TSTP Solution File: SYN661-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN661-1 : 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 : n023.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 03:35:36 EDT 2023
% Result : Unsatisfiable 1.83s 0.62s
% Output : Proof 2.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN661-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 19:06:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.83/0.62 Command-line arguments: --flatten
% 1.83/0.62
% 1.83/0.62 % SZS status Unsatisfiable
% 1.83/0.62
% 2.21/0.64 % SZS output start Proof
% 2.21/0.64 Take the following subset of the input axioms:
% 2.21/0.64 fof(c28_is_p22_1, negated_conjecture, p22(c28)).
% 2.21/0.64 fof(not_p2_19, negated_conjecture, ![X96]: ~p2(X96, f16(X96, f9(f17(c31))))).
% 2.21/0.64 fof(p10_11, negated_conjecture, p10(c37, c34)).
% 2.21/0.64 fof(p25_12, negated_conjecture, p25(c36, c33)).
% 2.21/0.64 fof(p25_13, negated_conjecture, p25(c32, c36)).
% 2.21/0.64 fof(p2_30, negated_conjecture, ![X35, X36, X37]: (p2(X36, X37) | (~p2(X35, X36) | ~p2(X35, X37)))).
% 2.21/0.64 fof(p2_40, negated_conjecture, p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))).
% 2.21/0.64 fof(p2_49, negated_conjecture, ![X42]: (p2(f11(f4(X42), c34), f11(f4(c32), c34)) | (~p25(X42, c33) | ~p25(c32, X42)))).
% 2.21/0.64 fof(p2_6, negated_conjecture, ![X35_2]: p2(X35_2, X35_2)).
% 2.21/0.64
% 2.21/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.21/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.21/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.21/0.64 fresh(y, y, x1...xn) = u
% 2.21/0.64 C => fresh(s, t, x1...xn) = v
% 2.21/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 2.21/0.64 variables of u and v.
% 2.21/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.21/0.64 input problem has no model of domain size 1).
% 2.21/0.64
% 2.21/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 2.21/0.64
% 2.21/0.64 Axiom 1 (c28_is_p22_1): p22(c28) = true2.
% 2.21/0.64 Axiom 2 (p10_11): p10(c37, c34) = true2.
% 2.21/0.64 Axiom 3 (p25_13): p25(c32, c36) = true2.
% 2.21/0.64 Axiom 4 (p25_12): p25(c36, c33) = true2.
% 2.21/0.64 Axiom 5 (p2_6): p2(X, X) = true2.
% 2.21/0.64 Axiom 6 (p2_49): fresh51(X, X, Y) = true2.
% 2.21/0.64 Axiom 7 (p2_30): fresh15(X, X, Y, Z) = true2.
% 2.21/0.64 Axiom 8 (p2_49): fresh50(X, X, Y) = fresh51(p25(Y, c33), true2, Y).
% 2.21/0.64 Axiom 9 (p2_30): fresh16(X, X, Y, Z, W) = p2(Y, Z).
% 2.21/0.64 Axiom 10 (p2_30): fresh16(p2(X, Y), true2, Z, Y, X) = fresh15(p2(X, Z), true2, Z, Y).
% 2.21/0.64 Axiom 11 (p2_49): fresh50(p25(c32, X), true2, X) = p2(f11(f4(X), c34), f11(f4(c32), c34)).
% 2.21/0.64 Axiom 12 (p2_40): p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) = true2.
% 2.21/0.64
% 2.21/0.64 Lemma 13: p10(c37, c34) = p22(c28).
% 2.21/0.64 Proof:
% 2.21/0.64 p10(c37, c34)
% 2.21/0.64 = { by axiom 2 (p10_11) }
% 2.21/0.64 true2
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 p22(c28)
% 2.21/0.65
% 2.21/0.65 Lemma 14: fresh15(X, X, Y, Z) = p10(c37, c34).
% 2.21/0.65 Proof:
% 2.21/0.65 fresh15(X, X, Y, Z)
% 2.21/0.65 = { by axiom 7 (p2_30) }
% 2.21/0.65 true2
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 p22(c28)
% 2.21/0.65 = { by lemma 13 R->L }
% 2.21/0.65 p10(c37, c34)
% 2.21/0.65
% 2.21/0.65 Lemma 15: fresh16(p2(X, Y), p10(c37, c34), Z, Y, X) = fresh15(p2(X, Z), p10(c37, c34), Z, Y).
