TSTP Solution File: SYN653-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN653-1 : 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 : n010.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 03:35:35 EDT 2023
% Result : Unsatisfiable 3.46s 0.81s
% Output : Proof 3.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN653-1 : 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
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 19:20:19 EDT 2023
% 0.12/0.34 % CPUTime :
% 3.46/0.81 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 3.46/0.81
% 3.46/0.81 % SZS status Unsatisfiable
% 3.46/0.81
% 3.46/0.82 % SZS output start Proof
% 3.46/0.82 Take the following subset of the input axioms:
% 3.46/0.82 fof(not_p12_10, negated_conjecture, ~p12(f13(c22), f13(c23))).
% 3.46/0.82 fof(p12_13, negated_conjecture, ![X34, X35]: (p12(f13(X34), f13(X35)) | ~p7(X34, X35))).
% 3.46/0.82 fof(p12_24, negated_conjecture, ![X31, X32, X33]: (p12(X32, X33) | (~p12(X31, X32) | ~p12(X31, X33)))).
% 3.46/0.82 fof(p12_37, negated_conjecture, ![X43, X37, X38, X39, X40, X41, X36, X42]: (p12(f13(X36), f13(f17(X37, X38, X39, X40, X41, X36, X42, X43))) | ~p21(f11(X38, X39, X36, X42, X43, X40), X41))).
% 3.46/0.82 fof(p12_9, negated_conjecture, ![X31_2]: p12(X31_2, X31_2)).
% 3.46/0.82 fof(p21_27, negated_conjecture, p21(f11(c24, c25, c22, c26, c27, c28), f11(c29, c30, c23, c31, c32, c33))).
% 3.46/0.82 fof(p3_48, negated_conjecture, ![X43_2, X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2]: (p3(X41_2, f11(f19(X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2, X43_2), f18(X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2, X43_2), f17(X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2, X43_2), f16(X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2, X43_2), f15(X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2, X43_2), f14(X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2, X43_2))) | ~p21(f11(X38_2, X39_2, X36_2, X42_2, X43_2, X40_2), X41_2))).
% 3.46/0.82 fof(p7_19, negated_conjecture, ![X139, X140, X141]: (p7(X140, X141) | (~p7(X139, X140) | ~p7(X139, X141)))).
% 3.46/0.82 fof(p7_32, negated_conjecture, ![X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14]: (p7(X7, X12) | ~p3(f11(X5, X6, X7, X8, X9, X3), f11(X10, X11, X12, X13, X14, X4)))).
% 3.46/0.82 fof(p7_4, negated_conjecture, ![X139_2]: p7(X139_2, X139_2)).
% 3.46/0.82
% 3.46/0.82 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.46/0.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.46/0.82 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.46/0.82 fresh(y, y, x1...xn) = u
% 3.46/0.82 C => fresh(s, t, x1...xn) = v
% 3.46/0.82 where fresh is a fresh function symbol and x1..xn are the free
% 3.46/0.82 variables of u and v.
% 3.46/0.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.46/0.82 input problem has no model of domain size 1).
% 3.46/0.82
% 3.46/0.82 The encoding turns the above axioms into the following unit equations and goals:
% 3.46/0.82
% 3.46/0.82 Axiom 1 (p7_4): p7(X, X) = true2.
% 3.46/0.82 Axiom 2 (p12_9): p12(X, X) = true2.
% 3.46/0.82 Axiom 3 (p12_13): fresh32(X, X, Y, Z) = true2.
% 3.46/0.82 Axiom 4 (p12_24): fresh30(X, X, Y, Z) = true2.
% 3.46/0.82 Axiom 5 (p7_19): fresh10(X, X, Y, Z) = true2.
% 3.46/0.82 Axiom 6 (p7_32): fresh9(X, X, Y, Z) = true2.
% 3.46/0.82 Axiom 7 (p12_24): fresh31(X, X, Y, Z, W) = p12(Y, Z).
% 3.46/0.82 Axiom 8 (p7_19): fresh11(X, X, Y, Z, W) = p7(Y, Z).
% 3.46/0.82 Axiom 9 (p12_13): fresh32(p7(X, Y), true2, X, Y) = p12(f13(X), f13(Y)).
% 3.46/0.82 Axiom 10 (p12_24): fresh31(p12(X, Y), true2, Z, Y, X) = fresh30(p12(X, Z), true2, Z, Y).
% 3.46/0.82 Axiom 11 (p7_19): fresh11(p7(X, Y), true2, Z, Y, X) = fresh10(p7(X, Z), true2, Z, Y).
% 3.46/0.82 Axiom 12 (p12_37): fresh29(X, X, Y, Z, W, V, U, T, S, X2) = true2.
% 3.46/0.82 Axiom 13 (p3_48): fresh18(X, X, Y, Z, W, V, U, T, S, X2) = true2.
% 3.46/0.82 Axiom 14 (p21_27): p21(f11(c24, c25, c22, c26, c27, c28), f11(c29, c30, c23, c31, c32, c33)) = true2.
% 3.46/0.82 Axiom 15 (p12_37): fresh29(p21(f11(X, Y, Z, W, V, U), T), true2, Z, S, X, Y, U, T, W, V) = p12(f13(Z), f13(f17(S, X, Y, U, T, Z, W, V))).
