TSTP Solution File: LCL644+1.020 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL644+1.020 : 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 08:19:42 EDT 2023
% Result : Theorem 12.42s 2.01s
% Output : Proof 14.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL644+1.020 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu Aug 24 19:55:23 EDT 2023
% 0.16/0.36 % CPUTime :
% 12.42/2.01 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 12.42/2.01
% 12.42/2.01 % SZS status Theorem
% 12.42/2.01
% 12.42/2.01 % SZS output start Proof
% 12.42/2.01 Take the following subset of the input axioms:
% 14.97/2.47 fof(main, conjecture, ~?[X]: ~(~(![Y]: (~r1(X, Y) | (~(p21(Y) & ![X2]: (~r1(Y, X2) | p21(X2))) | p20(Y))) | (![Y2]: (~r1(X, Y2) | (p21(Y2) | ~(p20(Y2) & (![X2]: (~r1(Y2, X2) | p20(X2)) & p20(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p21(X2) & ![Y3]: (~r1(X2, Y3) | p21(Y3))) | p20(X2))) | (p21(Y2) | ~(p20(Y2) & (![X2]: (~r1(Y2, X2) | p20(X2)) & p20(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p21(Y2) & ![X2]: (~r1(Y2, X2) | p21(X2))) | (p20(Y2) | ![X2]: (~r1(Y2, X2) | (p21(X2) | ~(p20(X2) & (![Y3]: (~r1(X2, Y3) | p20(Y3)) & p20(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p21(Y2) & ![X2]: (~r1(Y2, X2) | p21(X2))) | (p20(Y2) | (p21(Y2) | ~(p20(Y2) & (![X2]: (~r1(Y2, X2) | p20(X2)) & p20(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p20(Y2) & ![X2]: (~r1(Y2, X2) | p20(X2))) | p19(Y2))) | (![Y2]: (~r1(X, Y2) | (p20(Y2) | ~(p19(Y2) & (![X2]: (~r1(Y2, X2) | p19(X2)) & p19(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p20(X2) & ![Y3]: (~r1(X2, Y3) | p20(Y3))) | p19(X2))) | (p20(Y2) | ~(p19(Y2) & (![X2]: (~r1(Y2, X2) | p19(X2)) & p19(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p20(Y2) & ![X2]: (~r1(Y2, X2) | p20(X2))) | (p19(Y2) | ![X2]: (~r1(Y2, X2) | (p20(X2) | ~(p19(X2) & (![Y3]: (~r1(X2, Y3) | p19(Y3)) & p19(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p20(Y2) & ![X2]: (~r1(Y2, X2) | p20(X2))) | (p19(Y2) | (p20(Y2) | ~(p19(Y2) & (![X2]: (~r1(Y2, X2) | p19(X2)) & p19(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p19(Y2) & ![X2]: (~r1(Y2, X2) | p19(X2))) | p18(Y2))) | (![Y2]: (~r1(X, Y2) | (p19(Y2) | ~(p18(Y2) & (![X2]: (~r1(Y2, X2) | p18(X2)) & p18(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p19(X2) & ![Y3]: (~r1(X2, Y3) | p19(Y3))) | p18(X2))) | (p19(Y2) | ~(p18(Y2) & (![X2]: (~r1(Y2, X2) | p18(X2)) & p18(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p19(Y2) & ![X2]: (~r1(Y2, X2) | p19(X2))) | (p18(Y2) | ![X2]: (~r1(Y2, X2) | (p19(X2) | ~(p18(X2) & (![Y3]: (~r1(X2, Y3) | p18(Y3)) & p18(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p19(Y2) & ![X2]: (~r1(Y2, X2) | p19(X2))) | (p18(Y2) | (p19(Y2) | ~(p18(Y2) & (![X2]: (~r1(Y2, X2) | p18(X2)) & p18(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p18(Y2) & ![X2]: (~r1(Y2, X2) | p18(X2))) | p17(Y2))) | (![Y2]: (~r1(X, Y2) | (p18(Y2) | ~(p17(Y2) & (![X2]: (~r1(Y2, X2) | p17(X2)) & p17(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p18(X2) & ![Y3]: (~r1(X2, Y3) | p18(Y3))) | p17(X2))) | (p18(Y2) | ~(p17(Y2) & (![X2]: (~r1(Y2, X2) | p17(X2)) & p17(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p18(Y2) & ![X2]: (~r1(Y2, X2) | p18(X2))) | (p17(Y2) | ![X2]: (~r1(Y2, X2) | (p18(X2) | ~(p17(X2) & (![Y3]: (~r1(X2, Y3) | p17(Y3)) & p17(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p18(Y2) & ![X2]: (~r1(Y2, X2) | p18(X2))) | (p17(Y2) | (p18(Y2) | ~(p17(Y2) & (![X2]: (~r1(Y2, X2) | p17(X2)) & p17(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p17(Y2) & ![X2]: (~r1(Y2, X2) | p17(X2))) | p16(Y2))) | (![Y2]: (~r1(X, Y2) | (p17(Y2) | ~(p16(Y2) & (![X2]: (~r1(Y2, X2) | p16(X2)) & p16(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p17(X2) & ![Y3]: (~r1(X2, Y3) | p17(Y3))) | p16(X2))) | (p17(Y2) | ~(p16(Y2) & (![X2]: (~r1(Y2, X2) | p16(X2)) & p16(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p17(Y2) & ![X2]: (~r1(Y2, X2) | p17(X2))) | (p16(Y2) | ![X2]: (~r1(Y2, X2) | (p17(X2) | ~(p16(X2) & (![Y3]: (~r1(X2, Y3) | p16(Y3)) & p16(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p17(Y2) & ![X2]: (~r1(Y2, X2) | p17(X2))) | (p16(Y2) | (p17(Y2) | ~(p16(Y2) & (![X2]: (~r1(Y2, X2) | p16(X2)) & p16(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p16(Y2) & ![X2]: (~r1(Y2, X2) | p16(X2))) | p15(Y2))) | (![Y2]: (~r1(X, Y2) | (p16(Y2) | ~(p15(Y2) & (![X2]: (~r1(Y2, X2) | p15(X2)) & p15(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p16(X2) & ![Y3]: (~r1(X2, Y3) | p16(Y3))) | p15(X2))) | (p16(Y2) | ~(p15(Y2) & (![X2]: (~r1(Y2, X2) | p15(X2)) & p15(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p16(Y2) & ![X2]: (~r1(Y2, X2) | p16(X2))) | (p15(Y2) | ![X2]: (~r1(Y2, X2) | (p16(X2) | ~(p15(X2) & (![Y3]: (~r1(X2, Y3) | p15(Y3)) & p15(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p16(Y2) & ![X2]: (~r1(Y2, X2) | p16(X2))) | (p15(Y2) | (p16(Y2) | ~(p15(Y2) & (![X2]: (~r1(Y2, X2) | p15(X2)) & p15(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p15(Y2) & ![X2]: (~r1(Y2, X2) | p15(X2))) | p14(Y2))) | (![Y2]: (~r1(X, Y2) | (p15(Y2) | ~(p14(Y2) & (![X2]: (~r1(Y2, X2) | p14(X2)) & p14(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p15(X2) & ![Y3]: (~r1(X2, Y3) | p15(Y3))) | p14(X2))) | (p15(Y2) | ~(p14(Y2) & (![X2]: (~r1(Y2, X2) | p14(X2)) & p14(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p15(Y2) & ![X2]: (~r1(Y2, X2) | p15(X2))) | (p14(Y2) | ![X2]: (~r1(Y2, X2) | (p15(X2) | ~(p14(X2) & (![Y3]: (~r1(X2, Y3) | p14(Y3)) & p14(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p15(Y2) & ![X2]: (~r1(Y2, X2) | p15(X2))) | (p14(Y2) | (p15(Y2) | ~(p14(Y2) & (![X2]: (~r1(Y2, X2) | p14(X2)) & p14(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p14(Y2) & ![X2]: (~r1(Y2, X2) | p14(X2))) | p13(Y2))) | (![Y2]: (~r1(X, Y2) | (p14(Y2) | ~(p13(Y2) & (![X2]: (~r1(Y2, X2) | p13(X2)) & p13(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p14(X2) & ![Y3]: (~r1(X2, Y3) | p14(Y3))) | p13(X2))) | (p14(Y2) | ~(p13(Y2) & (![X2]: (~r1(Y2, X2) | p13(X2)) & p13(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p14(Y2) & ![X2]: (~r1(Y2, X2) | p14(X2))) | (p13(Y2) | ![X2]: (~r1(Y2, X2) | (p14(X2) | ~(p13(X2) & (![Y3]: (~r1(X2, Y3) | p13(Y3)) & p13(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p14(Y2) & ![X2]: (~r1(Y2, X2) | p14(X2))) | (p13(Y2) | (p14(Y2) | ~(p13(Y2) & (![X2]: (~r1(Y2, X2) | p13(X2)) & p13(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p13(Y2) & ![X2]: (~r1(Y2, X2) | p13(X2))) | p12(Y2))) | (![Y2]: (~r1(X, Y2) | (p13(Y2) | ~(p12(Y2) & (![X2]: (~r1(Y2, X2) | p12(X2)) & p12(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p13(X2) & ![Y3]: (~r1(X2, Y3) | p13(Y3))) | p12(X2))) | (p13(Y2) | ~(p12(Y2) & (![X2]: (~r1(Y2, X2) | p12(X2)) & p12(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p13(Y2) & ![X2]: (~r1(Y2, X2) | p13(X2))) | (p12(Y2) | ![X2]: (~r1(Y2, X2) | (p13(X2) | ~(p12(X2) & (![Y3]: (~r1(X2, Y3) | p12(Y3)) & p12(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p13(Y2) & ![X2]: (~r1(Y2, X2) | p13(X2))) | (p12(Y2) | (p13(Y2) | ~(p12(Y2) & (![X2]: (~r1(Y2, X2) | p12(X2)) & p12(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p12(Y2) & ![X2]: (~r1(Y2, X2) | p12(X2))) | p11(Y2))) | (![Y2]: (~r1(X, Y2) | (p12(Y2) | ~(p11(Y2) & (![X2]: (~r1(Y2, X2) | p11(X2)) & p11(Y2))))) | ~(![Y2]: (~r1(X, Y2) | (![X2]: (~r1(Y2, X2) | (~(p12(X2) & ![Y3]: (~r1(X2, Y3) | p12(Y3))) | p11(X2))) | (p12(Y2) | ~(p11(Y2) & (![X2]: (~r1(Y2, X2) | p11(X2)) & p11(Y2)))))) & (![Y2]: (~r1(X, Y2) | (~(p12(Y2) & ![X2]: (~r1(Y2, X2) | p12(X2))) | (p11(Y2) | ![X2]: (~r1(Y2, X2) | (p12(X2) | ~(p11(X2) & (![Y3]: (~r1(X2, Y3) | p11(Y3)) & p11(X2)))))))) & ![Y2]: (~r1(X, Y2) | (~(p12(Y2) & ![X2]: (~r1(Y2, X2) | p12(X2))) | (p11(Y2) | (p12(Y2) | ~(p11(Y2) & (![X2]: (~r1(Y2, X2) | p11(X2)) & p11(Y2))))))))))) | (~(![Y2]: (~r1(X, Y2) | (~(p11(Y2) & ![X2]: (~r1(Y2, X2) | p11(X2))) | p10(Y2))) | (![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) | (p20(Y2) | ~(![X2]: (~r1(Y2, X2) | p20(X2)) & p20(Y2)))) | (![Y2]: (~r1(X, Y2) | (p20(Y2) | ~(![X2]: (~r1(Y2, X2) | p20(X2)) & p20(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) | (~(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))))))))))))))))))))))))))))))))).
% 14.97/2.47
% 14.97/2.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 14.97/2.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 14.97/2.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 14.97/2.47 fresh(y, y, x1...xn) = u
% 14.97/2.47 C => fresh(s, t, x1...xn) = v
% 14.97/2.47 where fresh is a fresh function symbol and x1..xn are the free
% 14.97/2.47 variables of u and v.
% 14.97/2.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 14.97/2.47 input problem has no model of domain size 1).
% 14.97/2.47
% 14.97/2.47 The encoding turns the above axioms into the following unit equations and goals:
% 14.97/2.47
% 14.97/2.47 Axiom 1 (main_2): p20(y20) = true.
% 14.97/2.47 Axiom 2 (main_3): p20(y19) = true.
% 14.97/2.47
% 14.97/2.47 Goal 1 (main_216): p20(y19) = true.
% 14.97/2.47 Proof:
% 14.97/2.47 p20(y19)
% 14.97/2.47 = { by axiom 2 (main_3) }
% 14.97/2.47 true
% 14.97/2.47
% 14.97/2.47 Goal 2 (main_215): p20(y20) = true.
% 14.97/2.47 Proof:
% 14.97/2.47 p20(y20)
% 14.97/2.47 = { by axiom 1 (main_2) }
% 14.97/2.47 true
% 14.97/2.47 % SZS output end Proof
% 14.97/2.47
% 14.97/2.47 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------