TSTP Solution File: LCL644+1.005 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL644+1.005 : 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 : n029.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 0.22s 0.56s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL644+1.005 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.19/0.36 % Computer : n029.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Fri Aug 25 00:28:39 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.56 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.56
% 0.22/0.56 % SZS status Theorem
% 0.22/0.56
% 0.22/0.56 % SZS output start Proof
% 0.22/0.56 Take the following subset of the input axioms:
% 0.22/0.62 fof(main, conjecture, ~?[X]: ~(~(![Y]: (~r1(X, Y) | (~(p6(Y) & ![X2]: (~r1(Y, X2) | p6(X2))) | p5(Y))) | (![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) | (~(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) | (p5(Y2) | ~(![X2]: (~r1(Y2, X2) | p5(X2)) & p5(Y2)))) | (![Y2]: (~r1(X, Y2) | (p5(Y2) | ~(![X2]: (~r1(Y2, X2) | p5(X2)) & p5(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)))))))))))))))))).
% 0.22/0.62
% 0.22/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.62 fresh(y, y, x1...xn) = u
% 0.22/0.62 C => fresh(s, t, x1...xn) = v
% 0.22/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.62 variables of u and v.
% 0.22/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.62 input problem has no model of domain size 1).
% 0.22/0.62
% 0.22/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.62
% 0.22/0.62 Axiom 1 (main_2): p5(y5) = true.
% 0.22/0.62 Axiom 2 (main_3): p5(y4) = true.
% 0.22/0.62
% 0.22/0.62 Goal 1 (main_66): p5(y4) = true.
% 0.22/0.62 Proof:
% 0.22/0.62 p5(y4)
% 0.22/0.62 = { by axiom 2 (main_3) }
% 0.22/0.62 true
% 0.22/0.62
% 0.22/0.62 Goal 2 (main_65): p5(y5) = true.
% 0.22/0.62 Proof:
% 0.22/0.62 p5(y5)
% 0.22/0.62 = { by axiom 1 (main_2) }
% 0.22/0.62 true
% 0.22/0.62 % SZS output end Proof
% 0.22/0.62
% 0.22/0.62 RESULT: Theorem (the conjecture is true).
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