.18  --bmc1_pre_inst_reach_state             false
% 3.73/1.18  --bmc1_out_unsat_core                   false
% 3.73/1.18  --bmc1_aig_witness_out                  false
% 3.73/1.18  --bmc1_verbose                          false
% 3.73/1.18  --bmc1_dump_clauses_tptp                false
% 3.73/1.18  --bmc1_dump_unsat_core_tptp             false
% 3.73/1.18  --bmc1_dump_file                        -
% 3.73/1.18  --bmc1_ucm_expand_uc_limit              128
% 3.73/1.18  --bmc1_ucm_n_expand_iterations          6
% 3.73/1.18  --bmc1_ucm_extend_mode                  1
% 3.73/1.18  --bmc1_ucm_init_mode                    2
% 3.73/1.18  --bmc1_ucm_cone_mode                    none
% 3.73/1.18  --bmc1_ucm_reduced_relation_type        0
% 3.73/1.18  --bmc1_ucm_relax_model                  4
% 3.73/1.18  --bmc1_ucm_full_tr_after_sat            true
% 3.73/1.18  --bmc1_ucm_expand_neg_assumptions       false
% 3.73/1.18  --bmc1_ucm_layered_model                none
% 3.73/1.18  --bmc1_ucm_max_lemma_size               10
% 3.73/1.18  
% 3.73/1.18  ------ AIG Options
% 3.73/1.18  
% 3.73/1.18  --aig_mode                              false
% 3.73/1.18  
% 3.73/1.18  ------ Instantiation Options
% 3.73/1.18  
% 3.73/1.18  --instantiation_flag                    true
% 3.73/1.18  --inst_sos_flag                         false
% 3.73/1.18  --inst_sos_phase                        true
% 3.73/1.18  --inst_sos_sth_lit_sel                  [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb]
% 3.73/1.18  --inst_lit_sel                          [+prop;+sign;+ground;-num_var;-num_symb]
% 3.73/1.18  --inst_lit_sel_side                     num_symb
% 3.73/1.18  --inst_solver_per_active                1400
% 3.73/1.18  --inst_solver_calls_frac                1.
% 3.73/1.18  --inst_to_smt_solver                    true
% 3.73/1.18  --inst_passive_queue_type               priority_queues
% 3.73/1.18  --inst_passive_queues                   [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.73/1.18  --inst_passive_queues_freq              [25;2]
% 3.73/1.18  --inst_dismatching                      true
% 3.73/1.18  --inst_eager_unprocessed_to_passive     true
% 3.73/1.18  --inst_unprocessed_bound                1000
% 3.73/1.18  --inst_prop_sim_given                   true
% 3.73/1.18  --inst_prop_sim_new                     false
% 3.73/1.18  --inst_subs_new                         false
% 3.73/1.18  --inst_eq_res_simp                      false
% 3.73/1.18  --inst_subs_given                       false
% 3.73/1.18  --inst_orphan_elimination               true
% 3.73/1.18  --inst_learning_loop_flag               true
% 3.73/1.18  --inst_learning_start                   3000
% 3.73/1.18  --inst_learning_factor                  2
% 3.73/1.18  --inst_start_prop_sim_after_learn       3
% 3.73/1.18  --inst_sel_renew                        solver
% 3.73/1.18  --inst_lit_activity_flag                true
% 3.73/1.18  --inst_restr_to_given                   false
% 3.73/1.18  --inst_activity_threshold               500
% 3.73/1.18  
% 3.73/1.18  ------ Resolution Options
% 3.73/1.18  
% 3.73/1.18  --resolution_flag                       false
% 3.73/1.18  --res_lit_sel                           adaptive
% 3.73/1.18  --res_lit_sel_side                      none
% 3.73/1.18  --res_ordering                          kbo
% 3.73/1.18  --res_to_prop_solver                    active
% 3.73/1.18  --res_prop_simpl_new                    false
% 3.73/1.18  --res_prop_simpl_given                  true
% 3.73/1.18  --res_to_smt_solver                     true
% 3.73/1.18  --res_passive_queue_type                priority_queues
% 3.73/1.18  --res_passive_queues                    [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.73/1.18  --res_passive_queues_freq               [15;5]
% 3.73/1.18  --res_forward_subs                      full
% 3.73/1.18  --res_backward_subs                     full
% 3.73/1.18  --res_forward_subs_resolution           true
% 3.73/1.18  --res_backward_subs_resolution          true
% 3.73/1.18  --res_orphan_elimination                true
% 3.73/1.18  --res_time_limit                        300.
