TSTP Solution File: SYN590-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN590-1 : 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 : n002.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 03:35:22 EDT 2023
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.20s
% 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 : SYN590-1 : 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
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 18:30:03 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.51 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.51
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 Take the following subset of the input axioms:
% 0.20/0.52 fof(c16_is_p11_3, negated_conjecture, p11(c16)).
% 0.20/0.52 fof(not_p11_25, negated_conjecture, ![X34, X35]: (~p11(X34) | (~p12(X35, c15) | ~p3(f4(X34), f6(X35))))).
% 0.20/0.52 fof(p10_19, negated_conjecture, ![X4]: (p10(f4(f9(X4)), f4(X4)) | ~p11(X4))).
% 0.20/0.52 fof(p10_26, negated_conjecture, ![X0, X1, X2, X3]: (p10(X0, X1) | (~p3(X2, X0) | (~p3(X3, X1) | ~p10(X2, X3))))).
% 0.20/0.52 fof(p11_9, negated_conjecture, ![X4_2]: (p11(f9(X4_2)) | ~p11(X4_2))).
% 0.20/0.52 fof(p12_11, negated_conjecture, ![X5, X6]: (p12(X5, X6) | ~p10(f6(X5), f6(X6)))).
% 0.20/0.52 fof(p3_18, negated_conjecture, ![X24]: (p3(f4(X24), f6(f8(X24))) | ~p11(X24))).
% 0.20/0.52 fof(p3_8, negated_conjecture, p3(f4(c16), f6(c15))).
% 0.20/0.52
% 0.20/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.52 fresh(y, y, x1...xn) = u
% 0.20/0.52 C => fresh(s, t, x1...xn) = v
% 0.20/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.52 variables of u and v.
% 0.20/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.52 input problem has no model of domain size 1).
% 0.20/0.52
% 0.20/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.52
% 0.20/0.52 Axiom 1 (c16_is_p11_3): p11(c16) = true2.
% 0.20/0.52 Axiom 2 (p10_19): fresh22(X, X, Y) = true2.
% 0.20/0.52 Axiom 3 (p11_9): fresh15(X, X, Y) = true2.
% 0.20/0.52 Axiom 4 (p3_18): fresh7(X, X, Y) = true2.
% 0.20/0.52 Axiom 5 (p10_26): fresh26(X, X, Y, Z) = true2.
% 0.20/0.52 Axiom 6 (p11_9): fresh15(p11(X), true2, X) = p11(f9(X)).
% 0.20/0.52 Axiom 7 (p12_11): fresh14(X, X, Y, Z) = true2.
% 0.20/0.52 Axiom 8 (p3_8): p3(f4(c16), f6(c15)) = true2.
% 0.20/0.52 Axiom 9 (p10_26): fresh18(X, X, Y, Z, W) = p10(Y, Z).
% 0.20/0.52 Axiom 10 (p10_19): fresh22(p11(X), true2, X) = p10(f4(f9(X)), f4(X)).
% 0.20/0.52 Axiom 11 (p3_18): fresh7(p11(X), true2, X) = p3(f4(X), f6(f8(X))).
% 0.20/0.52 Axiom 12 (p10_26): fresh25(X, X, Y, Z, W, V) = fresh26(p3(W, Y), true2, Y, Z).
% 0.20/0.52 Axiom 13 (p10_26): fresh25(p10(X, Y), true2, Z, W, X, Y) = fresh18(p3(Y, W), true2, Z, W, X).
% 0.20/0.52 Axiom 14 (p12_11): fresh14(p10(f6(X), f6(Y)), true2, X, Y) = p12(X, Y).
% 0.20/0.52
% 0.20/0.52 Lemma 15: p11(f9(c16)) = true2.
% 0.20/0.52 Proof:
% 0.20/0.52 p11(f9(c16))
% 0.20/0.52 = { by axiom 6 (p11_9) R->L }
% 0.20/0.52 fresh15(p11(c16), true2, c16)
% 0.20/0.52 = { by axiom 1 (c16_is_p11_3) }
% 0.20/0.52 fresh15(true2, true2, c16)
% 0.20/0.52 = { by axiom 3 (p11_9) }
% 0.20/0.52 true2
% 0.20/0.52
% 0.20/0.52 Goal 1 (not_p11_25): tuple(p11(X), p3(f4(X), f6(Y)), p12(Y, c15)) = tuple(true2, true2, true2).
% 0.20/0.52 The goal is true when:
% 0.20/0.52 X = f9(c16)
% 0.20/0.52 Y = f8(f9(c16))
% 0.20/0.52
% 0.20/0.52 Proof:
% 0.20/0.52 tuple(p11(f9(c16)), p3(f4(f9(c16)), f6(f8(f9(c16)))), p12(f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 11 (p3_18) R->L }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), p12(f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 14 (p12_11) R->L }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(p10(f6(f8(f9(c16))), f6(c15)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 9 (p10_26) R->L }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh18(true2, true2, f6(f8(f9(c16))), f6(c15), f4(f9(c16))), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 8 (p3_8) R->L }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh18(p3(f4(c16), f6(c15)), true2, f6(f8(f9(c16))), f6(c15), f4(f9(c16))), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 13 (p10_26) R->L }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh25(p10(f4(f9(c16)), f4(c16)), true2, f6(f8(f9(c16))), f6(c15), f4(f9(c16)), f4(c16)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 10 (p10_19) R->L }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh25(fresh22(p11(c16), true2, c16), true2, f6(f8(f9(c16))), f6(c15), f4(f9(c16)), f4(c16)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 1 (c16_is_p11_3) }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh25(fresh22(true2, true2, c16), true2, f6(f8(f9(c16))), f6(c15), f4(f9(c16)), f4(c16)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 2 (p10_19) }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh25(true2, true2, f6(f8(f9(c16))), f6(c15), f4(f9(c16)), f4(c16)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 12 (p10_26) }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh26(p3(f4(f9(c16)), f6(f8(f9(c16)))), true2, f6(f8(f9(c16))), f6(c15)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 11 (p3_18) R->L }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh26(fresh7(p11(f9(c16)), true2, f9(c16)), true2, f6(f8(f9(c16))), f6(c15)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by lemma 15 }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh26(fresh7(true2, true2, f9(c16)), true2, f6(f8(f9(c16))), f6(c15)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 4 (p3_18) }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(fresh26(true2, true2, f6(f8(f9(c16))), f6(c15)), true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 5 (p10_26) }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), fresh14(true2, true2, f8(f9(c16)), c15))
% 0.20/0.52 = { by axiom 7 (p12_11) }
% 0.20/0.52 tuple(p11(f9(c16)), fresh7(p11(f9(c16)), true2, f9(c16)), true2)
% 0.20/0.52 = { by lemma 15 }
% 0.20/0.52 tuple(true2, fresh7(p11(f9(c16)), true2, f9(c16)), true2)
% 0.20/0.52 = { by lemma 15 }
% 0.20/0.52 tuple(true2, fresh7(true2, true2, f9(c16)), true2)
% 0.20/0.52 = { by axiom 4 (p3_18) }
% 0.20/0.52 tuple(true2, true2, true2)
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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