% 2.21/0.65 Proof:
% 2.21/0.65 fresh16(p2(X, Y), p10(c37, c34), Z, Y, X)
% 2.21/0.65 = { by lemma 13 }
% 2.21/0.65 fresh16(p2(X, Y), p22(c28), Z, Y, X)
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) }
% 2.21/0.65 fresh16(p2(X, Y), true2, Z, Y, X)
% 2.21/0.65 = { by axiom 10 (p2_30) }
% 2.21/0.65 fresh15(p2(X, Z), true2, Z, Y)
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 fresh15(p2(X, Z), p22(c28), Z, Y)
% 2.21/0.65 = { by lemma 13 R->L }
% 2.21/0.65 fresh15(p2(X, Z), p10(c37, c34), Z, Y)
% 2.21/0.65
% 2.21/0.65 Goal 1 (not_p2_19): p2(X, f16(X, f9(f17(c31)))) = true2.
% 2.21/0.65 The goal is true when:
% 2.21/0.65 X = f11(f4(c36), c34)
% 2.21/0.65
% 2.21/0.65 Proof:
% 2.21/0.65 p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 9 (p2_30) R->L }
% 2.21/0.65 fresh16(p10(c37, c34), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))), f11(f4(c32), c34))
% 2.21/0.65 = { by lemma 13 }
% 2.21/0.65 fresh16(p22(c28), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))), f11(f4(c32), c34))
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) }
% 2.21/0.65 fresh16(true2, p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))), f11(f4(c32), c34))
% 2.21/0.65 = { by axiom 12 (p2_40) R->L }
% 2.21/0.65 fresh16(p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31)))), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))), f11(f4(c32), c34))
% 2.21/0.65 = { by lemma 15 }
% 2.21/0.65 fresh15(p2(f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 9 (p2_30) R->L }
% 2.21/0.65 fresh15(fresh16(p10(c37, c34), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 13 }
% 2.21/0.65 fresh15(fresh16(p22(c28), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) }
% 2.21/0.65 fresh15(fresh16(true2, p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 5 (p2_6) R->L }
% 2.21/0.65 fresh15(fresh16(p2(f11(f4(c36), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 15 }
% 2.21/0.65 fresh15(fresh15(p2(f11(f4(c36), c34), f11(f4(c32), c34)), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 11 (p2_49) R->L }
% 2.21/0.65 fresh15(fresh15(fresh50(p25(c32, c36), true2, c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 fresh15(fresh15(fresh50(p25(c32, c36), p22(c28), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 13 R->L }
% 2.21/0.65 fresh15(fresh15(fresh50(p25(c32, c36), p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 3 (p25_13) }
% 2.21/0.65 fresh15(fresh15(fresh50(true2, p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 fresh15(fresh15(fresh50(p22(c28), p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 13 R->L }
% 2.21/0.65 fresh15(fresh15(fresh50(p10(c37, c34), p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 8 (p2_49) }
% 2.21/0.65 fresh15(fresh15(fresh51(p25(c36, c33), true2, c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 fresh15(fresh15(fresh51(p25(c36, c33), p22(c28), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 13 R->L }
% 2.21/0.65 fresh15(fresh15(fresh51(p25(c36, c33), p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 4 (p25_12) }
% 2.21/0.65 fresh15(fresh15(fresh51(true2, p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 fresh15(fresh15(fresh51(p22(c28), p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 13 R->L }
% 2.21/0.65 fresh15(fresh15(fresh51(p10(c37, c34), p10(c37, c34), c36), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 6 (p2_49) }
% 2.21/0.65 fresh15(fresh15(true2, p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) R->L }
% 2.21/0.65 fresh15(fresh15(p22(c28), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 13 R->L }
% 2.21/0.65 fresh15(fresh15(p10(c37, c34), p10(c37, c34), f11(f4(c32), c34), f11(f4(c36), c34)), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 14 }
% 2.21/0.65 fresh15(p10(c37, c34), p10(c37, c34), f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))
% 2.21/0.65 = { by lemma 14 }
% 2.21/0.65 p10(c37, c34)
% 2.21/0.65 = { by lemma 13 }
% 2.21/0.65 p22(c28)
% 2.21/0.65 = { by axiom 1 (c28_is_p22_1) }
% 2.21/0.65 true2
% 2.21/0.65 % SZS output end Proof
% 2.21/0.65
% 2.21/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------