TSTP Solution File: SYN556-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN556-1 : 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 : n032.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 03:35:14 EDT 2023
% Result : Unsatisfiable 0.14s 0.72s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN556-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sat Aug 26 21:39:29 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.72 Command-line arguments: --flatten
% 0.14/0.72
% 0.14/0.72 % SZS status Unsatisfiable
% 0.14/0.72
% 0.14/0.76 % SZS output start Proof
% 0.14/0.76 Take the following subset of the input axioms:
% 0.14/0.76 fof(not_p3_9, negated_conjecture, ~p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))).
% 0.14/0.76 fof(p2_1, negated_conjecture, ![X0]: p2(X0, X0)).
% 0.14/0.76 fof(p2_10, negated_conjecture, ![X3, X4, X5, X6]: (p2(f5(X3, X4), f5(X5, X6)) | (~p2(X3, X5) | ~p2(X4, X6)))).
% 0.14/0.76 fof(p2_11, negated_conjecture, ![X11, X12, X13, X14]: (p2(f8(X11, X12), f8(X13, X14)) | (~p2(X12, X14) | ~p3(X11, X13)))).
% 0.14/0.76 fof(p2_3, negated_conjecture, p2(c10, c13)).
% 0.14/0.76 fof(p3_12, negated_conjecture, ![X18, X19, X20, X21, X22, X23]: (p3(f4(X18, X19, X20), f4(X21, X22, X23)) | (~p2(X19, X22) | (~p3(X20, X23) | ~p2(X18, X21))))).
% 0.14/0.76 fof(p3_2, negated_conjecture, ![X15]: p3(X15, X15)).
% 0.14/0.76 fof(p3_7, negated_conjecture, ![X16, X17, X15_2]: (p3(X16, X17) | (~p3(X15_2, X16) | ~p3(X15_2, X17)))).
% 0.14/0.76 fof(p3_8, negated_conjecture, p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))).
% 0.14/0.76
% 0.14/0.76 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.76 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.76 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.76 fresh(y, y, x1...xn) = u
% 0.14/0.76 C => fresh(s, t, x1...xn) = v
% 0.14/0.76 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.76 variables of u and v.
% 0.14/0.76 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.76 input problem has no model of domain size 1).
% 0.14/0.76
% 0.14/0.76 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.76
% 0.14/0.76 Axiom 1 (p3_2): p3(X, X) = true.
% 0.14/0.76 Axiom 2 (p2_1): p2(X, X) = true.
% 0.14/0.76 Axiom 3 (p2_3): p2(c10, c13) = true.
% 0.14/0.76 Axiom 4 (p3_7): fresh(X, X, Y, Z) = true.
% 0.14/0.76 Axiom 5 (p3_7): fresh2(X, X, Y, Z, W) = p3(Y, Z).
% 0.14/0.76 Axiom 6 (p2_10): fresh11(X, X, Y, Z, W, V) = true.
% 0.14/0.76 Axiom 7 (p2_11): fresh8(X, X, Y, Z, W, V) = true.
% 0.14/0.76 Axiom 8 (p2_10): fresh10(X, X, Y, Z, W, V) = p2(f5(Y, Z), f5(W, V)).
% 0.14/0.76 Axiom 9 (p2_11): fresh9(X, X, Y, Z, W, V) = p2(f8(Y, Z), f8(W, V)).
% 0.14/0.76 Axiom 10 (p3_7): fresh2(p3(X, Y), true, Z, Y, X) = fresh(p3(X, Z), true, Z, Y).
% 0.14/0.76 Axiom 11 (p3_12): fresh13(X, X, Y, Z, W, V, U, T) = true.
% 0.14/0.76 Axiom 12 (p2_10): fresh10(p2(X, Y), true, Z, X, W, Y) = fresh11(p2(Z, W), true, Z, X, W, Y).
% 0.14/0.76 Axiom 13 (p2_11): fresh9(p3(X, Y), true, X, Z, Y, W) = fresh8(p2(Z, W), true, X, Z, Y, W).
% 0.14/0.76 Axiom 14 (p3_12): fresh3(X, X, Y, Z, W, V, U, T) = p3(f4(Y, Z, W), f4(T, V, U)).
