TSTP Solution File: SYN651-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN651-1 : 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 : n001.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 03:35:34 EDT 2023
% Result : Unsatisfiable 0.19s 0.68s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN651-1 : 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
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 20:32:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.68 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.68
% 0.19/0.68 % SZS status Unsatisfiable
% 0.19/0.68
% 0.19/0.68 % SZS output start Proof
% 0.19/0.68 Take the following subset of the input axioms:
% 0.19/0.68 fof(not_p23_28, negated_conjecture, ~p23(f5(f7(f10(c24, f12(c25, f12(c25, c26))), c27), c28), c29)).
% 0.19/0.68 fof(p23_13, negated_conjecture, p23(f5(c27, c28), c30)).
% 0.19/0.69 fof(p23_26, negated_conjecture, p23(f5(f7(f10(c24, f12(c25, c26)), c27), c30), c29)).
% 0.19/0.69 fof(p23_41, negated_conjecture, ![X45, X46, X47, X48]: (p23(f5(X45, f14(f16(f18(f20(c31, X46), X47), X45), X48)), X48) | ~p23(f5(f7(f10(c24, f12(c25, X46)), X45), X47), X48))).
% 0.19/0.69 fof(p23_43, negated_conjecture, ![X51, X45_2, X46_2, X47_2, X48_2]: (p23(f5(f7(f10(c24, f12(c25, X46_2)), X45_2), X47_2), X48_2) | (~p23(f5(X45_2, X51), X48_2) | ~p23(f5(f7(f10(c24, X46_2), X45_2), X47_2), X51)))).
% 0.19/0.69 fof(p23_44, negated_conjecture, ![X49, X50, X52]: (p23(f5(f7(f10(c24, f12(c25, c26)), c27), X49), X50) | (~p23(f5(c27, X49), X52) | ~p23(f5(f7(f10(c24, c26), c27), X52), X50)))).
% 0.19/0.69 fof(p23_45, negated_conjecture, ![X45_2, X46_2, X47_2, X48_2]: (p23(f5(f7(f10(c24, X46_2), X45_2), X47_2), f14(f16(f18(f20(c31, X46_2), X47_2), X45_2), X48_2)) | ~p23(f5(f7(f10(c24, f12(c25, X46_2)), X45_2), X47_2), X48_2))).
% 0.19/0.69
% 0.19/0.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.69 fresh(y, y, x1...xn) = u
% 0.19/0.69 C => fresh(s, t, x1...xn) = v
% 0.19/0.69 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.69 variables of u and v.
% 0.19/0.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.69 input problem has no model of domain size 1).
% 0.19/0.69
% 0.19/0.69 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.69
% 0.19/0.69 Axiom 1 (p23_13): p23(f5(c27, c28), c30) = true.
% 0.19/0.69 Axiom 2 (p23_44): fresh53(X, X, Y, Z) = true.
% 0.19/0.69 Axiom 3 (p23_41): fresh28(X, X, Y, Z, W, V) = true.
% 0.19/0.69 Axiom 4 (p23_43): fresh25(X, X, Y, Z, W, V) = true.
% 0.19/0.69 Axiom 5 (p23_45): fresh24(X, X, Y, Z, W, V) = true.
% 0.19/0.69 Axiom 6 (p23_44): fresh52(X, X, Y, Z, W) = fresh53(p23(f5(c27, Y), W), true, Y, Z).
% 0.19/0.69 Axiom 7 (p23_43): fresh26(X, X, Y, Z, W, V, U) = p23(f5(f7(f10(c24, f12(c25, Y)), Z), W), V).
% 0.19/0.69 Axiom 8 (p23_26): p23(f5(f7(f10(c24, f12(c25, c26)), c27), c30), c29) = true.
% 0.19/0.69 Axiom 9 (p23_44): fresh52(p23(f5(f7(f10(c24, c26), c27), X), Y), true, Z, Y, X) = p23(f5(f7(f10(c24, f12(c25, c26)), c27), Z), Y).
% 0.19/0.69 Axiom 10 (p23_43): fresh26(p23(f5(f7(f10(c24, X), Y), Z), W), true, X, Y, Z, V, W) = fresh25(p23(f5(Y, W), V), true, X, Y, Z, V).
% 0.19/0.69 Axiom 11 (p23_41): fresh28(p23(f5(f7(f10(c24, f12(c25, X)), Y), Z), W), true, Y, X, Z, W) = p23(f5(Y, f14(f16(f18(f20(c31, X), Z), Y), W)), W).