% 3.73/1.18  
% 3.73/1.18  ------ Superposition Options
% 3.73/1.18  
% 3.73/1.18  --superposition_flag                    false
% 3.73/1.18  --sup_passive_queue_type                priority_queues
% 3.73/1.18  --sup_passive_queues                    [[-conj_dist;-num_symb];[+score;+min_def_symb;-max_atom_input_occur;+conj_non_prolific_symb];[+age;-num_symb];[+score;-num_symb]]
% 3.73/1.18  --sup_passive_queues_freq               [8;1;4;4]
% 3.73/1.18  --twee_lhs_weight                       4
% 3.73/1.18  --sup_set_join                          false
% 3.73/1.18  --sup_set_join_goals                    true
% 3.73/1.18  --sup_set_join_limit                    1000
% 3.73/1.18  --demod_completeness_check              fast
% 3.73/1.18  --demod_use_ground                      true
% 3.73/1.18  --sup_unprocessed_bound                 0
% 3.73/1.18  --sup_to_prop_solver                    passive
% 3.73/1.18  --sup_prop_simpl_new                    true
% 3.73/1.18  --sup_prop_simpl_given                  true
% 3.73/1.18  --sup_fun_splitting                     false
% 3.73/1.18  --sup_iter_deepening                    2
% 3.73/1.18  --sup_restarts_mult                     12
% 3.73/1.18  --sup_score                             sim_d_gen
% 3.73/1.18  --sup_share_score_frac                  0.2
% 3.73/1.18  --sup_share_max_num_cl                  500
% 3.73/1.18  --sup_ordering                          kbo
% 3.73/1.18  --sup_symb_ordering                     invfreq
% 3.73/1.18  --sup_term_weight                       default
% 3.73/1.18  
% 3.73/1.18  ------ Superposition Simplification Setup
% 3.73/1.18  
% 3.73/1.18  --sup_indices_passive                   [LightNormIndex;FwDemodIndex]
% 3.73/1.18  --sup_full_triv                         [SMTSimplify;PropSubs]
% 3.73/1.18  --sup_full_fw                           [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 3.73/1.18  --sup_full_bw                           [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 3.73/1.18  --sup_immed_triv                        []
% 3.73/1.18  --sup_immed_fw_main                     [ACNormalisation;FwLightNorm;FwUnitSubsAndRes]
% 3.73/1.18  --sup_immed_fw_immed                    [ACNormalisation;FwUnitSubsAndRes]
% 3.73/1.18  --sup_immed_bw_main                     [BwUnitSubsAndRes;BwDemod]
% 3.73/1.18  --sup_immed_bw_immed                    [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 3.73/1.18  --sup_input_triv                        [Unflattening;SMTSimplify]
% 3.73/1.18  --sup_input_fw                          [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 3.73/1.18  --sup_input_bw                          [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 3.73/1.18  --sup_full_fixpoint                     true
% 3.73/1.18  --sup_main_fixpoint                     true
% 3.73/1.18  --sup_immed_fixpoint                    false
% 3.73/1.18  --sup_input_fixpoint                    true
% 3.73/1.18  --sup_cache_sim                         none
% 3.73/1.18  --sup_smt_interval                      500
% 3.73/1.18  --sup_bw_gjoin_interval                 0
% 3.73/1.18  
% 3.73/1.18  ------ Combination Options
% 3.73/1.18  
% 3.73/1.18  --comb_mode                             clause_based
% 3.73/1.18  --comb_inst_mult                        5
% 3.73/1.18  --comb_res_mult                         1
% 3.73/1.18  --comb_sup_mult                         8
% 3.73/1.18  --comb_sup_deep_mult                    2
% 3.73/1.18  
% 3.73/1.18  ------ Debug Options
% 3.73/1.18  
% 3.73/1.18  --dbg_backtrace                         false
% 3.73/1.18  --dbg_dump_prop_clauses                 false
% 3.73/1.18  --dbg_dump_prop_clauses_file            -
% 3.73/1.18  --dbg_out_stat                          false
% 3.73/1.18  --dbg_just_parse                        false
% 3.73/1.18  
% 3.73/1.18  
% 3.73/1.18  
% 3.73/1.18  
% 3.73/1.18  ------ Proving...
% 3.73/1.18  
% 3.73/1.18  
% 3.73/1.18  % SZS status CounterSatisfiable for theBenchmark.p
% 3.73/1.18  
% 3.73/1.18  ------ Building Model...Done
% 3.73/1.18  
% 3.73/1.18  %------ The model is defined over ground terms (initial term algebra).
% 3.73/1.18  %------ Predicates are defined as (\forall x_1,..,x_n  ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n)))) 
% 3.73/1.18  %------ where \phi is a formula over the term algebra.
% 3.73/1.18  %------ If we have equality in the problem then it is also defined as a predicate above, 
% 3.73/1.18  %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type
% 3.73/1.18  %------ See help for --sat_out_model for different model outputs.
% 3.73/1.18  %------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
% 3.73/1.18  %------ where the first argument stands for the sort ($i in the unsorted case)
% 3.73/1.18  % SZS output start Model for theBenchmark.p
% See solution above
% 3.73/1.18  
%------------------------------------------------------------------------------