% 0.14/0.76 Axiom 15 (p3_12): fresh12(X, X, Y, Z, W, V, U, T) = fresh13(p2(Y, T), true, Y, Z, W, V, U, T).
% 0.14/0.76 Axiom 16 (p3_12): fresh12(p3(X, Y), true, Z, W, X, V, Y, U) = fresh3(p2(W, V), true, Z, W, X, V, Y, U).
% 0.14/0.76 Axiom 17 (p3_8): p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)) = true.
% 0.14/0.76
% 0.14/0.76 Lemma 18: fresh(X, X, Y, Z) = p2(c10, c13).
% 0.14/0.76 Proof:
% 0.14/0.76 fresh(X, X, Y, Z)
% 0.14/0.76 = { by axiom 4 (p3_7) }
% 0.14/0.76 true
% 0.14/0.76 = { by axiom 3 (p2_3) R->L }
% 0.14/0.76 p2(c10, c13)
% 0.14/0.76
% 0.14/0.76 Lemma 19: fresh2(p3(X, Y), p2(c10, c13), Z, Y, X) = fresh(p3(X, Z), p2(c10, c13), Z, Y).
% 0.14/0.76 Proof:
% 0.14/0.76 fresh2(p3(X, Y), p2(c10, c13), Z, Y, X)
% 0.14/0.76 = { by axiom 3 (p2_3) }
% 0.14/0.76 fresh2(p3(X, Y), true, Z, Y, X)
% 0.14/0.76 = { by axiom 10 (p3_7) }
% 0.14/0.76 fresh(p3(X, Z), true, Z, Y)
% 0.14/0.76 = { by axiom 3 (p2_3) R->L }
% 0.14/0.76 fresh(p3(X, Z), p2(c10, c13), Z, Y)
% 0.14/0.76
% 0.14/0.76 Lemma 20: p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)) = p2(c10, c13).
% 0.14/0.76 Proof:
% 0.14/0.76 p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11))
% 0.14/0.76 = { by axiom 17 (p3_8) }
% 0.14/0.76 true
% 0.14/0.76 = { by axiom 3 (p2_3) R->L }
% 0.14/0.76 p2(c10, c13)
% 0.14/0.76
% 0.14/0.76 Lemma 21: fresh(p3(X, Y), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), Y, X) = p3(Y, X).
% 0.14/0.76 Proof:
% 0.14/0.76 fresh(p3(X, Y), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), Y, X)
% 0.14/0.76 = { by lemma 20 }
% 0.14/0.76 fresh(p3(X, Y), p2(c10, c13), Y, X)
% 0.14/0.76 = { by lemma 19 R->L }
% 0.14/0.76 fresh2(p3(X, X), p2(c10, c13), Y, X, X)
% 0.14/0.76 = { by axiom 1 (p3_2) }
% 0.14/0.76 fresh2(true, p2(c10, c13), Y, X, X)
% 0.14/0.76 = { by axiom 3 (p2_3) R->L }
% 0.14/0.76 fresh2(p2(c10, c13), p2(c10, c13), Y, X, X)
% 0.14/0.76 = { by axiom 5 (p3_7) }
% 0.14/0.77 p3(Y, X)
% 0.14/0.77
% 0.14/0.77 Goal 1 (not_p3_9): p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)) = true.