% 0.19/0.69 Axiom 12 (p23_45): fresh24(p23(f5(f7(f10(c24, f12(c25, X)), Y), Z), W), true, X, Y, Z, W) = p23(f5(f7(f10(c24, X), Y), Z), f14(f16(f18(f20(c31, X), Z), Y), W)).
% 0.19/0.69
% 0.19/0.69 Lemma 13: fresh26(X, X, c26, c27, c30, c29, Y) = true.
% 0.19/0.69 Proof:
% 0.19/0.69 fresh26(X, X, c26, c27, c30, c29, Y)
% 0.19/0.69 = { by axiom 7 (p23_43) }
% 0.19/0.69 p23(f5(f7(f10(c24, f12(c25, c26)), c27), c30), c29)
% 0.19/0.69 = { by axiom 8 (p23_26) }
% 0.19/0.69 true
% 0.19/0.69
% 0.19/0.69 Goal 1 (not_p23_28): p23(f5(f7(f10(c24, f12(c25, f12(c25, c26))), c27), c28), c29) = true.
% 0.19/0.69 Proof:
% 0.19/0.69 p23(f5(f7(f10(c24, f12(c25, f12(c25, c26))), c27), c28), c29)
% 0.19/0.69 = { by axiom 7 (p23_43) R->L }
% 0.19/0.69 fresh26(true, true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 2 (p23_44) R->L }
% 0.19/0.69 fresh26(fresh53(true, true, c28, f14(f16(f18(f20(c31, c26), c30), c27), c29)), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 1 (p23_13) R->L }
% 0.19/0.69 fresh26(fresh53(p23(f5(c27, c28), c30), true, c28, f14(f16(f18(f20(c31, c26), c30), c27), c29)), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 6 (p23_44) R->L }
% 0.19/0.69 fresh26(fresh52(true, true, c28, f14(f16(f18(f20(c31, c26), c30), c27), c29), c30), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 5 (p23_45) R->L }
% 0.19/0.69 fresh26(fresh52(fresh24(true, true, c26, c27, c30, c29), true, c28, f14(f16(f18(f20(c31, c26), c30), c27), c29), c30), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by lemma 13 R->L }
% 0.19/0.69 fresh26(fresh52(fresh24(fresh26(X, X, c26, c27, c30, c29, Y), true, c26, c27, c30, c29), true, c28, f14(f16(f18(f20(c31, c26), c30), c27), c29), c30), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 7 (p23_43) }
% 0.19/0.69 fresh26(fresh52(fresh24(p23(f5(f7(f10(c24, f12(c25, c26)), c27), c30), c29), true, c26, c27, c30, c29), true, c28, f14(f16(f18(f20(c31, c26), c30), c27), c29), c30), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 12 (p23_45) }
% 0.19/0.69 fresh26(fresh52(p23(f5(f7(f10(c24, c26), c27), c30), f14(f16(f18(f20(c31, c26), c30), c27), c29)), true, c28, f14(f16(f18(f20(c31, c26), c30), c27), c29), c30), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 9 (p23_44) }
% 0.19/0.69 fresh26(p23(f5(f7(f10(c24, f12(c25, c26)), c27), c28), f14(f16(f18(f20(c31, c26), c30), c27), c29)), true, f12(c25, c26), c27, c28, c29, f14(f16(f18(f20(c31, c26), c30), c27), c29))
% 0.19/0.69 = { by axiom 10 (p23_43) }
% 0.19/0.69 fresh25(p23(f5(c27, f14(f16(f18(f20(c31, c26), c30), c27), c29)), c29), true, f12(c25, c26), c27, c28, c29)
% 0.19/0.69 = { by axiom 11 (p23_41) R->L }
% 0.19/0.69 fresh25(fresh28(p23(f5(f7(f10(c24, f12(c25, c26)), c27), c30), c29), true, c27, c26, c30, c29), true, f12(c25, c26), c27, c28, c29)
% 0.19/0.69 = { by axiom 7 (p23_43) R->L }
% 0.19/0.69 fresh25(fresh28(fresh26(Z, Z, c26, c27, c30, c29, W), true, c27, c26, c30, c29), true, f12(c25, c26), c27, c28, c29)
% 0.19/0.69 = { by lemma 13 }
% 0.19/0.69 fresh25(fresh28(true, true, c27, c26, c30, c29), true, f12(c25, c26), c27, c28, c29)
% 0.19/0.69 = { by axiom 3 (p23_41) }
% 0.19/0.69 fresh25(true, true, f12(c25, c26), c27, c28, c29)
% 0.19/0.69 = { by axiom 4 (p23_43) }
% 0.19/0.69 true
% 0.19/0.69 % SZS output end Proof
% 0.19/0.69
% 0.19/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
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