% 3.46/0.82 Axiom 16 (p7_32): fresh9(p3(f11(X, Y, Z, W, V, U), f11(T, S, X2, Y2, Z2, W2)), true2, Z, X2) = p7(Z, X2).
% 3.46/0.82 Axiom 17 (p3_48): fresh18(p21(f11(X, Y, Z, W, V, U), T), true2, T, S, X, Y, U, Z, W, V) = p3(T, f11(f19(S, X, Y, U, T, Z, W, V), f18(S, X, Y, U, T, Z, W, V), f17(S, X, Y, U, T, Z, W, V), f16(S, X, Y, U, T, Z, W, V), f15(S, X, Y, U, T, Z, W, V), f14(S, X, Y, U, T, Z, W, V))).
% 3.46/0.82
% 3.46/0.82 Lemma 18: fresh30(p12(X, Y), true2, Y, X) = p12(Y, X).
% 3.46/0.82 Proof:
% 3.46/0.82 fresh30(p12(X, Y), true2, Y, X)
% 3.46/0.82 = { by axiom 10 (p12_24) R->L }
% 3.46/0.82 fresh31(p12(X, X), true2, Y, X, X)
% 3.46/0.82 = { by axiom 2 (p12_9) }
% 3.46/0.82 fresh31(true2, true2, Y, X, X)
% 3.46/0.82 = { by axiom 7 (p12_24) }
% 3.46/0.82 p12(Y, X)
% 3.46/0.82
% 3.46/0.82 Goal 1 (not_p12_10): p12(f13(c22), f13(c23)) = true2.
% 3.46/0.82 Proof:
% 3.46/0.82 p12(f13(c22), f13(c23))
% 3.46/0.82 = { by lemma 18 R->L }
% 3.46/0.82 fresh30(p12(f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 7 (p12_24) R->L }
% 3.46/0.82 fresh30(fresh31(true2, true2, f13(c23), f13(c22), f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 4 (p12_24) R->L }
% 3.46/0.82 fresh30(fresh31(fresh30(true2, true2, f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), f13(c22)), true2, f13(c23), f13(c22), f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 12 (p12_37) R->L }
% 3.46/0.82 fresh30(fresh31(fresh30(fresh29(true2, true2, c22, X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c26, c27), true2, f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), f13(c22)), true2, f13(c23), f13(c22), f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 14 (p21_27) R->L }
% 3.46/0.82 fresh30(fresh31(fresh30(fresh29(p21(f11(c24, c25, c22, c26, c27, c28), f11(c29, c30, c23, c31, c32, c33)), true2, c22, X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c26, c27), true2, f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), f13(c22)), true2, f13(c23), f13(c22), f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 15 (p12_37) }
% 3.46/0.82 fresh30(fresh31(fresh30(p12(f13(c22), f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), f13(c22)), true2, f13(c23), f13(c22), f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by lemma 18 }
% 3.46/0.82 fresh30(fresh31(p12(f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), f13(c22)), true2, f13(c23), f13(c22), f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 10 (p12_24) }
% 3.46/0.82 fresh30(fresh30(p12(f13(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), f13(c23)), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 9 (p12_13) R->L }
% 3.46/0.82 fresh30(fresh30(fresh32(p7(f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.82 = { by axiom 8 (p7_19) R->L }
% 3.46/0.82 fresh30(fresh30(fresh32(fresh11(true2, true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23, c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 1 (p7_4) R->L }
% 3.46/0.83 fresh30(fresh30(fresh32(fresh11(p7(c23, c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23, c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 11 (p7_19) }
% 3.46/0.83 fresh30(fresh30(fresh32(fresh10(p7(c23, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 16 (p7_32) R->L }
% 3.46/0.83 fresh30(fresh30(fresh32(fresh10(fresh9(p3(f11(c29, c30, c23, c31, c32, c33), f11(f19(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), f18(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), f16(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), f15(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), f14(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27))), true2, c23, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 17 (p3_48) R->L }
% 3.46/0.83 fresh30(fresh30(fresh32(fresh10(fresh9(fresh18(p21(f11(c24, c25, c22, c26, c27, c28), f11(c29, c30, c23, c31, c32, c33)), true2, f11(c29, c30, c23, c31, c32, c33), X, c24, c25, c28, c22, c26, c27), true2, c23, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 14 (p21_27) }
% 3.46/0.83 fresh30(fresh30(fresh32(fresh10(fresh9(fresh18(true2, true2, f11(c29, c30, c23, c31, c32, c33), X, c24, c25, c28, c22, c26, c27), true2, c23, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 13 (p3_48) }
% 3.46/0.83 fresh30(fresh30(fresh32(fresh10(fresh9(true2, true2, c23, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27)), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 6 (p7_32) }
% 3.46/0.83 fresh30(fresh30(fresh32(fresh10(true2, true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 5 (p7_19) }
% 3.46/0.83 fresh30(fresh30(fresh32(true2, true2, f17(X, c24, c25, c28, f11(c29, c30, c23, c31, c32, c33), c22, c26, c27), c23), true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 3 (p12_13) }
% 3.46/0.83 fresh30(fresh30(true2, true2, f13(c23), f13(c22)), true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 4 (p12_24) }
% 3.46/0.83 fresh30(true2, true2, f13(c22), f13(c23))
% 3.46/0.83 = { by axiom 4 (p12_24) }
% 3.46/0.83 true2
% 3.46/0.83 % SZS output end Proof
% 3.46/0.83
% 3.46/0.83 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------