TSTP Solution File: SYN707-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN707-1 : 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 : n020.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 03:35:47 EDT 2023
% Result : Unsatisfiable 23.65s 3.42s
% Output : Proof 23.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : SYN707-1 : TPTP v8.1.2. Released v2.5.0.
% 0.11/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.36 % Computer : n020.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 20:26:14 EDT 2023
% 0.13/0.36 % CPUTime :
% 23.65/3.42 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 23.65/3.42
% 23.65/3.42 % SZS status Unsatisfiable
% 23.65/3.42
% 23.65/3.44 % SZS output start Proof
% 23.65/3.44 Take the following subset of the input axioms:
% 23.65/3.44 fof(c56_is_p38_1, negated_conjecture, p38(c56)).
% 23.65/3.44 fof(f11_is_p38_64, negated_conjecture, p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))).
% 23.65/3.44 fof(not_p39_69, negated_conjecture, ~p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))).
% 23.65/3.44 fof(p10_3, negated_conjecture, ![X0]: p10(X0, X0)).
% 23.65/3.44 fof(p10_66, negated_conjecture, p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))).
% 23.65/3.44 fof(p16_36, negated_conjecture, ![X27]: (p16(f19(f15(X27)), f28(f19(X27))) | ~p38(X27))).
% 23.65/3.44 fof(p16_8, negated_conjecture, ![X18]: p16(X18, X18)).
% 23.65/3.44 fof(p37_13, negated_conjecture, p37(f15(c56), c48)).
% 23.65/3.44 fof(p37_51, negated_conjecture, ![X93, X94, X96, X95]: (p37(X93, X94) | (~p10(X96, X94) | (~p37(X95, X96) | ~p10(X95, X93))))).
% 23.65/3.44 fof(p38_15, negated_conjecture, ![X27_2]: (p38(f15(X27_2)) | ~p38(X27_2))).
% 23.65/3.44 fof(p39_52, negated_conjecture, ![X99, X100, X102, X101]: (p39(X99, X100) | (~p16(X102, X100) | (~p39(X101, X102) | ~p16(X101, X99))))).
% 23.65/3.44 fof(p39_54, negated_conjecture, ![X91, X92]: (p39(f19(X91), f19(X92)) | (~p38(X92) | (~p38(X91) | ~p37(X91, X92))))).
% 23.65/3.44
% 23.65/3.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 23.65/3.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 23.65/3.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 23.65/3.44 fresh(y, y, x1...xn) = u
% 23.65/3.44 C => fresh(s, t, x1...xn) = v
% 23.65/3.44 where fresh is a fresh function symbol and x1..xn are the free
% 23.65/3.44 variables of u and v.
% 23.65/3.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 23.65/3.44 input problem has no model of domain size 1).
% 23.65/3.44
% 23.65/3.44 The encoding turns the above axioms into the following unit equations and goals:
% 23.65/3.44
% 23.65/3.44 Axiom 1 (c56_is_p38_1): p38(c56) = true.
% 23.65/3.44 Axiom 2 (p16_8): p16(X, X) = true.
% 23.65/3.44 Axiom 3 (p10_3): p10(X, X) = true.
% 23.65/3.44 Axiom 4 (p37_13): p37(f15(c56), c48) = true.
% 23.65/3.44 Axiom 5 (p16_36): fresh46(X, X, Y) = true.
% 23.65/3.44 Axiom 6 (p38_15): fresh17(X, X, Y) = true.
% 23.65/3.44 Axiom 7 (p37_51): fresh71(X, X, Y, Z) = true.
% 23.65/3.44 Axiom 8 (p39_52): fresh69(X, X, Y, Z) = true.
% 23.65/3.44 Axiom 9 (p39_54): fresh65(X, X, Y, Z) = true.
% 23.65/3.44 Axiom 10 (p38_15): fresh17(p38(X), true, X) = p38(f15(X)).
% 23.65/3.44 Axiom 11 (p39_54): fresh13(X, X, Y, Z) = p39(f19(Y), f19(Z)).
% 23.65/3.44 Axiom 12 (p39_54): fresh64(X, X, Y, Z) = fresh65(p38(Y), true, Y, Z).
% 23.65/3.44 Axiom 13 (p37_51): fresh18(X, X, Y, Z, W) = p37(Y, Z).
