TSTP Solution File: SYN569-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN569-1 : 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 : n021.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 03:35:17 EDT 2023
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN569-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % 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 : n021.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 19:07:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Command-line arguments: --flatten
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 Take the following subset of the input axioms:
% 0.20/0.53 fof(not_p8_20, negated_conjecture, ![X41]: (~p8(X41, c12) | (~p8(c11, X41) | ~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))))).
% 0.20/0.53 fof(p10_7, negated_conjecture, ![X4, X5]: (p10(X4, X5) | ~p8(X4, X5))).
% 0.20/0.53 fof(p2_1, negated_conjecture, ![X6]: p2(X6, X6)).
% 0.20/0.53 fof(p2_10, negated_conjecture, ![X7, X8, X6_2]: (p2(X7, X8) | (~p2(X6_2, X7) | ~p2(X6_2, X8)))).
% 0.20/0.53 fof(p2_11, negated_conjecture, ![X9, X10, X11, X12]: (p2(X9, X10) | (~p9(X11, X9, X12) | ~p9(X11, X10, X12)))).
% 0.20/0.53 fof(p2_15, negated_conjecture, p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))).
% 0.20/0.53 fof(p2_16, negated_conjecture, ![X15, X16, X17, X18]: (p2(f4(X15, X16), f4(X17, X18)) | (~p2(X15, X17) | ~p2(X16, X18)))).
% 0.20/0.53 fof(p8_3, negated_conjecture, p8(c14, c12)).
% 0.20/0.53 fof(p8_5, negated_conjecture, p8(c11, c14)).
% 0.20/0.53 fof(p9_12, negated_conjecture, ![X40]: (p9(c13, f3(X40), X40) | (~p10(X40, c12) | ~p10(c11, X40)))).
% 0.20/0.53 fof(p9_6, negated_conjecture, p9(c13, c15, c14)).
% 0.20/0.53
% 0.20/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.53 fresh(y, y, x1...xn) = u
% 0.20/0.53 C => fresh(s, t, x1...xn) = v
% 0.20/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.53 variables of u and v.
% 0.20/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.53 input problem has no model of domain size 1).
% 0.20/0.53
% 0.20/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.53
% 0.20/0.53 Axiom 1 (p8_3): p8(c14, c12) = true2.
% 0.20/0.53 Axiom 2 (p8_5): p8(c11, c14) = true2.
% 0.20/0.53 Axiom 3 (p2_1): p2(X, X) = true2.
% 0.20/0.53 Axiom 4 (p9_12): fresh(X, X, Y) = true2.
% 0.20/0.53 Axiom 5 (p9_6): p9(c13, c15, c14) = true2.
% 0.20/0.53 Axiom 6 (p10_7): fresh17(X, X, Y, Z) = true2.
% 0.20/0.54 Axiom 7 (p2_10): fresh15(X, X, Y, Z) = true2.
% 0.20/0.54 Axiom 8 (p2_11): fresh13(X, X, Y, Z) = true2.
% 0.20/0.54 Axiom 9 (p9_12): fresh2(X, X, Y) = p9(c13, f3(Y), Y).
% 0.20/0.54 Axiom 10 (p2_10): fresh16(X, X, Y, Z, W) = p2(Y, Z).
% 0.20/0.54 Axiom 11 (p9_12): fresh2(p10(c11, X), true2, X) = fresh(p10(X, c12), true2, X).
% 0.20/0.54 Axiom 12 (p10_7): fresh17(p8(X, Y), true2, X, Y) = p10(X, Y).
% 0.20/0.54 Axiom 13 (p2_11): fresh14(X, X, Y, Z, W, V) = p2(Y, Z).
% 0.20/0.54 Axiom 14 (p2_16): fresh11(X, X, Y, Z, W, V) = true2.
% 0.20/0.54 Axiom 15 (p2_16): fresh12(X, X, Y, Z, W, V) = p2(f4(Y, Z), f4(W, V)).
% 0.20/0.54 Axiom 16 (p2_10): fresh16(p2(X, Y), true2, Z, Y, X) = fresh15(p2(X, Z), true2, Z, Y).
% 0.20/0.54 Axiom 17 (p2_16): fresh12(p2(X, Y), true2, Z, X, W, Y) = fresh11(p2(Z, W), true2, Z, X, W, Y).
% 0.20/0.54 Axiom 18 (p2_11): fresh14(p9(X, Y, Z), true2, W, Y, X, Z) = fresh13(p9(X, W, Z), true2, W, Y).
% 0.20/0.54 Axiom 19 (p2_15): p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)) = true2.
% 0.20/0.54
% 0.20/0.54 Lemma 20: p8(c11, c14) = p8(c14, c12).
% 0.20/0.54 Proof:
% 0.20/0.54 p8(c11, c14)
% 0.20/0.54 = { by axiom 2 (p8_5) }
% 0.20/0.54 true2
% 0.20/0.54 = { by axiom 1 (p8_3) R->L }
% 0.20/0.54 p8(c14, c12)
% 0.20/0.54
% 0.20/0.54 Lemma 21: p2(X, X) = p8(c11, c14).
