TSTP Solution File: SYN557-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN557-1 : 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 : n005.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 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYN557-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 21:36:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Command-line arguments: --flatten
% 0.20/0.48
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 Take the following subset of the input axioms:
% 0.20/0.49 fof(not_p2_3, negated_conjecture, ~p2(c6, f3(c8, f5(c9)))).
% 0.20/0.49 fof(p2_1, negated_conjecture, ![X3]: p2(X3, X3)).
% 0.20/0.49 fof(p2_10, negated_conjecture, ![X12, X13, X14]: p2(f3(X12, f3(X13, X14)), f3(X13, f3(X12, X14)))).
% 0.20/0.49 fof(p2_12, negated_conjecture, p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9))))).
% 0.20/0.49 fof(p2_4, negated_conjecture, ![X10, X11]: p2(f3(X10, X11), f3(X11, X10))).
% 0.20/0.49 fof(p2_6, negated_conjecture, ![X4, X5, X3_2]: (p2(X4, X5) | (~p2(X3_2, X4) | ~p2(X3_2, X5)))).
% 0.20/0.49 fof(p2_8, negated_conjecture, ![X0, X1, X2]: (p2(X0, X1) | ~p2(f3(X0, X2), f3(X1, X2)))).
% 0.20/0.49
% 0.20/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.49 fresh(y, y, x1...xn) = u
% 0.20/0.49 C => fresh(s, t, x1...xn) = v
% 0.20/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.49 variables of u and v.
% 0.20/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.49 input problem has no model of domain size 1).
% 0.20/0.49
% 0.20/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.49
% 0.20/0.49 Axiom 1 (p2_1): p2(X, X) = true.
% 0.20/0.49 Axiom 2 (p2_6): fresh5(X, X, Y, Z) = true.
% 0.20/0.49 Axiom 3 (p2_8): fresh4(X, X, Y, Z) = true.
% 0.20/0.49 Axiom 4 (p2_6): fresh6(X, X, Y, Z, W) = p2(Y, Z).
% 0.20/0.49 Axiom 5 (p2_4): p2(f3(X, Y), f3(Y, X)) = true.
% 0.20/0.49 Axiom 6 (p2_6): fresh6(p2(X, Y), true, Z, Y, X) = fresh5(p2(X, Z), true, Z, Y).
% 0.20/0.49 Axiom 7 (p2_8): fresh4(p2(f3(X, Y), f3(Z, Y)), true, X, Z) = p2(X, Z).
% 0.20/0.49 Axiom 8 (p2_10): p2(f3(X, f3(Y, Z)), f3(Y, f3(X, Z))) = true.
% 0.20/0.49 Axiom 9 (p2_12): p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))) = true.
% 0.20/0.49
% 0.20/0.49 Lemma 10: fresh5(p2(X, Y), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), Y, X) = p2(Y, X).
% 0.20/0.49 Proof:
% 0.20/0.49 fresh5(p2(X, Y), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), Y, X)
% 0.20/0.49 = { by axiom 9 (p2_12) }
% 0.20/0.49 fresh5(p2(X, Y), true, Y, X)
% 0.20/0.49 = { by axiom 6 (p2_6) R->L }
% 0.20/0.49 fresh6(p2(X, X), true, Y, X, X)
% 0.20/0.49 = { by axiom 1 (p2_1) }
% 0.20/0.49 fresh6(true, true, Y, X, X)
% 0.20/0.49 = { by axiom 4 (p2_6) }
% 0.20/0.49 p2(Y, X)
% 0.20/0.49
% 0.20/0.49 Goal 1 (not_p2_3): p2(c6, f3(c8, f5(c9))) = true.
% 0.20/0.49 Proof:
% 0.20/0.49 p2(c6, f3(c8, f5(c9)))
% 0.20/0.49 = { by lemma 10 R->L }
% 0.20/0.49 fresh5(p2(f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.49 = { by axiom 7 (p2_8) R->L }
% 0.20/0.49 fresh5(fresh4(p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), true, f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.49 = { by axiom 9 (p2_12) R->L }
% 0.20/0.49 fresh5(fresh4(p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.49 = { by axiom 4 (p2_6) R->L }
% 0.20/0.49 fresh5(fresh4(fresh6(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.49 = { by axiom 9 (p2_12) }
% 0.20/0.49 fresh5(fresh4(fresh6(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), true, f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.49 = { by axiom 9 (p2_12) }
% 0.20/0.49 fresh5(fresh4(fresh6(true, true, f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 2 (p2_6) R->L }
% 0.20/0.50 fresh5(fresh4(fresh6(fresh5(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true, f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by lemma 10 }
% 0.20/0.50 fresh5(fresh4(fresh6(p2(f3(c8, f3(f5(c7), f5(c9))), f3(c6, f5(c7))), true, f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 6 (p2_6) }
% 0.20/0.50 fresh5(fresh4(fresh5(p2(f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), true, f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(p2(f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by lemma 10 R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(p2(f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 4 (p2_6) R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh6(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9))), f3(f5(c7), f3(c8, f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh6(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), true, f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9))), f3(f5(c7), f3(c8, f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh6(true, true, f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9))), f3(f5(c7), f3(c8, f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 8 (p2_10) R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh6(p2(f3(f5(c7), f3(c8, f5(c9))), f3(c8, f3(f5(c7), f5(c9)))), true, f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9))), f3(f5(c7), f3(c8, f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 6 (p2_6) }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh5(p2(f3(f5(c7), f3(c8, f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), true, f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh5(p2(f3(f5(c7), f3(c8, f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 5 (p2_4) }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh5(true, p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(fresh5(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 2 (p2_6) }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(true, p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(fresh5(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f3(f5(c7), f5(c9))), f3(f3(c8, f5(c9)), f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 2 (p2_6) }
% 0.20/0.50 fresh5(fresh4(fresh5(true, p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) R->L }
% 0.20/0.50 fresh5(fresh4(fresh5(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(f3(c8, f5(c9)), f5(c7)), f3(c6, f5(c7))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 2 (p2_6) }
% 0.20/0.50 fresh5(fresh4(true, p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) R->L }
% 0.20/0.50 fresh5(fresh4(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), f3(c8, f5(c9)), c6), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 3 (p2_8) }
% 0.20/0.50 fresh5(true, p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 9 (p2_12) R->L }
% 0.20/0.50 fresh5(p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), p2(f3(c6, f5(c7)), f3(c8, f3(f5(c7), f5(c9)))), c6, f3(c8, f5(c9)))
% 0.20/0.50 = { by axiom 2 (p2_6) }
% 0.20/0.50 true
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------