% 0.14/0.77 Proof:
% 0.14/0.77 p3(c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 21 R->L }
% 0.14/0.77 fresh(p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by axiom 5 (p3_7) R->L }
% 0.14/0.77 fresh(fresh2(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 20 }
% 0.14/0.77 fresh(fresh2(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p2(c10, c13), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 20 }
% 0.14/0.77 fresh(fresh2(p2(c10, c13), p2(c10, c13), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 18 R->L }
% 0.14/0.77 fresh(fresh2(fresh(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9), p2(c10, c13), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 21 }
% 0.14/0.77 fresh(fresh2(p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), c9), p2(c10, c13), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 19 }
% 0.14/0.77 fresh(fresh(p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p2(c10, c13), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 20 R->L }
% 0.14/0.77 fresh(fresh(p3(f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 21 R->L }
% 0.14/0.77 fresh(fresh(fresh(p3(f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by axiom 14 (p3_12) R->L }
% 0.14/0.77 fresh(fresh(fresh(fresh3(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.77 = { by lemma 20 }
% 0.14/0.78 fresh(fresh(fresh(fresh3(p2(c10, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(true, p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 6 (p2_10) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by lemma 20 }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(p2(c10, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(true, p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 7 (p2_11) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh8(p2(c10, c13), p2(c10, c13), c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh8(p2(c10, c13), true, c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 13 (p2_11) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh9(p3(c11, c11), true, c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh9(p3(c11, c11), p2(c10, c13), c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by lemma 20 R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh9(p3(c11, c11), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 1 (p3_2) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh9(true, p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh9(p2(c10, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by lemma 20 R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(fresh9(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c11, c10, c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 9 (p2_11) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(p2(f8(c11, c10), f8(c11, c13)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by lemma 20 }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(p2(f8(c11, c10), f8(c11, c13)), p2(c10, c13), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh11(p2(f8(c11, c10), f8(c11, c13)), true, f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 12 (p2_10) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh10(p2(f6(f7(c12)), f6(f7(c12))), true, f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh10(p2(f6(f7(c12)), f6(f7(c12))), p2(c10, c13), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 2 (p2_1) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh10(true, p2(c10, c13), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 3 (p2_3) R->L }
% 0.14/0.78 fresh(fresh(fresh(fresh3(fresh10(p2(c10, c13), p2(c10, c13), f8(c11, c10), f6(f7(c12)), f8(c11, c13), f6(f7(c12))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by axiom 8 (p2_10) }
% 0.14/0.78 fresh(fresh(fresh(fresh3(p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12)))), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.78 = { by lemma 20 }
% 0.14/0.78 fresh(fresh(fresh(fresh3(p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12)))), p2(c10, c13), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 3 (p2_3) }
% 0.14/0.79 fresh(fresh(fresh(fresh3(p2(f5(f8(c11, c10), f6(f7(c12))), f5(f8(c11, c13), f6(f7(c12)))), true, c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 16 (p3_12) R->L }
% 0.14/0.79 fresh(fresh(fresh(fresh12(p3(c11, c11), true, c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 3 (p2_3) R->L }
% 0.14/0.79 fresh(fresh(fresh(fresh12(p3(c11, c11), p2(c10, c13), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 1 (p3_2) }
% 0.14/0.79 fresh(fresh(fresh(fresh12(true, p2(c10, c13), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 3 (p2_3) R->L }
% 0.14/0.79 fresh(fresh(fresh(fresh12(p2(c10, c13), p2(c10, c13), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 15 (p3_12) }
% 0.14/0.79 fresh(fresh(fresh(fresh13(p2(c10, c13), true, c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 3 (p2_3) R->L }
% 0.14/0.79 fresh(fresh(fresh(fresh13(p2(c10, c13), p2(c10, c13), c10, f5(f8(c11, c10), f6(f7(c12))), c11, f5(f8(c11, c13), f6(f7(c12))), c11, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 11 (p3_12) }
% 0.14/0.79 fresh(fresh(fresh(true, p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by axiom 3 (p2_3) R->L }
% 0.14/0.79 fresh(fresh(fresh(p2(c10, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.79 = { by lemma 20 R->L }
% 0.14/0.79 fresh(fresh(fresh(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.80 = { by lemma 18 }
% 0.14/0.80 fresh(fresh(p2(c10, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.80 = { by lemma 20 R->L }
% 0.14/0.80 fresh(fresh(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11), c9), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.80 = { by lemma 18 }
% 0.14/0.80 fresh(p2(c10, c13), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.80 = { by lemma 20 R->L }
% 0.14/0.80 fresh(p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), p3(c9, f4(c13, f5(f8(c11, c13), f6(f7(c12))), c11)), c9, f4(c10, f5(f8(c11, c10), f6(f7(c12))), c11))
% 0.14/0.80 = { by lemma 18 }
% 0.14/0.80 p2(c10, c13)
% 0.14/0.80 = { by axiom 3 (p2_3) }
% 0.14/0.80 true
% 0.14/0.80 % SZS output end Proof
% 0.14/0.80
% 0.14/0.80 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------