TSTP Solution File: SYN701-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN701-1 : 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 : n026.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 03:35:46 EDT 2023
% Result : Unsatisfiable 4.06s 0.93s
% Output : Proof 4.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN701-1 : 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
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 17:56:48 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.06/0.93 Command-line arguments: --flatten
% 4.06/0.93
% 4.06/0.93 % SZS status Unsatisfiable
% 4.06/0.93
% 4.24/0.94 % SZS output start Proof
% 4.24/0.94 Take the following subset of the input axioms:
% 4.24/0.94 fof(c34_is_p25_1, negated_conjecture, p25(c34)).
% 4.24/0.94 fof(not_p2_56, negated_conjecture, ~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))).
% 4.24/0.94 fof(p10_7, negated_conjecture, ![X5]: p10(X5, X5)).
% 4.24/0.94 fof(p2_12, negated_conjecture, ![X43]: p2(X43, X43)).
% 4.24/0.94 fof(p2_16, negated_conjecture, p2(c44, c46)).
% 4.24/0.94 fof(p2_42, negated_conjecture, ![X44, X45, X43_2]: (p2(X44, X45) | (~p2(X43_2, X44) | ~p2(X43_2, X45)))).
% 4.24/0.94 fof(p2_55, negated_conjecture, p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))).
% 4.24/0.94 fof(p2_62, negated_conjecture, ![X46, X47, X48, X49]: (p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49) | ~p3(X46, X48)))).
% 4.24/0.94 fof(p3_31, negated_conjecture, ![X91, X92]: (p3(f4(X91), f4(X92)) | ~p2(X91, X92))).
% 4.24/0.94
% 4.24/0.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.24/0.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.24/0.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.24/0.94 fresh(y, y, x1...xn) = u
% 4.24/0.94 C => fresh(s, t, x1...xn) = v
% 4.24/0.94 where fresh is a fresh function symbol and x1..xn are the free
% 4.24/0.94 variables of u and v.
% 4.24/0.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.24/0.94 input problem has no model of domain size 1).
% 4.24/0.94
% 4.24/0.94 The encoding turns the above axioms into the following unit equations and goals:
% 4.24/0.94
% 4.24/0.94 Axiom 1 (c34_is_p25_1): p25(c34) = true2.
% 4.24/0.94 Axiom 2 (p10_7): p10(X, X) = true2.
% 4.24/0.94 Axiom 3 (p2_12): p2(X, X) = true2.
% 4.24/0.94 Axiom 4 (p2_16): p2(c44, c46) = true2.
% 4.24/0.94 Axiom 5 (p2_42): fresh27(X, X, Y, Z) = true2.
% 4.24/0.94 Axiom 6 (p3_31): fresh8(X, X, Y, Z) = true2.
% 4.24/0.94 Axiom 7 (p2_42): fresh28(X, X, Y, Z, W) = p2(Y, Z).
% 4.24/0.94 Axiom 8 (p2_62): fresh21(X, X, Y, Z, W, V) = true2.
% 4.24/0.94 Axiom 9 (p3_31): fresh8(p2(X, Y), true2, X, Y) = p3(f4(X), f4(Y)).
% 4.24/0.94 Axiom 10 (p2_62): fresh22(X, X, Y, Z, W, V) = p2(f11(Y, Z), f11(W, V)).
% 4.24/0.94 Axiom 11 (p2_42): fresh28(p2(X, Y), true2, Z, Y, X) = fresh27(p2(X, Z), true2, Z, Y).
% 4.24/0.94 Axiom 12 (p2_62): fresh22(p3(X, Y), true2, X, Z, Y, W) = fresh21(p10(Z, W), true2, X, Z, Y, W).
% 4.24/0.94 Axiom 13 (p2_55): p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43)) = true2.
% 4.24/0.94
% 4.24/0.94 Lemma 14: fresh27(X, X, Y, Z) = p25(c34).
