TSTP Solution File: SYN599-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN599-1 : 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 : n032.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 03:35:23 EDT 2023
% Result : Unsatisfiable 8.64s 1.43s
% Output : Proof 8.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SYN599-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sat Aug 26 20:43:29 EDT 2023
% 0.08/0.28 % CPUTime :
% 8.64/1.43 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 8.64/1.43
% 8.64/1.43 % SZS status Unsatisfiable
% 8.64/1.43
% 8.64/1.43 % SZS output start Proof
% 8.64/1.43 Take the following subset of the input axioms:
% 8.64/1.43 fof(c21_is_p18_2, negated_conjecture, p18(c21)).
% 8.64/1.43 fof(not_p19_27, negated_conjecture, ~p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))).
% 8.64/1.43 fof(p19_23, negated_conjecture, ![X4, X5, X6, X7]: (p19(X4, X5) | (~p7(X6, X4) | (~p7(X7, X5) | ~p19(X6, X7))))).
% 8.64/1.43 fof(p19_29, negated_conjecture, ![X8]: (p19(f15(f16(X8)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X8)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) | ~p18(X8))).
% 8.64/1.43 fof(p3_15, negated_conjecture, ![X27, X28]: (p3(f14(X27), f14(X28)) | ~p3(X27, X28))).
% 8.64/1.43 fof(p3_7, negated_conjecture, p3(f4(f6(c21)), c22)).
% 8.64/1.43 fof(p7_25, negated_conjecture, ![X47, X48, X49, X50]: (p7(f9(X47, X48), f9(X49, X50)) | (~p3(X48, X50) | ~p7(X47, X49)))).
% 8.64/1.43 fof(p7_26, negated_conjecture, ![X43, X44, X45, X46]: (p7(f8(X43, X44), f8(X45, X46)) | (~p7(X43, X45) | ~p7(X44, X46)))).
% 8.64/1.43 fof(p7_3, negated_conjecture, ![X34]: p7(X34, X34)).
% 8.64/1.43
% 8.64/1.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 8.64/1.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 8.64/1.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 8.64/1.43 fresh(y, y, x1...xn) = u
% 8.64/1.43 C => fresh(s, t, x1...xn) = v
% 8.64/1.43 where fresh is a fresh function symbol and x1..xn are the free
% 8.64/1.43 variables of u and v.
% 8.64/1.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 8.64/1.43 input problem has no model of domain size 1).
% 8.64/1.43
% 8.64/1.43 The encoding turns the above axioms into the following unit equations and goals:
% 8.64/1.43
% 8.64/1.43 Axiom 1 (c21_is_p18_2): p18(c21) = true.
% 8.64/1.43 Axiom 2 (p7_3): p7(X, X) = true.
% 8.64/1.43 Axiom 3 (p19_29): fresh24(X, X, Y) = true.
% 8.64/1.43 Axiom 4 (p3_7): p3(f4(f6(c21)), c22) = true.
% 8.64/1.43 Axiom 5 (p19_23): fresh33(X, X, Y, Z) = true.
% 8.64/1.43 Axiom 6 (p3_15): fresh15(X, X, Y, Z) = true.
% 8.64/1.43 Axiom 7 (p19_23): fresh25(X, X, Y, Z, W) = p19(Y, Z).
% 8.64/1.43 Axiom 8 (p7_26): fresh(X, X, Y, Z, W, V) = true.
% 8.64/1.43 Axiom 9 (p19_23): fresh32(X, X, Y, Z, W, V) = fresh33(p7(W, Y), true, Y, Z).
% 8.64/1.43 Axiom 10 (p3_15): fresh15(p3(X, Y), true, X, Y) = p3(f14(X), f14(Y)).
% 8.64/1.43 Axiom 11 (p7_25): fresh4(X, X, Y, Z, W, V) = p7(f9(Y, Z), f9(W, V)).
% 8.64/1.43 Axiom 12 (p7_25): fresh3(X, X, Y, Z, W, V) = true.
% 8.64/1.43 Axiom 13 (p7_26): fresh2(X, X, Y, Z, W, V) = p7(f8(Y, Z), f8(W, V)).
% 8.64/1.43 Axiom 14 (p19_23): fresh32(p19(X, Y), true, Z, W, X, Y) = fresh25(p7(Y, W), true, Z, W, X).
