TSTP Solution File: SYN611-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN611-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:35:26 EDT 2023
% Result : Unsatisfiable 0.19s 0.58s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN611-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 18:29:52 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.58 Command-line arguments: --flatten
% 0.19/0.58
% 0.19/0.58 % SZS status Unsatisfiable
% 0.19/0.58
% 0.19/0.60 % SZS output start Proof
% 0.19/0.60 Take the following subset of the input axioms:
% 0.19/0.60 fof(not_p17_28, negated_conjecture, ![X50]: ~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))).
% 0.19/0.60 fof(p17_20, negated_conjecture, ![X2, X3, X4, X5]: (p17(X2, X3) | (~p2(X4, X2) | (~p2(X5, X3) | ~p17(X4, X5))))).
% 0.19/0.60 fof(p17_29, negated_conjecture, p17(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20))))).
% 0.19/0.60 fof(p2_12, negated_conjecture, ![X16, X17]: (p2(f9(X16), f9(X17)) | ~p3(X16, X17))).
% 0.19/0.60 fof(p2_2, negated_conjecture, ![X11]: p2(X11, X11)).
% 0.19/0.60 fof(p3_19, negated_conjecture, ![X18, X19, X20]: (p3(X19, X20) | (~p3(X18, X19) | ~p3(X18, X20)))).
% 0.19/0.60 fof(p3_22, negated_conjecture, p3(f12(f4(f6(f7(f8(c20)))), c21), f4(f6(f7(f8(c20)))))).
% 0.19/0.60 fof(p3_24, negated_conjecture, ![X21, X22, X23, X24]: (p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23) | ~p3(X22, X24)))).
% 0.19/0.60 fof(p3_4, negated_conjecture, ![X18_2]: p3(X18_2, X18_2)).
% 0.19/0.60 fof(p3_6, negated_conjecture, p3(f12(c22, c21), c22)).
% 0.19/0.60 fof(p3_8, negated_conjecture, p3(f12(f15(c22), c21), f15(c22))).
% 0.19/0.60
% 0.19/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.60 fresh(y, y, x1...xn) = u
% 0.19/0.60 C => fresh(s, t, x1...xn) = v
% 0.19/0.60 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.60 variables of u and v.
% 0.19/0.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.60 input problem has no model of domain size 1).
% 0.19/0.60
% 0.19/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.60
% 0.19/0.60 Axiom 1 (p2_2): p2(X, X) = true2.
% 0.19/0.60 Axiom 2 (p3_4): p3(X, X) = true2.
% 0.19/0.60 Axiom 3 (p17_20): fresh29(X, X, Y, Z) = true2.
% 0.19/0.60 Axiom 4 (p2_12): fresh20(X, X, Y, Z) = true2.
% 0.19/0.60 Axiom 5 (p3_19): fresh13(X, X, Y, Z) = true2.
% 0.19/0.60 Axiom 6 (p3_6): p3(f12(c22, c21), c22) = true2.
% 0.19/0.60 Axiom 7 (p17_20): fresh23(X, X, Y, Z, W) = p17(Y, Z).
% 0.19/0.60 Axiom 8 (p3_19): fresh14(X, X, Y, Z, W) = p3(Y, Z).
% 0.19/0.60 Axiom 9 (p17_20): fresh28(X, X, Y, Z, W, V) = fresh29(p2(W, Y), true2, Y, Z).
% 0.19/0.60 Axiom 10 (p2_12): fresh20(p3(X, Y), true2, X, Y) = p2(f9(X), f9(Y)).
% 0.19/0.60 Axiom 11 (p3_24): fresh9(X, X, Y, Z, W, V) = true2.
% 0.19/0.60 Axiom 12 (p3_24): fresh10(X, X, Y, Z, W, V) = p3(f10(Y, Z), f10(W, V)).
% 0.19/0.60 Axiom 13 (p3_8): p3(f12(f15(c22), c21), f15(c22)) = true2.