% 23.65/3.44 Axiom 14 (p39_52): fresh14(X, X, Y, Z, W) = p39(Y, Z).
% 23.65/3.44 Axiom 15 (p16_36): fresh46(p38(X), true, X) = p16(f19(f15(X)), f28(f19(X))).
% 23.65/3.44 Axiom 16 (p37_51): fresh70(X, X, Y, Z, W, V) = fresh71(p10(W, Z), true, Y, Z).
% 23.65/3.44 Axiom 17 (p39_52): fresh68(X, X, Y, Z, W, V) = fresh69(p16(W, Z), true, Y, Z).
% 23.65/3.44 Axiom 18 (p39_54): fresh64(p37(X, Y), true, X, Y) = fresh13(p38(Y), true, X, Y).
% 23.65/3.44 Axiom 19 (p37_51): fresh70(p37(X, Y), true, Z, W, Y, X) = fresh18(p10(X, Z), true, Z, W, Y).
% 23.65/3.44 Axiom 20 (p39_52): fresh68(p39(X, Y), true, Z, W, Y, X) = fresh14(p16(X, Z), true, Z, W, Y).
% 23.65/3.44 Axiom 21 (f11_is_p38_64): p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) = true.
% 23.65/3.44 Axiom 22 (p10_66): p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) = true.
% 23.65/3.44
% 23.65/3.44 Goal 1 (not_p39_69): p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) = true.
% 23.65/3.44 Proof:
% 23.65/3.44 p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))
% 23.65/3.44 = { by axiom 14 (p39_52) R->L }
% 23.65/3.45 fresh14(true, true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))
% 23.65/3.45 = { by axiom 5 (p16_36) R->L }
% 23.65/3.45 fresh14(fresh46(true, true, c56), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))
% 23.65/3.45 = { by axiom 1 (c56_is_p38_1) R->L }
% 23.65/3.45 fresh14(fresh46(p38(c56), true, c56), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))
% 23.65/3.45 = { by axiom 15 (p16_36) }
% 23.65/3.45 fresh14(p16(f19(f15(c56)), f28(f19(c56))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))
% 23.65/3.45 = { by axiom 20 (p39_52) R->L }
% 23.65/3.45 fresh68(p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 11 (p39_54) R->L }
% 23.65/3.45 fresh68(fresh13(true, true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 21 (f11_is_p38_64) R->L }
% 23.65/3.45 fresh68(fresh13(p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 18 (p39_54) R->L }
% 23.65/3.45 fresh68(fresh64(p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 13 (p37_51) R->L }
% 23.65/3.45 fresh68(fresh64(fresh18(true, true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), c48), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 3 (p10_3) R->L }
% 23.65/3.45 fresh68(fresh64(fresh18(p10(f15(c56), f15(c56)), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), c48), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 19 (p37_51) R->L }
% 23.65/3.45 fresh68(fresh64(fresh70(p37(f15(c56), c48), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), c48, f15(c56)), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 4 (p37_13) }
% 23.65/3.45 fresh68(fresh64(fresh70(true, true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), c48, f15(c56)), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 16 (p37_51) }
% 23.65/3.45 fresh68(fresh64(fresh71(p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 22 (p10_66) }
% 23.65/3.45 fresh68(fresh64(fresh71(true, true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 7 (p37_51) }
% 23.65/3.45 fresh68(fresh64(true, true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 12 (p39_54) }
% 23.65/3.45 fresh68(fresh65(p38(f15(c56)), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 10 (p38_15) R->L }
% 23.65/3.45 fresh68(fresh65(fresh17(p38(c56), true, c56), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 1 (c56_is_p38_1) }
% 23.65/3.45 fresh68(fresh65(fresh17(true, true, c56), true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 6 (p38_15) }
% 23.65/3.45 fresh68(fresh65(true, true, f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 9 (p39_54) }
% 23.65/3.45 fresh68(true, true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f15(c56)))
% 23.65/3.45 = { by axiom 17 (p39_52) }
% 23.65/3.45 fresh69(p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))), true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))
% 23.65/3.45 = { by axiom 2 (p16_8) }
% 23.65/3.45 fresh69(true, true, f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))
% 23.65/3.45 = { by axiom 8 (p39_52) }
% 23.65/3.45 true
% 23.65/3.45 % SZS output end Proof
% 23.65/3.45
% 23.65/3.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------