TSTP Solution File: SYN659-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN659-1 : 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 : n015.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 03:35:36 EDT 2023
% Result : Unsatisfiable 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN659-1 : 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
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 20:35:23 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.21/0.60 Command-line arguments: --flatten
% 0.21/0.60
% 0.21/0.60 % SZS status Unsatisfiable
% 0.21/0.60
% 0.21/0.61 % SZS output start Proof
% 0.21/0.61 Take the following subset of the input axioms:
% 0.21/0.61 fof(c27_is_p22_1, negated_conjecture, p22(c27)).
% 0.21/0.61 fof(not_p24_39, negated_conjecture, ~p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))).
% 0.21/0.61 fof(p10_16, negated_conjecture, p10(f16(c36), c37)).
% 0.21/0.61 fof(p12_10, negated_conjecture, ![X13]: p12(X13, X13)).
% 0.21/0.61 fof(p12_29, negated_conjecture, p12(f13(f16(c39), f17(c39)), f13(c40, c41))).
% 0.21/0.61 fof(p14_37, negated_conjecture, ![X20, X21, X22]: (p14(X21, X22) | (~p14(X20, X21) | ~p14(X20, X22)))).
% 0.21/0.61 fof(p14_45, negated_conjecture, ![X23, X24, X25, X26]: (p14(f15(X23, X24), f15(X25, X26)) | (~p12(X24, X26) | ~p7(X23, X25)))).
% 0.21/0.61 fof(p14_9, negated_conjecture, ![X20_2]: p14(X20_2, X20_2)).
% 0.21/0.61 fof(p24_27, negated_conjecture, p24(f15(c29, f13(c40, c41)), f13(c32, c33))).
% 0.21/0.61 fof(p24_41, negated_conjecture, ![X67, X68, X70, X69]: (p24(X67, X68) | (~p14(X70, X67) | (~p24(X70, X69) | ~p12(X69, X68))))).
% 0.21/0.61 fof(p7_3, negated_conjecture, ![X87]: p7(X87, X87)).
% 0.21/0.61
% 0.21/0.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.61 fresh(y, y, x1...xn) = u
% 0.21/0.61 C => fresh(s, t, x1...xn) = v
% 0.21/0.61 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.61 variables of u and v.
% 0.21/0.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.61 input problem has no model of domain size 1).
% 0.21/0.61
% 0.21/0.61 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.61
% 0.21/0.61 Axiom 1 (c27_is_p22_1): p22(c27) = true.
% 0.21/0.61 Axiom 2 (p7_3): p7(X, X) = true.
% 0.21/0.61 Axiom 3 (p14_9): p14(X, X) = true.
% 0.21/0.61 Axiom 4 (p12_10): p12(X, X) = true.
% 0.21/0.61 Axiom 5 (p10_16): p10(f16(c36), c37) = true.
% 0.21/0.61 Axiom 6 (p24_41): fresh50(X, X, Y, Z) = true.
% 0.21/0.61 Axiom 7 (p14_37): fresh31(X, X, Y, Z) = true.
% 0.21/0.61 Axiom 8 (p14_37): fresh32(X, X, Y, Z, W) = p14(Y, Z).
% 0.21/0.61 Axiom 9 (p24_41): fresh20(X, X, Y, Z, W) = p24(Y, Z).
% 0.21/0.61 Axiom 10 (p24_41): fresh49(X, X, Y, Z, W, V) = fresh50(p14(W, Y), true, Y, Z).
% 0.21/0.61 Axiom 11 (p14_45): fresh29(X, X, Y, Z, W, V) = true.
% 0.21/0.61 Axiom 12 (p14_45): fresh30(X, X, Y, Z, W, V) = p14(f15(Y, Z), f15(W, V)).
% 0.21/0.61 Axiom 13 (p14_37): fresh32(p14(X, Y), true, Z, Y, X) = fresh31(p14(X, Z), true, Z, Y).
% 0.21/0.61 Axiom 14 (p24_41): fresh49(p24(X, Y), true, Z, W, X, Y) = fresh20(p12(Y, W), true, Z, W, X).
% 0.21/0.61 Axiom 15 (p14_45): fresh30(p12(X, Y), true, Z, X, W, Y) = fresh29(p7(Z, W), true, Z, X, W, Y).
% 0.21/0.61 Axiom 16 (p12_29): p12(f13(f16(c39), f17(c39)), f13(c40, c41)) = true.
% 0.21/0.61 Axiom 17 (p24_27): p24(f15(c29, f13(c40, c41)), f13(c32, c33)) = true.
% 0.21/0.61
% 0.21/0.61 Lemma 18: p10(f16(c36), c37) = p22(c27).
% 0.21/0.61 Proof:
% 0.21/0.61 p10(f16(c36), c37)
% 0.21/0.61 = { by axiom 5 (p10_16) }
% 0.21/0.61 true
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.61 p22(c27)
% 0.21/0.61
% 0.21/0.61 Goal 1 (not_p24_39): p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33)) = true.