% 8.64/1.43 Axiom 15 (p7_25): fresh4(p3(X, Y), true, Z, X, W, Y) = fresh3(p7(Z, W), true, Z, X, W, Y).
% 8.64/1.43 Axiom 16 (p7_26): fresh2(p7(X, Y), true, Z, X, W, Y) = fresh(p7(Z, W), true, Z, X, W, Y).
% 8.64/1.43 Axiom 17 (p19_29): fresh24(p18(X), true, X) = p19(f15(f16(X)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(X)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))).
% 8.64/1.43
% 8.64/1.43 Goal 1 (not_p19_27): p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))) = true.
% 8.64/1.43 Proof:
% 8.64/1.43 p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))
% 8.64/1.43 = { by axiom 7 (p19_23) R->L }
% 8.64/1.43 fresh25(true, true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.43 = { by axiom 8 (p7_26) R->L }
% 8.64/1.44 fresh25(fresh(true, true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 12 (p7_25) R->L }
% 8.64/1.44 fresh25(fresh(fresh3(true, true, f12(f10(f13(f11(c23)))), f14(f4(f6(c21))), f12(f10(f13(f11(c23)))), f14(c22)), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 2 (p7_3) R->L }
% 8.64/1.44 fresh25(fresh(fresh3(p7(f12(f10(f13(f11(c23)))), f12(f10(f13(f11(c23))))), true, f12(f10(f13(f11(c23)))), f14(f4(f6(c21))), f12(f10(f13(f11(c23)))), f14(c22)), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 15 (p7_25) R->L }
% 8.64/1.44 fresh25(fresh(fresh4(p3(f14(f4(f6(c21))), f14(c22)), true, f12(f10(f13(f11(c23)))), f14(f4(f6(c21))), f12(f10(f13(f11(c23)))), f14(c22)), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 10 (p3_15) R->L }
% 8.64/1.44 fresh25(fresh(fresh4(fresh15(p3(f4(f6(c21)), c22), true, f4(f6(c21)), c22), true, f12(f10(f13(f11(c23)))), f14(f4(f6(c21))), f12(f10(f13(f11(c23)))), f14(c22)), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 4 (p3_7) }
% 8.64/1.44 fresh25(fresh(fresh4(fresh15(true, true, f4(f6(c21)), c22), true, f12(f10(f13(f11(c23)))), f14(f4(f6(c21))), f12(f10(f13(f11(c23)))), f14(c22)), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 6 (p3_15) }
% 8.64/1.44 fresh25(fresh(fresh4(true, true, f12(f10(f13(f11(c23)))), f14(f4(f6(c21))), f12(f10(f13(f11(c23)))), f14(c22)), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 11 (p7_25) }
% 8.64/1.44 fresh25(fresh(p7(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f14(c22))), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 16 (p7_26) R->L }
% 8.64/1.44 fresh25(fresh2(p7(f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 2 (p7_3) }
% 8.64/1.44 fresh25(fresh2(true, true, f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))), f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 13 (p7_26) }
% 8.64/1.44 fresh25(p7(f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)))
% 8.64/1.44 = { by axiom 14 (p19_23) R->L }
% 8.64/1.44 fresh32(p19(f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23))))))))))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))
% 8.64/1.44 = { by axiom 17 (p19_29) R->L }
% 8.64/1.44 fresh32(fresh24(p18(c21), true, c21), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))
% 8.64/1.44 = { by axiom 1 (c21_is_p18_2) }
% 8.64/1.44 fresh32(fresh24(true, true, c21), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))
% 8.64/1.44 = { by axiom 3 (p19_29) }
% 8.64/1.44 fresh32(true, true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))), f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(f4(f6(c21)))), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))
% 8.64/1.44 = { by axiom 9 (p19_23) }
% 8.64/1.44 fresh33(p7(f15(f16(c21)), f15(f16(c21))), true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))
% 8.64/1.44 = { by axiom 2 (p7_3) }
% 8.64/1.44 fresh33(true, true, f15(f16(c21)), f8(f9(f12(f10(f13(f11(c23)))), f14(c22)), f9(f12(f10(f13(f11(c23)))), f10(f11(f11(f11(f11(f11(f11(f11(c23)))))))))))
% 8.64/1.44 = { by axiom 5 (p19_23) }
% 8.64/1.44 true
% 8.64/1.44 % SZS output end Proof
% 8.64/1.44
% 8.64/1.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------