% 0.20/0.54 Proof:
% 0.20/0.54 p2(X, X)
% 0.20/0.54 = { by axiom 3 (p2_1) }
% 0.20/0.54 true2
% 0.20/0.54 = { by axiom 1 (p8_3) R->L }
% 0.20/0.54 p8(c14, c12)
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 p8(c11, c14)
% 0.20/0.54
% 0.20/0.54 Lemma 22: fresh17(X, X, Y, Z) = p8(c11, c14).
% 0.20/0.54 Proof:
% 0.20/0.54 fresh17(X, X, Y, Z)
% 0.20/0.54 = { by axiom 6 (p10_7) }
% 0.20/0.54 true2
% 0.20/0.54 = { by axiom 1 (p8_3) R->L }
% 0.20/0.54 p8(c14, c12)
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 p8(c11, c14)
% 0.20/0.54
% 0.20/0.54 Lemma 23: fresh15(X, X, Y, Z) = p8(c11, c14).
% 0.20/0.54 Proof:
% 0.20/0.54 fresh15(X, X, Y, Z)
% 0.20/0.54 = { by axiom 7 (p2_10) }
% 0.20/0.54 true2
% 0.20/0.54 = { by axiom 1 (p8_3) R->L }
% 0.20/0.54 p8(c14, c12)
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 p8(c11, c14)
% 0.20/0.54
% 0.20/0.54 Lemma 24: fresh17(p8(X, Y), p8(c11, c14), X, Y) = p10(X, Y).
% 0.20/0.54 Proof:
% 0.20/0.54 fresh17(p8(X, Y), p8(c11, c14), X, Y)
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 fresh17(p8(X, Y), p8(c14, c12), X, Y)
% 0.20/0.54 = { by axiom 1 (p8_3) }
% 0.20/0.54 fresh17(p8(X, Y), true2, X, Y)
% 0.20/0.54 = { by axiom 12 (p10_7) }
% 0.20/0.54 p10(X, Y)
% 0.20/0.54
% 0.20/0.54 Lemma 25: fresh16(p2(X, Y), p8(c11, c14), Z, Y, X) = fresh15(p2(X, Z), p8(c11, c14), Z, Y).
% 0.20/0.54 Proof:
% 0.20/0.54 fresh16(p2(X, Y), p8(c11, c14), Z, Y, X)
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 fresh16(p2(X, Y), p8(c14, c12), Z, Y, X)
% 0.20/0.54 = { by axiom 1 (p8_3) }
% 0.20/0.54 fresh16(p2(X, Y), true2, Z, Y, X)
% 0.20/0.54 = { by axiom 16 (p2_10) }
% 0.20/0.54 fresh15(p2(X, Z), true2, Z, Y)
% 0.20/0.54 = { by axiom 1 (p8_3) R->L }
% 0.20/0.54 fresh15(p2(X, Z), p8(c14, c12), Z, Y)
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 fresh15(p2(X, Z), p8(c11, c14), Z, Y)
% 0.20/0.54
% 0.20/0.54 Lemma 26: fresh15(p2(X, Y), p8(c11, c14), Y, X) = p2(Y, X).
% 0.20/0.54 Proof:
% 0.20/0.54 fresh15(p2(X, Y), p8(c11, c14), Y, X)
% 0.20/0.54 = { by lemma 25 R->L }
% 0.20/0.54 fresh16(p2(X, X), p8(c11, c14), Y, X, X)
% 0.20/0.54 = { by lemma 21 }
% 0.20/0.54 fresh16(p8(c11, c14), p8(c11, c14), Y, X, X)
% 0.20/0.54 = { by axiom 10 (p2_10) }
% 0.20/0.54 p2(Y, X)
% 0.20/0.54
% 0.20/0.54 Goal 1 (not_p8_20): tuple(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X))), p8(X, c12), p8(c11, X)) = tuple(true2, true2, true2).
