TPTP Problem File: PRV043+1.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : PRV043+1.s : ProoVer 2026
% Proof    : Problems/PRV043+1.p
%------------------------------------------------------------------------------
% SZS output start Proof
fof(a1,axiom,
    ( b1
  <=> ( b2
    <=> ( b3
      <=> ( b4
        <=> ( b5
          <=> ( b6
            <=> ( b7
              <=> ( b8
                <=> ( b9
                  <=> ( b10
                    <=> ( b11
                      <=> ( b12
                        <=> ( b13
                          <=> ( b14
                            <=> ( b15
                              <=> ( b16
                                <=> ( b17
                                  <=> ( b18
                                    <=> ( b19
                                      <=> ( b20
                                        <=> ( b21
                                          <=> ( b22
                                            <=> ( b23
                                              <=> ( b24
                                                <=> ( b25
                                                  <=> ( b26
                                                    <=> ( b27
                                                      <=> ( b28
                                                        <=> ( b29
                                                          <=> ( b30
                                                            <=> ( b31
                                                              <=> ( b32
                                                                <=> ( b33
                                                                  <=> ( b34
                                                                    <=> ( b35
                                                                      <=> ( b36
                                                                        <=> ( b37
                                                                          <=> ( b38
                                                                            <=> ( b39
                                                                              <=> ( b40
                                                                                <=> ( b41
                                                                                  <=> ( b42
                                                                                    <=> ( b43
                                                                                      <=> ( b44
                                                                                        <=> ( b45
                                                                                          <=> ( b46
                                                                                            <=> ( b47
                                                                                              <=> ( b48
                                                                                                <=> ( b49
                                                                                                  <=> ( b50
                                                                                                    <=> ( b51
                                                                                                      <=> ( b52
                                                                                                        <=> ( b53
                                                                                                          <=> ( b54
                                                                                                            <=> ( b55
                                                                                                              <=> ( b56
                                                                                                                <=> ( b57
                                                                                                                  <=> ( b58
                                                                                                                    <=> ( b59
                                                                                                                      <=> ( b60
                                                                                                                        <=> ( b61
                                                                                                                          <=> ( b62
                                                                                                                            <=> ( b63
                                                                                                                              <=> ( b64
                                                                                                                                <=> ( b65
                                                                                                                                  <=> ( b66
                                                                                                                                    <=> ( b67
                                                                                                                                      <=> ( b68
                                                                                                                                        <=> ( b69
                                                                                                                                          <=> ( b70
                                                                                                                                            <=> ( b71
                                                                                                                                              <=> ( b72
                                                                                                                                                <=> ( b73
                                                                                                                                                  <=> ( b74
                                                                                                                                                    <=> ( b75
                                                                                                                                                      <=> ( b76
                                                                                                                                                        <=> ( b77
                                                                                                                                                          <=> ( b78
                                                                                                                                                            <=> ( b79
                                                                                                                                                              <=> ( b80
                                                                                                                                                                <=> ( b81
                                                                                                                                                                  <=> ( b82
                                                                                                                                                                    <=> ( b83
                                                                                                                                                                      <=> ( b84
                                                                                                                                                                        <=> ( b85
                                                                                                                                                                          <=> ( b86
                                                                                                                                                                            <=> ( b87
                                                                                                                                                                              <=> ( b88
                                                                                                                                                                                <=> ( b89
                                                                                                                                                                                  <=> ( b90
                                                                                                                                                                                    <=> ( b91
                                                                                                                                                                                      <=> ( b92
                                                                                                                                                                                        <=> ( b93
                                                                                                                                                                                          <=> ( b94
                                                                                                                                                                                            <=> ( b95
                                                                                                                                                                                              <=> ( b96
                                                                                                                                                                                                <=> ( b97
                                                                                                                                                                                                  <=> ( b98
                                                                                                                                                                                                    <=> ( b99
                                                                                                                                                                                                      <=> b100 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('Problems/PRV043+1.p',a1) ).