% 0.19/0.60 Axiom 14 (p3_19): fresh14(p3(X, Y), true2, Z, Y, X) = fresh13(p3(X, Z), true2, Z, Y).
% 0.19/0.60 Axiom 15 (p17_20): fresh28(p17(X, Y), true2, Z, W, X, Y) = fresh23(p2(Y, W), true2, Z, W, X).
% 0.19/0.60 Axiom 16 (p3_24): fresh10(p3(X, Y), true2, Z, X, W, Y) = fresh9(p3(Z, W), true2, Z, X, W, Y).
% 0.19/0.60 Axiom 17 (p3_22): p3(f12(f4(f6(f7(f8(c20)))), c21), f4(f6(f7(f8(c20))))) = true2.
% 0.19/0.60 Axiom 18 (p17_29): p17(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20)))) = true2.
% 0.19/0.60
% 0.19/0.60 Lemma 19: p3(f12(f15(c22), c21), f15(c22)) = p3(f12(c22, c21), c22).
% 0.19/0.60 Proof:
% 0.19/0.60 p3(f12(f15(c22), c21), f15(c22))
% 0.19/0.60 = { by axiom 13 (p3_8) }
% 0.19/0.60 true2
% 0.19/0.60 = { by axiom 6 (p3_6) R->L }
% 0.19/0.61 p3(f12(c22, c21), c22)
% 0.19/0.61
% 0.19/0.61 Goal 1 (not_p17_28): p17(f9(f10(f14(f4(f9(c19)), c19), f12(X, c21))), f6(f7(f8(c20)))) = true2.
% 0.19/0.61 The goal is true when:
% 0.19/0.61 X = f4(f6(f7(f8(c20))))
% 0.19/0.61
% 0.19/0.61 Proof:
% 0.19/0.61 p17(f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 7 (p17_20) R->L }
% 0.19/0.61 fresh23(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))))
% 0.19/0.61 = { by lemma 19 }
% 0.19/0.61 fresh23(p3(f12(c22, c21), c22), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))))
% 0.19/0.61 = { by axiom 6 (p3_6) }
% 0.19/0.61 fresh23(true2, p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))))
% 0.19/0.61 = { by axiom 1 (p2_2) R->L }
% 0.19/0.61 fresh23(p2(f6(f7(f8(c20))), f6(f7(f8(c20)))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))))
% 0.19/0.61 = { by lemma 19 }
% 0.19/0.61 fresh23(p2(f6(f7(f8(c20))), f6(f7(f8(c20)))), p3(f12(c22, c21), c22), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))))
% 0.19/0.61 = { by axiom 6 (p3_6) }
% 0.19/0.61 fresh23(p2(f6(f7(f8(c20))), f6(f7(f8(c20)))), true2, f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))))
% 0.19/0.61 = { by axiom 15 (p17_20) R->L }
% 0.19/0.61 fresh28(p17(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20)))), true2, f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 6 (p3_6) R->L }
% 0.19/0.61 fresh28(p17(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20)))), p3(f12(c22, c21), c22), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20))))
% 0.19/0.61 = { by lemma 19 R->L }
% 0.19/0.61 fresh28(p17(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20)))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 18 (p17_29) }
% 0.19/0.61 fresh28(true2, p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 6 (p3_6) R->L }
% 0.19/0.61 fresh28(p3(f12(c22, c21), c22), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20))))
% 0.19/0.61 = { by lemma 19 R->L }
% 0.19/0.61 fresh28(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))), f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 9 (p17_20) }
% 0.19/0.61 fresh29(p2(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)))), true2, f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 6 (p3_6) R->L }
% 0.19/0.61 fresh29(p2(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)))), p3(f12(c22, c21), c22), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by lemma 19 R->L }
% 0.19/0.61 fresh29(p2(f9(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 10 (p2_12) R->L }
% 0.19/0.61 fresh29(fresh20(p3(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), true2, f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 6 (p3_6) R->L }
% 0.19/0.61 fresh29(fresh20(p3(f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 8 (p3_19) R->L }
% 0.19/0.61 fresh29(fresh20(fresh14(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by lemma 19 }
% 0.19/0.61 fresh29(fresh20(fresh14(p3(f12(c22, c21), c22), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 6 (p3_6) }
% 0.19/0.61 fresh29(fresh20(fresh14(true2, p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 2 (p3_4) R->L }
% 0.19/0.61 fresh29(fresh20(fresh14(p3(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by lemma 19 }
% 0.19/0.61 fresh29(fresh20(fresh14(p3(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 6 (p3_6) }
