TSTP Solution File: SYN654-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN654-1 : 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 : n011.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 4.65s 0.96s
% Output : Proof 4.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN654-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.14 % 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 : n011.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 21:43:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.65/0.96 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 4.65/0.96
% 4.65/0.96 % SZS status Unsatisfiable
% 4.65/0.96
% 4.65/0.97 % SZS output start Proof
% 4.65/0.97 Take the following subset of the input axioms:
% 4.65/0.97 fof(not_p8_10, negated_conjecture, ~p8(c22, c23)).
% 4.65/0.97 fof(p21_27, negated_conjecture, p21(f11(c24, c25, c26, c22, c27, c28), f11(c29, c30, c31, c23, c32, c33))).
% 4.65/0.97 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))).
% 4.65/0.97 fof(p8_18, negated_conjecture, ![X158, X159, X160]: (p8(X159, X160) | (~p8(X158, X159) | ~p8(X158, X160)))).
% 4.65/0.97 fof(p8_3, negated_conjecture, ![X158_2]: p8(X158_2, X158_2)).
% 4.65/0.97 fof(p8_31, negated_conjecture, ![X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14]: (p8(X8, X13) | ~p3(f11(X5, X6, X7, X8, X9, X3), f11(X10, X11, X12, X13, X14, X4)))).
% 4.65/0.97 fof(p8_36, negated_conjecture, ![X43_2, X37_2, X38_2, X39_2, X40_2, X41_2, X36_2, X42_2]: (p8(X42_2, f16(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))).
% 4.65/0.97
% 4.65/0.97 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.65/0.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.65/0.97 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.65/0.97 fresh(y, y, x1...xn) = u
% 4.65/0.97 C => fresh(s, t, x1...xn) = v
% 4.65/0.97 where fresh is a fresh function symbol and x1..xn are the free
% 4.65/0.97 variables of u and v.
% 4.65/0.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.65/0.97 input problem has no model of domain size 1).
% 4.65/0.97
% 4.65/0.97 The encoding turns the above axioms into the following unit equations and goals:
% 4.65/0.97
% 4.65/0.97 Axiom 1 (p8_3): p8(X, X) = true2.
% 4.65/0.97 Axiom 2 (p8_18): fresh7(X, X, Y, Z) = true2.
% 4.65/0.97 Axiom 3 (p8_31): fresh6(X, X, Y, Z) = true2.
% 4.65/0.97 Axiom 4 (p8_18): fresh8(X, X, Y, Z, W) = p8(Y, Z).
% 4.65/0.97 Axiom 5 (p8_18): fresh8(p8(X, Y), true2, Z, Y, X) = fresh7(p8(X, Z), true2, Z, Y).
% 4.65/0.97 Axiom 6 (p3_48): fresh18(X, X, Y, Z, W, V, U, T, S, X2) = true2.
% 4.65/0.97 Axiom 7 (p8_36): fresh5(X, X, Y, Z, W, V, U, T, S, X2) = true2.
% 4.65/0.97 Axiom 8 (p21_27): p21(f11(c24, c25, c26, c22, c27, c28), f11(c29, c30, c31, c23, c32, c33)) = true2.
% 4.65/0.97 Axiom 9 (p8_31): fresh6(p3(f11(X, Y, Z, W, V, U), f11(T, S, X2, Y2, Z2, W2)), true2, W, Y2) = p8(W, Y2).
% 4.65/0.97 Axiom 10 (p8_36): fresh5(p21(f11(X, Y, Z, W, V, U), T), true2, W, S, X, Y, U, T, Z, V) = p8(W, f16(S, X, Y, U, T, Z, W, V)).
% 4.65/0.97 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))).
% 4.65/0.97
% 4.65/0.97 Lemma 12: fresh7(p8(X, Y), true2, Y, X) = p8(Y, X).
