TSTP Solution File: LCL644+1.010 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL644+1.010 : TPTP v8.1.2. Released v4.0.0.
% 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 : n028.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 : Thu Aug 31 08:19:41 EDT 2023
% Result : Theorem 3.63s 0.86s
% Output : Proof 4.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL644+1.010 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 00:31:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.63/0.86 Command-line arguments: --no-flatten-goal
% 3.63/0.86
% 3.63/0.86 % SZS status Theorem
% 3.63/0.86
% 3.63/0.86 % SZS output start Proof
% 3.63/0.86 Take the following subset of the input axioms:
% 4.71/1.03 fof(main, conjecture, ~?[X]: ~(~(![Y]: (~r1(X, Y) | (~(p11(Y) & ![X2]: (~r1(Y, X2) | p11(X2))) | p10(Y))) | (![Y2]: (~r1(X, Y2) | (p11(Y2) | ~(p10(Y2) & (![X2]: (~r1(Y2, X2) | p10(X2)) & p10(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p11(X2) & ![Y3]: (~r1(X2, Y3) | p11(Y3))) | p10(X2))) | (p11(Y2) | ~(p10(Y2) & (![X2]: (~r1(Y2, X2) | p10(X2)) & p10(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p11(Y2) & ![X2]: (~r1(Y2, X2) | p11(X2))) | (p10(Y2) | ![X2]: (~r1(Y2, X2) | (p11(X2) | ~(p10(X2) & (![Y3]: (~r1(X2, Y3) | p10(Y3)) & p10(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p11(Y2) & ![X2]: (~r1(Y2, X2) | p11(X2))) | (p10(Y2) | (p11(Y2) | ~(p10(Y2) & (![X2]: (~r1(Y2, X2) | p10(X2)) & p10(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p10(Y2) & ![X2]: (~r1(Y2, X2) | p10(X2))) | p9(Y2))) | (![Y2]: (~r1(X, Y2) | (p10(Y2) | ~(p9(Y2) & (![X2]: (~r1(Y2, X2) | p9(X2)) & p9(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p10(X2) & ![Y3]: (~r1(X2, Y3) | p10(Y3))) | p9(X2))) | (p10(Y2) | ~(p9(Y2) & (![X2]: (~r1(Y2, X2) | p9(X2)) & p9(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p10(Y2) & ![X2]: (~r1(Y2, X2) | p10(X2))) | (p9(Y2) | ![X2]: (~r1(Y2, X2) | (p10(X2) | ~(p9(X2) & (![Y3]: (~r1(X2, Y3) | p9(Y3)) & p9(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p10(Y2) & ![X2]: (~r1(Y2, X2) | p10(X2))) | (p9(Y2) | (p10(Y2) | ~(p9(Y2) & (![X2]: (~r1(Y2, X2) | p9(X2)) & p9(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p9(Y2) & ![X2]: (~r1(Y2, X2) | p9(X2))) | p8(Y2))) | (![Y2]: (~r1(X, Y2) | (p9(Y2) | ~(p8(Y2) & (![X2]: (~r1(Y2, X2) | p8(X2)) & p8(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p9(X2) & ![Y3]: (~r1(X2, Y3) | p9(Y3))) | p8(X2))) | (p9(Y2) | ~(p8(Y2) & (![X2]: (~r1(Y2, X2) | p8(X2)) & p8(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p9(Y2) & ![X2]: (~r1(Y2, X2) | p9(X2))) | (p8(Y2) | ![X2]: (~r1(Y2, X2) | (p9(X2) | ~(p8(X2) & (![Y3]: (~r1(X2, Y3) | p8(Y3)) & p8(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p9(Y2) & ![X2]: (~r1(Y2, X2) | p9(X2))) | (p8(Y2) | (p9(Y2) | ~(p8(Y2) & (![X2]: (~r1(Y2, X2) | p8(X2)) & p8(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p8(Y2) & ![X2]: (~r1(Y2, X2) | p8(X2))) | p7(Y2))) | (![Y2]: (~r1(X, Y2) | (p8(Y2) | ~(p7(Y2) & (![X2]: (~r1(Y2, X2) | p7(X2)) & p7(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p8(X2) & ![Y3]: (~r1(X2, Y3) | p8(Y3))) | p7(X2))) | (p8(Y2) | ~(p7(Y2) & (![X2]: (~r1(Y2, X2) | p7(X2)) & p7(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p8(Y2) & ![X2]: (~r1(Y2, X2) | p8(X2))) | (p7(Y2) | ![X2]: (~r1(Y2, X2) | (p8(X2) | ~(p7(X2) & (![Y3]: (~r1(X2, Y3) | p7(Y3)) & p7(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p8(Y2) & ![X2]: (~r1(Y2, X2) | p8(X2))) | (p7(Y2) | (p8(Y2) | ~(p7(Y2) & (![X2]: (~r1(Y2, X2) | p7(X2)) & p7(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p7(Y2) & ![X2]: (~r1(Y2, X2) | p7(X2))) | p6(Y2))) | (![Y2]: (~r1(X, Y2) | (p7(Y2) | ~(p6(Y2) & (![X2]: (~r1(Y2, X2) | p6(X2)) & p6(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p7(X2) & ![Y3]: (~r1(X2, Y3) | p7(Y3))) | p6(X2))) | (p7(Y2) | ~(p6(Y2) & (![X2]: (~r1(Y2, X2) | p6(X2)) & p6(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p7(Y2) & ![X2]: (~r1(Y2, X2) | p7(X2))) | (p6(Y2) | ![X2]: (~r1(Y2, X2) | (p7(X2) | ~(p6(X2) & (![Y3]: (~r1(X2, Y3) | p6(Y3)) & p6(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p7(Y2) & ![X2]: (~r1(Y2, X2) | p7(X2))) | (p6(Y2) | (p7(Y2) | ~(p6(Y2) & (![X2]: (~r1(Y2, X2) | p6(X2)) & p6(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p6(Y2) & ![X2]: (~r1(Y2, X2) | p6(X2))) | p5(Y2))) | (![Y2]: (~r1(X, Y2) | (p6(Y2) | ~(p5(Y2) & (![X2]: (~r1(Y2, X2) | p5(X2)) & p5(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p6(X2) & ![Y3]: (~r1(X2, Y3) | p6(Y3))) | p5(X2))) | (p6(Y2) | ~(p5(Y2) & (![X2]: (~r1(Y2, X2) | p5(X2)) & p5(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p6(Y2) & ![X2]: (~r1(Y2, X2) | p6(X2))) | (p5(Y2) | ![X2]: (~r1(Y2, X2) | (p6(X2) | ~(p5(X2) & (![Y3]: (~r1(X2, Y3) | p5(Y3)) & p5(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p6(Y2) & ![X2]: (~r1(Y2, X2) | p6(X2))) | (p5(Y2) | (p6(Y2) | ~(p5(Y2) & (![X2]: (~r1(Y2, X2) | p5(X2)) & p5(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p5(Y2) & ![X2]: (~r1(Y2, X2) | p5(X2))) | p4(Y2))) | (![Y2]: (~r1(X, Y2) | (p5(Y2) | ~(p4(Y2) & (![X2]: (~r1(Y2, X2) | p4(X2)) & p4(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p5(X2) & ![Y3]: (~r1(X2, Y3) | p5(Y3))) | p4(X2))) | (p5(Y2) | ~(p4(Y2) & (![X2]: (~r1(Y2, X2) | p4(X2)) & p4(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p5(Y2) & ![X2]: (~r1(Y2, X2) | p5(X2))) | (p4(Y2) | ![X2]: (~r1(Y2, X2) | (p5(X2) | ~(p4(X2) & (![Y3]: (~r1(X2, Y3) | p4(Y3)) & p4(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p5(Y2) & ![X2]: (~r1(Y2, X2) | p5(X2))) | (p4(Y2) | (p5(Y2) | ~(p4(Y2) & (![X2]: (~r1(Y2, X2) | p4(X2)) & p4(Y2))))))))))) | (![Y2]: (~r1(X, Y2) | (p10(Y2) | ~(![X2]: (~r1(Y2, X2) | p10(X2)) & p10(Y2)))) | (![Y2]: (~r1(X, Y2) | (p10(Y2) | ~(![X2]: (~r1(Y2, X2) | p10(X2)) & p10(Y2)))) | (~(![Y2]: (~r1(X, Y2) | (~(p4(Y2) & ![X2]: (~r1(Y2, X2) | p4(X2))) | p3(Y2))) | (![Y2]: (~r1(X, Y2) | (p4(Y2) | ~(p3(Y2) & (![X2]: (~r1(Y2, X2) | p3(X2)) & p3(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p4(X2) & ![Y3]: (~r1(X2, Y3) | p4(Y3))) | p3(X2))) | (p4(Y2) | ~(p3(Y2) & (![X2]: (~r1(Y2, X2) | p3(X2)) & p3(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p4(Y2) & ![X2]: (~r1(Y2, X2) | p4(X2))) | (p3(Y2) | ![X2]: (~r1(Y2, X2) | (p4(X2) | ~(p3(X2) & (![Y3]: (~r1(X2, Y3) | p3(Y3)) & p3(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p4(Y2) & ![X2]: (~r1(Y2, X2) | p4(X2))) | (p3(Y2) | (p4(Y2) | ~(p3(Y2) & (![X2]: (~r1(Y2, X2) | p3(X2)) & p3(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p3(Y2) & ![X2]: (~r1(Y2, X2) | p3(X2))) | p2(Y2))) | (![Y2]: (~r1(X, Y2) | (p3(Y2) | ~(p2(Y2) & (![X2]: (~r1(Y2, X2) | p2(X2)) & p2(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p3(X2) & ![Y3]: (~r1(X2, Y3) | p3(Y3))) | p2(X2))) | (p3(Y2) | ~(p2(Y2) & (![X2]: (~r1(Y2, X2) | p2(X2)) & p2(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p3(Y2) & ![X2]: (~r1(Y2, X2) | p3(X2))) | (p2(Y2) | ![X2]: (~r1(Y2, X2) | (p3(X2) | ~(p2(X2) & (![Y3]: (~r1(X2, Y3) | p2(Y3)) & p2(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p3(Y2) & ![X2]: (~r1(Y2, X2) | p3(X2))) | (p2(Y2) | (p3(Y2) | ~(p2(Y2) & (![X2]: (~r1(Y2, X2) | p2(X2)) & p2(Y2))))))))))) | ~(![Y2]: (~r1(X, Y2) | (~(p2(Y2) & ![X2]: (~r1(Y2, X2) | p2(X2))) | p1(Y2))) | (![Y2]: (~r1(X, Y2) | (p2(Y2) | ~(p1(Y2) & (![X2]: (~r1(Y2, X2) | p1(X2)) & p1(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p2(X2) & ![Y3]: (~r1(X2, Y3) | p2(Y3))) | p1(X2))) | (p2(Y2) | ~(p1(Y2) & (![X2]: (~r1(Y2, X2) | p1(X2)) & p1(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p2(Y2) & ![X2]: (~r1(Y2, X2) | p2(X2))) | (p1(Y2) | ![X2]: (~r1(Y2, X2) | (p2(X2) | ~(p1(X2) & (![Y3]: (~r1(X2, Y3) | p1(Y3)) & p1(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p2(Y2) & ![X2]: (~r1(Y2, X2) | p2(X2))) | (p1(Y2) | (p2(Y2) | ~(p1(Y2) & (![X2]: (~r1(Y2, X2) | p1(X2)) & p1(Y2))))))))))))))))))))))).
% 4.71/1.03
% 4.71/1.03 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.71/1.03 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.71/1.03 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.71/1.03 fresh(y, y, x1...xn) = u
% 4.71/1.03 C => fresh(s, t, x1...xn) = v
% 4.71/1.03 where fresh is a fresh function symbol and x1..xn are the free
% 4.71/1.03 variables of u and v.
% 4.71/1.03 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.71/1.03 input problem has no model of domain size 1).
% 4.71/1.03
% 4.71/1.03 The encoding turns the above axioms into the following unit equations and goals:
% 4.71/1.03
% 4.71/1.03 Axiom 1 (main_2): p10(y11) = true.
% 4.71/1.03 Axiom 2 (main_3): p10(y10) = true.
% 4.71/1.03
% 4.71/1.03 Goal 1 (main_116): p10(y10) = true.
% 4.71/1.03 Proof:
% 4.71/1.03 p10(y10)
% 4.71/1.03 = { by axiom 2 (main_3) }
% 4.71/1.03 true
% 4.71/1.03
% 4.71/1.03 Goal 2 (main_115): p10(y11) = true.
% 4.71/1.03 Proof:
% 4.71/1.03 p10(y11)
% 4.71/1.03 = { by axiom 1 (main_2) }
% 4.71/1.03 true
% 4.71/1.03 % SZS output end Proof
% 4.71/1.03
% 4.71/1.03 RESULT: Theorem (the conjecture is true).
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