fof(c,conjecture,
    ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( b1
                                                                                                                                                                                                      <=> b2 )
                                                                                                                                                                                                    <=> b3 )
                                                                                                                                                                                                  <=> b4 )
                                                                                                                                                                                                <=> b5 )
                                                                                                                                                                                              <=> b6 )
                                                                                                                                                                                            <=> b7 )
                                                                                                                                                                                          <=> b8 )
                                                                                                                                                                                        <=> b9 )
                                                                                                                                                                                      <=> b10 )
                                                                                                                                                                                    <=> b11 )
                                                                                                                                                                                  <=> b12 )
                                                                                                                                                                                <=> b13 )
                                                                                                                                                                              <=> b14 )
                                                                                                                                                                            <=> b15 )
                                                                                                                                                                          <=> b16 )
                                                                                                                                                                        <=> b17 )
                                                                                                                                                                      <=> b18 )
                                                                                                                                                                    <=> b19 )
                                                                                                                                                                  <=> b20 )
                                                                                                                                                                <=> b21 )
                                                                                                                                                              <=> b22 )
                                                                                                                                                            <=> b23 )
                                                                                                                                                          <=> b24 )
                                                                                                                                                        <=> b25 )
                                                                                                                                                      <=> b26 )
                                                                                                                                                    <=> b27 )
                                                                                                                                                  <=> b28 )
                                                                                                                                                <=> b29 )
                                                                                                                                              <=> b30 )
                                                                                                                                            <=> b31 )
                                                                                                                                          <=> b32 )
                                                                                                                                        <=> b33 )
                                                                                                                                      <=> b34 )
                                                                                                                                    <=> b35 )
                                                                                                                                  <=> b36 )
                                                                                                                                <=> b37 )
                                                                                                                              <=> b38 )
                                                                                                                            <=> b39 )
                                                                                                                          <=> b40 )
                                                                                                                        <=> b41 )
                                                                                                                      <=> b42 )
                                                                                                                    <=> b43 )
                                                                                                                  <=> b44 )
                                                                                                                <=> b45 )
                                                                                                              <=> b46 )
                                                                                                            <=> b47 )
                                                                                                          <=> b48 )
                                                                                                        <=> b49 )
                                                                                                      <=> b50 )
                                                                                                    <=> b51 )
                                                                                                  <=> b52 )
                                                                                                <=> b53 )
                                                                                              <=> b54 )
                                                                                            <=> b55 )
                                                                                          <=> b56 )
                                                                                        <=> b57 )
                                                                                      <=> b58 )
                                                                                    <=> b59 )
                                                                                  <=> b60 )
                                                                                <=> b61 )
                                                                              <=> b62 )
                                                                            <=> b63 )
                                                                          <=> b64 )
                                                                        <=> b65 )
                                                                      <=> b66 )
                                                                    <=> b67 )
                                                                  <=> b68 )
                                                                <=> b69 )
                                                              <=> b70 )
                                                            <=> b71 )
                                                          <=> b72 )
                                                        <=> b73 )
                                                      <=> b74 )
                                                    <=> b75 )
                                                  <=> b76 )
                                                <=> b77 )
                                              <=> b78 )
                                            <=> b79 )
                                          <=> b80 )
                                        <=> b81 )
                                      <=> b82 )
                                    <=> b83 )
                                  <=> b84 )
                                <=> b85 )
                              <=> b86 )
                            <=> b87 )
                          <=> b88 )
                        <=> b89 )
                      <=> b90 )
                    <=> b91 )
                  <=> b92 )
                <=> b93 )
              <=> b94 )
            <=> b95 )
          <=> b96 )
        <=> b97 )
      <=> b98 )
    <=> b99 )
  <=> b100 ),
    file('Problems/PRV043+1.p',c) ).

fof(s,plain,
    ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( b1
                                                                                                                                                                                                      <=> b2 )
                                                                                                                                                                                                    <=> b3 )
                                                                                                                                                                                                  <=> b4 )
                                                                                                                                                                                                <=> b5 )
                                                                                                                                                                                              <=> b6 )
                                                                                                                                                                                            <=> b7 )
                                                                                                                                                                                          <=> b8 )
                                                                                                                                                                                        <=> b9 )
                                                                                                                                                                                      <=> b10 )
                                                                                                                                                                                    <=> b11 )
                                                                                                                                                                                  <=> b12 )
                                                                                                                                                                                <=> b13 )
                                                                                                                                                                              <=> b14 )
                                                                                                                                                                            <=> b15 )
                                                                                                                                                                          <=> b16 )
                                                                                                                                                                        <=> b17 )
                                                                                                                                                                      <=> b18 )
                                                                                                                                                                    <=> b19 )
                                                                                                                                                                  <=> b20 )
                                                                                                                                                                <=> b21 )
                                                                                                                                                              <=> b22 )
                                                                                                                                                            <=> b23 )
                                                                                                                                                          <=> b24 )
                                                                                                                                                        <=> b25 )
                                                                                                                                                      <=> b26 )
                                                                                                                                                    <=> b27 )
                                                                                                                                                  <=> b28 )
                                                                                                                                                <=> b29 )
                                                                                                                                              <=> b30 )
                                                                                                                                            <=> b31 )
                                                                                                                                          <=> b32 )
                                                                                                                                        <=> b33 )
                                                                                                                                      <=> b34 )
                                                                                                                                    <=> b35 )
                                                                                                                                  <=> b36 )
                                                                                                                                <=> b37 )
                                                                                                                              <=> b38 )
                                                                                                                            <=> b39 )
                                                                                                                          <=> b40 )
                                                                                                                        <=> b41 )
                                                                                                                      <=> b42 )
                                                                                                                    <=> b43 )
                                                                                                                  <=> b44 )
                                                                                                                <=> b45 )
                                                                                                              <=> b46 )
                                                                                                            <=> b47 )
                                                                                                          <=> b48 )
                                                                                                        <=> b49 )
                                                                                                      <=> b50 )
                                                                                                    <=> b51 )
                                                                                                  <=> b52 )
                                                                                                <=> b53 )
                                                                                              <=> b54 )
                                                                                            <=> b55 )
                                                                                          <=> b56 )
                                                                                        <=> b57 )
                                                                                      <=> b58 )
                                                                                    <=> b59 )
                                                                                  <=> b60 )
                                                                                <=> b61 )
                                                                              <=> b62 )
                                                                            <=> b63 )
                                                                          <=> b64 )
                                                                        <=> b65 )
                                                                      <=> b66 )
                                                                    <=> b67 )
                                                                  <=> b68 )
                                                                <=> b69 )
                                                              <=> b70 )
                                                            <=> b71 )
                                                          <=> b72 )
                                                        <=> b73 )
                                                      <=> b74 )
                                                    <=> b75 )
                                                  <=> b76 )
                                                <=> b77 )
                                              <=> b78 )
                                            <=> b79 )
                                          <=> b80 )
                                        <=> b81 )
                                      <=> b82 )
                                    <=> b83 )
                                  <=> b84 )
                                <=> b85 )
                              <=> b86 )
                            <=> b87 )
                          <=> b88 )
                        <=> b89 )
                      <=> b90 )
                    <=> b91 )
                  <=> b92 )
                <=> b93 )
              <=> b94 )
            <=> b95 )
          <=> b96 )
        <=> b97 )
      <=> b98 )
    <=> b99 )
  <=> b100 ),
    inference(reassociate,[status(thm)],[a1]) ).

