TSTP Solution File: SYN632-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN632-1 : 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 : n023.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 03:35:31 EDT 2023
% Result : Unsatisfiable 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN632-1 : TPTP v8.1.2. Released v2.5.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 21:09:11 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.52 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.52
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 Take the following subset of the input axioms:
% 0.19/0.54 fof(not_p21_35, negated_conjecture, ![X77]: (~p21(f5(c22, c23), X77) | ~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27))).
% 0.19/0.54 fof(p21_23, negated_conjecture, ![X34, X35, X37, X36]: (p21(X34, X35) | (~p3(X37, X35) | (~p4(X36, X34) | ~p21(X36, X37))))).
% 0.19/0.54 fof(p21_24, negated_conjecture, p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)).
% 0.19/0.54 fof(p21_34, negated_conjecture, ![X43, X44, X42]: (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | ~p3(X43, X44))).
% 0.19/0.54 fof(p21_36, negated_conjecture, ![X38, X39, X40, X41]: (p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41) | ~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41))).
% 0.19/0.54 fof(p21_38, negated_conjecture, ![X38_2, X39_2, X40_2, X41_2]: (p21(f5(f7(f10(c24, X39_2), X38_2), X40_2), f14(f16(f18(f20(c29, X39_2), X40_2), X38_2), X41_2)) | ~p21(f5(f7(f10(c24, f12(c28, X39_2)), X38_2), X40_2), X41_2))).
% 0.19/0.54 fof(p2_7, negated_conjecture, ![X27]: p2(X27, X27)).
% 0.19/0.54 fof(p3_17, negated_conjecture, ![X46, X47, X48]: (p3(X47, X48) | (~p3(X46, X47) | ~p3(X46, X48)))).
% 0.19/0.54 fof(p3_33, negated_conjecture, ![X43_2, X44_2, X42_2]: (p3(X43_2, X44_2) | ~p21(f5(f7(f10(c24, f12(c25, c26)), X42_2), X43_2), X44_2))).
% 0.19/0.54 fof(p3_6, negated_conjecture, ![X46_2]: p3(X46_2, X46_2)).
% 0.19/0.54 fof(p4_31, negated_conjecture, ![X56, X57, X58, X59]: (p4(f5(X56, X57), f5(X58, X59)) | (~p2(X56, X58) | ~p3(X57, X59)))).
% 0.19/0.54
% 0.19/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.54 fresh(y, y, x1...xn) = u
% 0.19/0.54 C => fresh(s, t, x1...xn) = v
% 0.19/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.54 variables of u and v.
% 0.19/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.54 input problem has no model of domain size 1).
% 0.19/0.54
% 0.19/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.54
% 0.19/0.54 Axiom 1 (p3_6): p3(X, X) = true2.
% 0.19/0.54 Axiom 2 (p2_7): p2(X, X) = true2.
% 0.19/0.54 Axiom 3 (p21_23): fresh47(X, X, Y, Z) = true2.
% 0.19/0.54 Axiom 4 (p3_17): fresh18(X, X, Y, Z) = true2.
% 0.19/0.54 Axiom 5 (p3_33): fresh15(X, X, Y, Z) = true2.
% 0.19/0.54 Axiom 6 (p21_23): fresh29(X, X, Y, Z, W) = p21(Y, Z).
% 0.19/0.54 Axiom 7 (p21_34): fresh28(X, X, Y, Z, W) = true2.
% 0.19/0.54 Axiom 8 (p3_17): fresh19(X, X, Y, Z, W) = p3(Y, Z).
% 0.19/0.54 Axiom 9 (p21_23): fresh46(X, X, Y, Z, W, V) = fresh47(p4(V, Y), true2, Y, Z).
% 0.19/0.54 Axiom 10 (p21_36): fresh27(X, X, Y, Z, W, V) = true2.
% 0.19/0.54 Axiom 11 (p21_38): fresh24(X, X, Y, Z, W, V) = true2.
% 0.19/0.54 Axiom 12 (p4_31): fresh12(X, X, Y, Z, W, V) = p4(f5(Y, Z), f5(W, V)).
% 0.19/0.54 Axiom 13 (p4_31): fresh11(X, X, Y, Z, W, V) = true2.
% 0.19/0.54 Axiom 14 (p3_17): fresh19(p3(X, Y), true2, Z, Y, X) = fresh18(p3(X, Z), true2, Z, Y).
% 0.19/0.54 Axiom 15 (p21_23): fresh46(p21(X, Y), true2, Z, W, Y, X) = fresh29(p3(Y, W), true2, Z, W, X).
% 0.19/0.54 Axiom 16 (p4_31): fresh12(p2(X, Y), true2, X, Z, Y, W) = fresh11(p3(Z, W), true2, X, Z, Y, W).
% 0.19/0.54 Axiom 17 (p21_34): fresh28(p3(X, Y), true2, Z, X, Y) = p21(f5(f7(f10(c24, f12(c25, c26)), Z), X), Y).
% 0.19/0.54 Axiom 18 (p21_37): fresh26(X, X, Y, Z, W, V, U) = p21(f5(f7(f10(c24, f12(c28, Y)), Z), W), V).