% 4.24/0.94 Proof:
% 4.24/0.94 fresh27(X, X, Y, Z)
% 4.24/0.94 = { by axiom 5 (p2_42) }
% 4.24/0.94 true2
% 4.24/0.94 = { by axiom 1 (c34_is_p25_1) R->L }
% 4.24/0.94 p25(c34)
% 4.24/0.94
% 4.24/0.94 Lemma 15: fresh28(p2(X, Y), p25(c34), Z, Y, X) = fresh27(p2(X, Z), p25(c34), Z, Y).
% 4.24/0.94 Proof:
% 4.24/0.94 fresh28(p2(X, Y), p25(c34), Z, Y, X)
% 4.24/0.94 = { by axiom 1 (c34_is_p25_1) }
% 4.24/0.94 fresh28(p2(X, Y), true2, Z, Y, X)
% 4.24/0.94 = { by axiom 11 (p2_42) }
% 4.24/0.94 fresh27(p2(X, Z), true2, Z, Y)
% 4.24/0.94 = { by axiom 1 (c34_is_p25_1) R->L }
% 4.24/0.94 fresh27(p2(X, Z), p25(c34), Z, Y)
% 4.24/0.94
% 4.24/0.94 Goal 1 (not_p2_56): p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) = true2.
% 4.24/0.94 Proof:
% 4.24/0.94 p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.94 = { by axiom 7 (p2_42) R->L }
% 4.24/0.94 fresh28(p25(c34), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by lemma 14 R->L }
% 4.24/0.95 fresh28(fresh27(p25(c34), p25(c34), f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) }
% 4.24/0.95 fresh28(fresh27(true2, p25(c34), f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by axiom 13 (p2_55) R->L }
% 4.24/0.95 fresh28(fresh27(p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43)), p25(c34), f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by lemma 15 R->L }
% 4.24/0.95 fresh28(fresh28(p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by axiom 3 (p2_12) }
% 4.24/0.95 fresh28(fresh28(true2, p25(c34), f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) R->L }
% 4.24/0.95 fresh28(fresh28(p25(c34), p25(c34), f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by axiom 7 (p2_42) }
% 4.24/0.95 fresh28(p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))
% 4.24/0.95 = { by lemma 15 }
% 4.24/0.95 fresh27(p2(f11(f4(c44), c43), f11(f4(c46), c43)), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 10 (p2_62) R->L }
% 4.24/0.95 fresh27(fresh22(p25(c34), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) }
% 4.24/0.95 fresh27(fresh22(true2, p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 6 (p3_31) R->L }
% 4.24/0.95 fresh27(fresh22(fresh8(p25(c34), p25(c34), c44, c46), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) }
% 4.24/0.95 fresh27(fresh22(fresh8(true2, p25(c34), c44, c46), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 4 (p2_16) R->L }
% 4.24/0.95 fresh27(fresh22(fresh8(p2(c44, c46), p25(c34), c44, c46), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) }
% 4.24/0.95 fresh27(fresh22(fresh8(p2(c44, c46), true2, c44, c46), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 9 (p3_31) }
% 4.24/0.95 fresh27(fresh22(p3(f4(c44), f4(c46)), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) }
% 4.24/0.95 fresh27(fresh22(p3(f4(c44), f4(c46)), true2, f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 12 (p2_62) }
% 4.24/0.95 fresh27(fresh21(p10(c43, c43), true2, f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) R->L }
% 4.24/0.95 fresh27(fresh21(p10(c43, c43), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 2 (p10_7) }
% 4.24/0.95 fresh27(fresh21(true2, p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) R->L }
% 4.24/0.95 fresh27(fresh21(p25(c34), p25(c34), f4(c44), c43, f4(c46), c43), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 8 (p2_62) }
% 4.24/0.95 fresh27(true2, p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) R->L }
% 4.24/0.95 fresh27(p25(c34), p25(c34), f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))
% 4.24/0.95 = { by lemma 14 }
% 4.24/0.95 p25(c34)
% 4.24/0.95 = { by axiom 1 (c34_is_p25_1) }
% 4.24/0.95 true2
% 4.24/0.95 % SZS output end Proof
% 4.24/0.95
% 4.24/0.95 RESULT: Unsatisfiable (the axioms are contradictory).
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