% 0.20/0.54 The goal is true when:
% 0.20/0.54 X = c14
% 0.20/0.54
% 0.20/0.54 Proof:
% 0.20/0.54 tuple(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.54 = { by lemma 26 R->L }
% 0.20/0.54 tuple(fresh15(p2(f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.54 = { by axiom 10 (p2_10) R->L }
% 0.20/0.54 tuple(fresh15(fresh16(p8(c11, c14), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.54 = { by lemma 23 R->L }
% 0.20/0.54 tuple(fresh15(fresh16(fresh15(p8(c11, c14), p8(c11, c14), f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 tuple(fresh15(fresh16(fresh15(p8(c14, c12), p8(c11, c14), f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.54 = { by axiom 1 (p8_3) }
% 0.20/0.54 tuple(fresh15(fresh16(fresh15(true2, p8(c11, c14), f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.54 = { by axiom 19 (p2_15) R->L }
% 0.20/0.54 tuple(fresh15(fresh16(fresh15(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), p8(c11, c14), f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 26 }
% 0.20/0.55 tuple(fresh15(fresh16(p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 25 }
% 0.20/0.55 tuple(fresh15(fresh15(p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 26 R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(p2(f4(f5(c12, c11), f3(c14)), f4(f5(c12, c11), c15)), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 15 (p2_16) R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(p8(c11, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 20 }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(p8(c14, c12), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 1 (p8_3) }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(true2, p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 8 (p2_11) R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(p8(c11, c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 20 }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(p8(c14, c12), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 1 (p8_3) }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(true2, p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 4 (p9_12) R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh(p8(c11, c14), p8(c11, c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 22 R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh(fresh17(p8(c11, c14), p8(c11, c14), c14, c12), p8(c11, c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 20 }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh(fresh17(p8(c14, c12), p8(c11, c14), c14, c12), p8(c11, c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 24 }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh(p10(c14, c12), p8(c11, c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 20 }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh(p10(c14, c12), p8(c14, c12), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 1 (p8_3) }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh(p10(c14, c12), true2, c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 11 (p9_12) R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh2(p10(c11, c14), true2, c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by axiom 1 (p8_3) R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh2(p10(c11, c14), p8(c14, c12), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 20 R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh2(p10(c11, c14), p8(c11, c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 24 R->L }
% 0.20/0.55 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh2(fresh17(p8(c11, c14), p8(c11, c14), c11, c14), p8(c11, c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.55 = { by lemma 22 }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(fresh2(p8(c11, c14), p8(c11, c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 9 (p9_12) }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(p9(c13, f3(c14), c14), p8(c11, c14), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(p9(c13, f3(c14), c14), p8(c14, c12), f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 1 (p8_3) }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh13(p9(c13, f3(c14), c14), true2, f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 18 (p2_11) R->L }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh14(p9(c13, c15, c14), true2, f3(c14), c15, c13, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 1 (p8_3) R->L }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh14(p9(c13, c15, c14), p8(c14, c12), f3(c14), c15, c13, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh14(p9(c13, c15, c14), p8(c11, c14), f3(c14), c15, c13, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 5 (p9_6) }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh14(true2, p8(c11, c14), f3(c14), c15, c13, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 1 (p8_3) R->L }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh14(p8(c14, c12), p8(c11, c14), f3(c14), c15, c13, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(fresh14(p8(c11, c14), p8(c11, c14), f3(c14), c15, c13, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 13 (p2_11) }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(p2(f3(c14), c15), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(p2(f3(c14), c15), p8(c14, c12), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 1 (p8_3) }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh12(p2(f3(c14), c15), true2, f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 17 (p2_16) }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh11(p2(f5(c12, c11), f5(c12, c11)), true2, f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 1 (p8_3) R->L }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh11(p2(f5(c12, c11), f5(c12, c11)), p8(c14, c12), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh11(p2(f5(c12, c11), f5(c12, c11)), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by lemma 21 }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(fresh11(p8(c11, c14), p8(c11, c14), f5(c12, c11), f3(c14), f5(c12, c11), c15), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 14 (p2_16) }
% 0.20/0.56 tuple(fresh15(fresh15(fresh15(true2, p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.56 = { by axiom 1 (p8_3) R->L }
% 0.20/0.57 tuple(fresh15(fresh15(fresh15(p8(c14, c12), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.57 = { by lemma 20 R->L }
% 0.20/0.57 tuple(fresh15(fresh15(fresh15(p8(c11, c14), p8(c11, c14), f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.57 = { by lemma 23 }
% 0.20/0.57 tuple(fresh15(fresh15(p8(c11, c14), p8(c11, c14), f4(f5(c12, c11), f3(c14)), f5(f7(c13, c12), f7(c13, c11))), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.57 = { by lemma 23 }
% 0.20/0.57 tuple(fresh15(p8(c11, c14), p8(c11, c14), f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))), p8(c14, c12), p8(c11, c14))
% 0.20/0.57 = { by lemma 23 }
% 0.20/0.57 tuple(p8(c11, c14), p8(c14, c12), p8(c11, c14))
% 0.20/0.57 = { by lemma 20 R->L }
% 0.20/0.57 tuple(p8(c11, c14), p8(c11, c14), p8(c11, c14))
% 0.20/0.57 = { by lemma 20 }
% 0.20/0.57 tuple(p8(c14, c12), p8(c11, c14), p8(c11, c14))
% 0.20/0.57 = { by lemma 20 }
% 0.20/0.57 tuple(p8(c14, c12), p8(c14, c12), p8(c11, c14))
% 0.20/0.57 = { by lemma 20 }
% 0.20/0.57 tuple(p8(c14, c12), p8(c14, c12), p8(c14, c12))
% 0.20/0.57 = { by axiom 1 (p8_3) }
% 0.20/0.57 tuple(true2, p8(c14, c12), p8(c14, c12))
% 0.20/0.57 = { by axiom 1 (p8_3) }
% 0.20/0.57 tuple(true2, true2, p8(c14, c12))
% 0.20/0.57 = { by axiom 1 (p8_3) }
% 0.20/0.57 tuple(true2, true2, true2)
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------