% 0.21/0.61 Proof:
% 0.21/0.61 p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by axiom 9 (p24_41) R->L }
% 0.21/0.61 fresh20(p10(f16(c36), c37), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)))
% 0.21/0.61 = { by lemma 18 }
% 0.21/0.61 fresh20(p22(c27), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)))
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) }
% 0.21/0.61 fresh20(true, p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)))
% 0.21/0.61 = { by axiom 4 (p12_10) R->L }
% 0.21/0.61 fresh20(p12(f13(c32, c33), f13(c32, c33)), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)))
% 0.21/0.61 = { by lemma 18 }
% 0.21/0.61 fresh20(p12(f13(c32, c33), f13(c32, c33)), p22(c27), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)))
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) }
% 0.21/0.61 fresh20(p12(f13(c32, c33), f13(c32, c33)), true, f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)))
% 0.21/0.61 = { by axiom 14 (p24_41) R->L }
% 0.21/0.61 fresh49(p24(f15(c29, f13(c40, c41)), f13(c32, c33)), true, f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)), f13(c32, c33))
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.61 fresh49(p24(f15(c29, f13(c40, c41)), f13(c32, c33)), p22(c27), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)), f13(c32, c33))
% 0.21/0.61 = { by lemma 18 R->L }
% 0.21/0.61 fresh49(p24(f15(c29, f13(c40, c41)), f13(c32, c33)), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)), f13(c32, c33))
% 0.21/0.61 = { by axiom 17 (p24_27) }
% 0.21/0.61 fresh49(true, p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)), f13(c32, c33))
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.61 fresh49(p22(c27), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)), f13(c32, c33))
% 0.21/0.61 = { by lemma 18 R->L }
% 0.21/0.61 fresh49(p10(f16(c36), c37), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33), f15(c29, f13(c40, c41)), f13(c32, c33))
% 0.21/0.61 = { by axiom 10 (p24_41) }
% 0.21/0.61 fresh50(p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), true, f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.61 fresh50(p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p22(c27), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by lemma 18 R->L }
% 0.21/0.61 fresh50(p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by axiom 8 (p14_37) R->L }
% 0.21/0.61 fresh50(fresh32(p10(f16(c36), c37), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by lemma 18 }
% 0.21/0.61 fresh50(fresh32(p22(c27), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) }
% 0.21/0.61 fresh50(fresh32(true, p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by axiom 3 (p14_9) R->L }
% 0.21/0.61 fresh50(fresh32(p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by lemma 18 }
% 0.21/0.61 fresh50(fresh32(p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p22(c27), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.61 = { by axiom 1 (c27_is_p22_1) }
% 0.21/0.61 fresh50(fresh32(p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), true, f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 13 (p14_37) }
% 0.21/0.62 fresh50(fresh31(p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))), true, f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.62 fresh50(fresh31(p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))), p22(c27), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by lemma 18 R->L }
% 0.21/0.62 fresh50(fresh31(p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 12 (p14_45) R->L }
% 0.21/0.62 fresh50(fresh31(fresh30(p10(f16(c36), c37), p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by lemma 18 }
% 0.21/0.62 fresh50(fresh31(fresh30(p22(c27), p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 1 (c27_is_p22_1) }
% 0.21/0.62 fresh50(fresh31(fresh30(true, p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 16 (p12_29) R->L }
% 0.21/0.62 fresh50(fresh31(fresh30(p12(f13(f16(c39), f17(c39)), f13(c40, c41)), p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by lemma 18 }
% 0.21/0.62 fresh50(fresh31(fresh30(p12(f13(f16(c39), f17(c39)), f13(c40, c41)), p22(c27), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 1 (c27_is_p22_1) }
% 0.21/0.62 fresh50(fresh31(fresh30(p12(f13(f16(c39), f17(c39)), f13(c40, c41)), true, c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 15 (p14_45) }
% 0.21/0.62 fresh50(fresh31(fresh29(p7(c29, c29), true, c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.62 fresh50(fresh31(fresh29(p7(c29, c29), p22(c27), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by lemma 18 R->L }
% 0.21/0.62 fresh50(fresh31(fresh29(p7(c29, c29), p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 2 (p7_3) }
% 0.21/0.62 fresh50(fresh31(fresh29(true, p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.62 fresh50(fresh31(fresh29(p22(c27), p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by lemma 18 R->L }
% 0.21/0.62 fresh50(fresh31(fresh29(p10(f16(c36), c37), p10(f16(c36), c37), c29, f13(f16(c39), f17(c39)), c29, f13(c40, c41)), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 11 (p14_45) }
% 0.21/0.62 fresh50(fresh31(true, p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.62 fresh50(fresh31(p22(c27), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by lemma 18 R->L }
% 0.21/0.62 fresh50(fresh31(p10(f16(c36), c37), p10(f16(c36), c37), f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 7 (p14_37) }
% 0.21/0.62 fresh50(true, p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 1 (c27_is_p22_1) R->L }
% 0.21/0.62 fresh50(p22(c27), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by lemma 18 R->L }
% 0.21/0.62 fresh50(p10(f16(c36), c37), p10(f16(c36), c37), f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))
% 0.21/0.62 = { by axiom 6 (p24_41) }
% 0.21/0.62 true
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62
% 0.21/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------