TSTP Solution File: SYN655-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN655-1 : 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 : n009.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 3.26s 0.80s
% Output : Proof 3.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN655-1 : TPTP v8.1.2. Released v2.5.0.
% 0.06/0.13 % 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 : n009.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 19:13:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 3.26/0.80 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 3.26/0.80
% 3.26/0.80 % SZS status Unsatisfiable
% 3.26/0.80
% 3.26/0.81 % SZS output start Proof
% 3.26/0.81 Take the following subset of the input axioms:
% 3.61/0.81 fof(not_p9_10, negated_conjecture, ~p9(c22, c23)).
% 3.61/0.81 fof(p21_27, negated_conjecture, p21(f11(c24, c25, c26, c27, c22, c28), f11(c29, c30, c31, c32, c23, c33))).
% 3.61/0.81 fof(p3_48, negated_conjecture, ![X43, X37, X38, X39, X40, X41, X36, X42]: (p3(X41, f11(f19(X37, X38, X39, X40, X41, X36, X42, X43), f18(X37, X38, X39, X40, X41, X36, X42, X43), f17(X37, X38, X39, X40, X41, X36, X42, X43), f16(X37, X38, X39, X40, X41, X36, X42, X43), f15(X37, X38, X39, X40, X41, X36, X42, X43), f14(X37, X38, X39, X40, X41, X36, X42, X43))) | ~p21(f11(X38, X39, X36, X42, X43, X40), X41))).
% 3.61/0.81 fof(p9_17, negated_conjecture, ![X177, X178, X179]: (p9(X178, X179) | (~p9(X177, X178) | ~p9(X177, X179)))).
% 3.61/0.81 fof(p9_2, negated_conjecture, ![X177_2]: p9(X177_2, X177_2)).
% 3.61/0.81 fof(p9_30, negated_conjecture, ![X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14]: (p9(X9, X14) | ~p3(f11(X5, X6, X7, X8, X9, X3), f11(X10, X11, X12, X13, X14, X4)))).
% 3.61/0.81 fof(p9_35, negated_conjecture, ![X43_2, X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2]: (p9(X43_2, f15(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))).
% 3.61/0.81
% 3.61/0.81 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.61/0.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.61/0.81 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.61/0.81 fresh(y, y, x1...xn) = u
% 3.61/0.81 C => fresh(s, t, x1...xn) = v
% 3.61/0.81 where fresh is a fresh function symbol and x1..xn are the free
% 3.61/0.81 variables of u and v.
% 3.61/0.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.61/0.81 input problem has no model of domain size 1).
% 3.61/0.81
% 3.61/0.81 The encoding turns the above axioms into the following unit equations and goals:
% 3.61/0.81
% 3.61/0.81 Axiom 1 (p9_2): p9(X, X) = true2.
% 3.61/0.81 Axiom 2 (p9_17): fresh3(X, X, Y, Z) = true2.
% 3.61/0.81 Axiom 3 (p9_30): fresh2(X, X, Y, Z) = true2.
% 3.61/0.81 Axiom 4 (p9_17): fresh4(X, X, Y, Z, W) = p9(Y, Z).
% 3.61/0.81 Axiom 5 (p9_17): fresh4(p9(X, Y), true2, Z, Y, X) = fresh3(p9(X, Z), true2, Z, Y).
% 3.61/0.81 Axiom 6 (p9_35): fresh(X, X, Y, Z, W, V, U, T, S, X2) = true2.
% 3.61/0.81 Axiom 7 (p3_48): fresh18(X, X, Y, Z, W, V, U, T, S, X2) = true2.
% 3.61/0.81 Axiom 8 (p21_27): p21(f11(c24, c25, c26, c27, c22, c28), f11(c29, c30, c31, c32, c23, c33)) = true2.
% 3.61/0.81 Axiom 9 (p9_35): fresh(p21(f11(X, Y, Z, W, V, U), T), true2, V, S, X, Y, U, T, Z, W) = p9(V, f15(S, X, Y, U, T, Z, W, V)).
% 3.61/0.81 Axiom 10 (p9_30): fresh2(p3(f11(X, Y, Z, W, V, U), f11(T, S, X2, Y2, Z2, W2)), true2, V, Z2) = p9(V, Z2).
% 3.61/0.81 Axiom 11 (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))).
% 3.61/0.81
% 3.61/0.81 Lemma 12: fresh3(p9(X, Y), true2, Y, X) = p9(Y, X).