% 0.19/0.54 Axiom 19 (p21_24): p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27) = true2.
% 0.19/0.54 Axiom 20 (p3_33): fresh15(p21(f5(f7(f10(c24, f12(c25, c26)), X), Y), Z), true2, Y, Z) = p3(Y, Z).
% 0.19/0.54 Axiom 21 (p21_36): fresh27(p21(f5(f7(f10(c24, f12(c28, X)), Y), Z), W), true2, Y, X, Z, W) = p21(f5(Y, f14(f16(f18(f20(c29, X), Z), Y), W)), W).
% 0.19/0.54 Axiom 22 (p21_38): fresh24(p21(f5(f7(f10(c24, f12(c28, X)), Y), Z), W), true2, X, Y, Z, W) = p21(f5(f7(f10(c24, X), Y), Z), f14(f16(f18(f20(c29, X), Z), Y), W)).
% 0.19/0.54
% 0.19/0.54 Lemma 23: fresh26(X, X, f12(c25, c26), c22, c23, c27, Y) = true2.
% 0.19/0.54 Proof:
% 0.19/0.54 fresh26(X, X, f12(c25, c26), c22, c23, c27, Y)
% 0.19/0.54 = { by axiom 18 (p21_37) }
% 0.19/0.54 p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)
% 0.19/0.54 = { by axiom 19 (p21_24) }
% 0.19/0.54 true2
% 0.19/0.54
% 0.19/0.54 Goal 1 (not_p21_35): tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), X), c27), p21(f5(c22, c23), X)) = tuple(true2, true2).
% 0.19/0.54 The goal is true when:
% 0.19/0.54 X = c27
% 0.19/0.54
% 0.19/0.54 Proof:
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), p21(f5(c22, c23), c27))
% 0.19/0.54 = { by axiom 6 (p21_23) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh29(true2, true2, f5(c22, c23), c27, f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))
% 0.19/0.54 = { by axiom 1 (p3_6) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh29(p3(c27, c27), true2, f5(c22, c23), c27, f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))
% 0.19/0.54 = { by axiom 15 (p21_23) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh46(p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27), true2, f5(c22, c23), c27, c27, f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))
% 0.19/0.54 = { by axiom 21 (p21_36) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh46(fresh27(p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27), true2, c22, f12(c25, c26), c23, c27), true2, f5(c22, c23), c27, c27, f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))
% 0.19/0.54 = { by axiom 18 (p21_37) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh46(fresh27(fresh26(Z, Z, f12(c25, c26), c22, c23, c27, W), true2, c22, f12(c25, c26), c23, c27), true2, f5(c22, c23), c27, c27, f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))
% 0.19/0.54 = { by lemma 23 }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh46(fresh27(true2, true2, c22, f12(c25, c26), c23, c27), true2, f5(c22, c23), c27, c27, f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))
% 0.19/0.54 = { by axiom 10 (p21_36) }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh46(true2, true2, f5(c22, c23), c27, c27, f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))
% 0.19/0.54 = { by axiom 9 (p21_23) }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23)), true2, f5(c22, c23), c27))
% 0.19/0.54 = { by axiom 12 (p4_31) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh12(true2, true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.54 = { by axiom 2 (p2_7) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh12(p2(c22, c22), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.54 = { by axiom 16 (p4_31) }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.54 = { by axiom 8 (p3_17) R->L }
% 0.19/0.54 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh19(true2, true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23, c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 1 (p3_6) R->L }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh19(p3(c23, c23), true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23, c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 14 (p3_17) }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh18(p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 20 (p3_33) R->L }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh18(fresh15(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), true2, c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 22 (p21_38) R->L }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh18(fresh15(fresh24(p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27), true2, f12(c25, c26), c22, c23, c27), true2, c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 18 (p21_37) R->L }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh18(fresh15(fresh24(fresh26(X, X, f12(c25, c26), c22, c23, c27, Y), true2, f12(c25, c26), c22, c23, c27), true2, c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by lemma 23 }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh18(fresh15(fresh24(true2, true2, f12(c25, c26), c22, c23, c27), true2, c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 11 (p21_38) }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh18(fresh15(true2, true2, c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 5 (p3_33) }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(fresh18(true2, true2, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23), true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 4 (p3_17) }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(fresh11(true2, true2, c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c22, c23), true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 13 (p4_31) }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), fresh47(true2, true2, f5(c22, c23), c27))
% 0.19/0.55 = { by axiom 3 (p21_23) }
% 0.19/0.55 tuple(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27), true2)
% 0.19/0.55 = { by axiom 17 (p21_34) R->L }
% 0.19/0.55 tuple(fresh28(p3(c27, c27), true2, c22, c27, c27), true2)
% 0.19/0.55 = { by axiom 1 (p3_6) }
% 0.19/0.55 tuple(fresh28(true2, true2, c22, c27, c27), true2)
% 0.19/0.55 = { by axiom 7 (p21_34) }
% 0.19/0.55 tuple(true2, true2)
% 0.19/0.55 % SZS output end Proof
% 0.19/0.55
% 0.19/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------