fof(negc,negated_conjecture,
    ~ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( b1
                                                                                                                                                                                                        <=> b2 )
                                                                                                                                                                                                      <=> b3 )
                                                                                                                                                                                                    <=> b4 )
                                                                                                                                                                                                  <=> b5 )
                                                                                                                                                                                                <=> b6 )
                                                                                                                                                                                              <=> b7 )
                                                                                                                                                                                            <=> b8 )
                                                                                                                                                                                          <=> b9 )
                                                                                                                                                                                        <=> b10 )
                                                                                                                                                                                      <=> b11 )
                                                                                                                                                                                    <=> b12 )
                                                                                                                                                                                  <=> b13 )
                                                                                                                                                                                <=> b14 )
                                                                                                                                                                              <=> b15 )
                                                                                                                                                                            <=> b16 )
                                                                                                                                                                          <=> b17 )
                                                                                                                                                                        <=> b18 )
                                                                                                                                                                      <=> b19 )
                                                                                                                                                                    <=> b20 )
                                                                                                                                                                  <=> b21 )
                                                                                                                                                                <=> b22 )
                                                                                                                                                              <=> b23 )
                                                                                                                                                            <=> b24 )
                                                                                                                                                          <=> b25 )
                                                                                                                                                        <=> b26 )
                                                                                                                                                      <=> b27 )
                                                                                                                                                    <=> b28 )
                                                                                                                                                  <=> b29 )
                                                                                                                                                <=> b30 )
                                                                                                                                              <=> b31 )
                                                                                                                                            <=> b32 )
                                                                                                                                          <=> b33 )
                                                                                                                                        <=> b34 )
                                                                                                                                      <=> b35 )
                                                                                                                                    <=> b36 )
                                                                                                                                  <=> b37 )
                                                                                                                                <=> b38 )
                                                                                                                              <=> b39 )
                                                                                                                            <=> b40 )
                                                                                                                          <=> b41 )
                                                                                                                        <=> b42 )
                                                                                                                      <=> b43 )
                                                                                                                    <=> b44 )
                                                                                                                  <=> b45 )
                                                                                                                <=> b46 )
                                                                                                              <=> b47 )
                                                                                                            <=> b48 )
                                                                                                          <=> b49 )
                                                                                                        <=> b50 )
                                                                                                      <=> b51 )
                                                                                                    <=> b52 )
                                                                                                  <=> b53 )
                                                                                                <=> b54 )
                                                                                              <=> b55 )
                                                                                            <=> b56 )
                                                                                          <=> b57 )
                                                                                        <=> b58 )
                                                                                      <=> b59 )
                                                                                    <=> b60 )
                                                                                  <=> b61 )
                                                                                <=> b62 )
                                                                              <=> b63 )
                                                                            <=> b64 )
                                                                          <=> b65 )
                                                                        <=> b66 )
                                                                      <=> b67 )
                                                                    <=> b68 )
                                                                  <=> b69 )
                                                                <=> b70 )
                                                              <=> b71 )
                                                            <=> b72 )
                                                          <=> b73 )
                                                        <=> b74 )
                                                      <=> b75 )
                                                    <=> b76 )
                                                  <=> b77 )
                                                <=> b78 )
                                              <=> b79 )
                                            <=> b80 )
                                          <=> b81 )
                                        <=> b82 )
                                      <=> b83 )
                                    <=> b84 )
                                  <=> b85 )
                                <=> b86 )
                              <=> b87 )
                            <=> b88 )
                          <=> b89 )
                        <=> b90 )
                      <=> b91 )
                    <=> b92 )
                  <=> b93 )
                <=> b94 )
              <=> b95 )
            <=> b96 )
          <=> b97 )
        <=> b98 )
      <=> b99 )
    <=> b100 ),
    inference(negated_conjecture,[status(cth)],[c]) ).

fof(bot,plain,
    $false,
    inference(consequence,[status(thm)],[negc,s]) ).

% SZS output end Proof