% 3.61/0.81 Proof:
% 3.61/0.81 fresh3(p9(X, Y), true2, Y, X)
% 3.61/0.81 = { by axiom 5 (p9_17) R->L }
% 3.61/0.81 fresh4(p9(X, X), true2, Y, X, X)
% 3.61/0.81 = { by axiom 1 (p9_2) }
% 3.61/0.81 fresh4(true2, true2, Y, X, X)
% 3.61/0.81 = { by axiom 4 (p9_17) }
% 3.61/0.81 p9(Y, X)
% 3.61/0.81
% 3.61/0.81 Goal 1 (not_p9_10): p9(c22, c23) = true2.
% 3.61/0.81 Proof:
% 3.61/0.81 p9(c22, c23)
% 3.61/0.81 = { by lemma 12 R->L }
% 3.61/0.81 fresh3(p9(c23, c22), true2, c22, c23)
% 3.61/0.81 = { by axiom 4 (p9_17) R->L }
% 3.61/0.81 fresh3(fresh4(true2, true2, c23, c22, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, c22, c23)
% 3.61/0.81 = { by axiom 2 (p9_17) R->L }
% 3.61/0.81 fresh3(fresh4(fresh3(true2, true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c22), true2, c23, c22, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, c22, c23)
% 3.61/0.81 = { by axiom 6 (p9_35) R->L }
% 3.61/0.81 fresh3(fresh4(fresh3(fresh(true2, true2, c22, X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c22), true2, c23, c22, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, c22, c23)
% 3.61/0.81 = { by axiom 8 (p21_27) R->L }
% 3.61/0.82 fresh3(fresh4(fresh3(fresh(p21(f11(c24, c25, c26, c27, c22, c28), f11(c29, c30, c31, c32, c23, c33)), true2, c22, X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c22), true2, c23, c22, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, c22, c23)
% 3.61/0.82 = { by axiom 9 (p9_35) }
% 3.61/0.82 fresh3(fresh4(fresh3(p9(c22, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c22), true2, c23, c22, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, c22, c23)
% 3.61/0.82 = { by lemma 12 }
% 3.61/0.82 fresh3(fresh4(p9(f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c22), true2, c23, c22, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, c22, c23)
% 3.61/0.82 = { by axiom 5 (p9_17) }
% 3.61/0.82 fresh3(fresh3(p9(f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c23), true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by lemma 12 R->L }
% 3.61/0.82 fresh3(fresh3(fresh3(p9(c23, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c23), true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by axiom 10 (p9_30) R->L }
% 3.61/0.82 fresh3(fresh3(fresh3(fresh2(p3(f11(c29, c30, c31, c32, c23, c33), f11(f19(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), f18(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), f17(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), f16(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), f14(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22))), true2, c23, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c23), true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by axiom 11 (p3_48) R->L }
% 3.61/0.82 fresh3(fresh3(fresh3(fresh2(fresh18(p21(f11(c24, c25, c26, c27, c22, c28), f11(c29, c30, c31, c32, c23, c33)), true2, f11(c29, c30, c31, c32, c23, c33), X, c24, c25, c28, c26, c27, c22), true2, c23, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c23), true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by axiom 8 (p21_27) }
% 3.61/0.82 fresh3(fresh3(fresh3(fresh2(fresh18(true2, true2, f11(c29, c30, c31, c32, c23, c33), X, c24, c25, c28, c26, c27, c22), true2, c23, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c23), true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by axiom 7 (p3_48) }
% 3.61/0.82 fresh3(fresh3(fresh3(fresh2(true2, true2, c23, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22)), true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c23), true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by axiom 3 (p9_30) }
% 3.61/0.82 fresh3(fresh3(fresh3(true2, true2, f15(X, c24, c25, c28, f11(c29, c30, c31, c32, c23, c33), c26, c27, c22), c23), true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by axiom 2 (p9_17) }
% 3.61/0.82 fresh3(fresh3(true2, true2, c23, c22), true2, c22, c23)
% 3.61/0.82 = { by axiom 2 (p9_17) }
% 3.61/0.82 fresh3(true2, true2, c22, c23)
% 3.61/0.82 = { by axiom 2 (p9_17) }
% 3.61/0.82 true2
% 3.61/0.82 % SZS output end Proof
% 3.61/0.82
% 3.61/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------