% 0.19/0.61 fresh29(fresh20(fresh14(p3(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), true2, f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 14 (p3_19) }
% 0.19/0.61 fresh29(fresh20(fresh13(p3(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), true2, f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 6 (p3_6) R->L }
% 0.19/0.61 fresh29(fresh20(fresh13(p3(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by lemma 19 R->L }
% 0.19/0.61 fresh29(fresh20(fresh13(p3(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20)))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.61 = { by axiom 12 (p3_24) R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh10(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh10(p3(f12(c22, c21), c22), p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 6 (p3_6) }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh10(true2, p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 17 (p3_22) R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh10(p3(f12(f4(f6(f7(f8(c20)))), c21), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh10(p3(f12(f4(f6(f7(f8(c20)))), c21), f4(f6(f7(f8(c20))))), p3(f12(c22, c21), c22), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 6 (p3_6) }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh10(p3(f12(f4(f6(f7(f8(c20)))), c21), f4(f6(f7(f8(c20))))), true2, f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 16 (p3_24) }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh9(p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19)), true2, f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 6 (p3_6) R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh9(p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19)), p3(f12(c22, c21), c22), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh9(p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19)), p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 2 (p3_4) }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh9(true2, p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 6 (p3_6) R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh9(p3(f12(c22, c21), c22), p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(fresh9(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21), f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 11 (p3_24) }
% 0.19/0.62 fresh29(fresh20(fresh13(true2, p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 6 (p3_6) R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(p3(f12(c22, c21), c22), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 R->L }
% 0.19/0.62 fresh29(fresh20(fresh13(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 5 (p3_19) }
% 0.19/0.62 fresh29(fresh20(true2, p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 6 (p3_6) R->L }
% 0.19/0.62 fresh29(fresh20(p3(f12(c22, c21), c22), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 R->L }
% 0.19/0.62 fresh29(fresh20(p3(f12(f15(c22), c21), f15(c22)), p3(f12(c22, c21), c22), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 R->L }
% 0.19/0.62 fresh29(fresh20(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f10(f14(f4(f9(c19)), c19), f4(f6(f7(f8(c20))))), f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 4 (p2_12) }
% 0.19/0.62 fresh29(true2, p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 6 (p3_6) R->L }
% 0.19/0.62 fresh29(p3(f12(c22, c21), c22), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by lemma 19 R->L }
% 0.19/0.62 fresh29(p3(f12(f15(c22), c21), f15(c22)), p3(f12(f15(c22), c21), f15(c22)), f9(f10(f14(f4(f9(c19)), c19), f12(f4(f6(f7(f8(c20)))), c21))), f6(f7(f8(c20))))
% 0.19/0.62 = { by axiom 3 (p17_20) }
% 0.19/0.62 true2
% 0.19/0.62 = { by axiom 6 (p3_6) R->L }
% 0.19/0.62 p3(f12(c22, c21), c22)
% 0.19/0.62 = { by lemma 19 R->L }
% 0.19/0.62 p3(f12(f15(c22), c21), f15(c22))
% 0.19/0.62 = { by lemma 19 }
% 0.19/0.62 p3(f12(c22, c21), c22)
% 0.19/0.62 = { by axiom 6 (p3_6) }
% 0.19/0.62 true2
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62
% 0.19/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------