% 4.65/0.97 Proof:
% 4.65/0.97 fresh7(p8(X, Y), true2, Y, X)
% 4.65/0.97 = { by axiom 5 (p8_18) R->L }
% 4.65/0.97 fresh8(p8(X, X), true2, Y, X, X)
% 4.65/0.97 = { by axiom 1 (p8_3) }
% 4.65/0.97 fresh8(true2, true2, Y, X, X)
% 4.65/0.97 = { by axiom 4 (p8_18) }
% 4.65/0.97 p8(Y, X)
% 4.65/0.97
% 4.65/0.97 Goal 1 (not_p8_10): p8(c22, c23) = true2.
% 4.65/0.97 Proof:
% 4.65/0.97 p8(c22, c23)
% 4.65/0.97 = { by lemma 12 R->L }
% 4.65/0.97 fresh7(p8(c23, c22), true2, c22, c23)
% 4.65/0.97 = { by axiom 4 (p8_18) R->L }
% 4.65/0.97 fresh7(fresh8(true2, true2, c23, c22, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, c22, c23)
% 4.65/0.97 = { by axiom 2 (p8_18) R->L }
% 4.65/0.98 fresh7(fresh8(fresh7(true2, true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c22), true2, c23, c22, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, c22, c23)
% 4.65/0.98 = { by axiom 7 (p8_36) R->L }
% 4.65/0.98 fresh7(fresh8(fresh7(fresh5(true2, true2, c22, X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c27), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c22), true2, c23, c22, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, c22, c23)
% 4.65/0.98 = { by axiom 8 (p21_27) R->L }
% 4.65/0.98 fresh7(fresh8(fresh7(fresh5(p21(f11(c24, c25, c26, c22, c27, c28), f11(c29, c30, c31, c23, c32, c33)), true2, c22, X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c27), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c22), true2, c23, c22, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, c22, c23)
% 4.65/0.98 = { by axiom 10 (p8_36) }
% 4.65/0.98 fresh7(fresh8(fresh7(p8(c22, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c22), true2, c23, c22, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, c22, c23)
% 4.65/0.98 = { by lemma 12 }
% 4.65/0.98 fresh7(fresh8(p8(f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c22), true2, c23, c22, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, c22, c23)
% 4.65/0.98 = { by axiom 5 (p8_18) }
% 4.65/0.98 fresh7(fresh7(p8(f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c23), true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by lemma 12 R->L }
% 4.65/0.98 fresh7(fresh7(fresh7(p8(c23, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c23), true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by axiom 9 (p8_31) R->L }
% 4.65/0.98 fresh7(fresh7(fresh7(fresh6(p3(f11(c29, c30, c31, c23, c32, c33), f11(f19(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), f18(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), f17(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), f15(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), f14(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27))), true2, c23, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c23), true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by axiom 11 (p3_48) R->L }
% 4.65/0.98 fresh7(fresh7(fresh7(fresh6(fresh18(p21(f11(c24, c25, c26, c22, c27, c28), f11(c29, c30, c31, c23, c32, c33)), true2, f11(c29, c30, c31, c23, c32, c33), X, c24, c25, c28, c26, c22, c27), true2, c23, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c23), true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by axiom 8 (p21_27) }
% 4.65/0.98 fresh7(fresh7(fresh7(fresh6(fresh18(true2, true2, f11(c29, c30, c31, c23, c32, c33), X, c24, c25, c28, c26, c22, c27), true2, c23, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c23), true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by axiom 6 (p3_48) }
% 4.65/0.98 fresh7(fresh7(fresh7(fresh6(true2, true2, c23, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27)), true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c23), true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by axiom 3 (p8_31) }
% 4.65/0.98 fresh7(fresh7(fresh7(true2, true2, f16(X, c24, c25, c28, f11(c29, c30, c31, c23, c32, c33), c26, c22, c27), c23), true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by axiom 2 (p8_18) }
% 4.65/0.98 fresh7(fresh7(true2, true2, c23, c22), true2, c22, c23)
% 4.65/0.98 = { by axiom 2 (p8_18) }
% 4.65/0.98 fresh7(true2, true2, c22, c23)
% 4.65/0.98 = { by axiom 2 (p8_18) }
% 4.65/0.98 true2
% 4.65/0.98 % SZS output end Proof
% 4.65/0.98
% 4.65/0.98 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------