TSTP Solution File: PUZ037-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ037-2 : TPTP v8.1.2. Released v2.3.0.
% 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 : n017.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 13:24:02 EDT 2023
% Result : Unsatisfiable 3.54s 0.85s
% Output : Proof 3.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ037-2 : TPTP v8.1.2. Released v2.3.0.
% 0.07/0.13 % 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 : n017.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 : Sat Aug 26 21:58:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.54/0.85 Command-line arguments: --ground-connectedness --complete-subsets
% 3.54/0.85
% 3.54/0.85 % SZS status Unsatisfiable
% 3.54/0.85
% 3.54/0.87 % SZS output start Proof
% 3.54/0.87 Take the following subset of the input axioms:
% 3.54/0.87 fof(lzx, axiom, ![W7, W6, W5, W8, A1, W4, W1, W2, W3, Y1, Y2, Y3, X1, X2, X3, X4, X5, X6, X7, X8, X9, A2, A3, A4, A5, A6, A7, A8, A9, B1, B2, B3, B4, B5, B6, B7, B8, B9, C1, C2, C3, C4, C5, C6, C7, C8, C9, D1, D2, D3, D4, D5, D6, D7]: (~state(Y1, A1, A2, Y2, A3, A4, Y3, A5, A6, W7, W8, W1, X1, A7, A8, A9, B1, B2, B3, B4, X9, W6, B5, W2, X2, B6, B7, B8, B9, C1, C2, C3, X8, W5, W4, W3, X3, C4, C5, C6, C7, C8, C9, D1, X7, X4, D2, D3, X5, D4, D5, X6, D6, D7) | state(X1, A1, A2, X2, A3, A4, X3, A5, A6, W1, W2, W3, X4, A7, A8, A9, B1, B2, B3, B4, Y3, W8, B5, W4, X5, B6, B7, B8, B9, C1, C2, C3, Y2, W7, W6, W5, X6, C4, C5, C6, C7, C8, C9, D1, Y1, X7, D2, D3, X8, D4, D5, X9, D6, D7))).
% 3.54/0.87 fof(make_like_this, negated_conjecture, ~state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w)).
% 3.54/0.87 fof(mxy, axiom, ![D8, D9, E1, E2, E3, E4, E5, E6, A1_2, Y1_2, Y2_2, Y3_2, X1_2, X2_2, X3_2, X4_2, X5_2, X6_2, X7_2, X8_2, X9_2, A2_2, A3_2, A4_2, A5_2, A6_2, A7_2, A8_2, A9_2, B1_2, B2_2, B3_2, B4_2, B5_2, B6_2, B7_2, B8_2, B9_2, C1_2, C2_2, C3_2, C4_2, C5_2, C6_2, C7_2, C8_2, C9_2, D1_2, D2_2, D3_2, D4_2, D5_2, D6_2, D7_2]: (~state(A1_2, A2_2, A3_2, A4_2, A5_2, A6_2, A7_2, A8_2, A9_2, B1_2, B2_2, B3_2, B4_2, B5_2, B6_2, B7_2, B8_2, B9_2, C1_2, C2_2, C3_2, Y1_2, Y2_2, Y3_2, X1_2, X2_2, X3_2, X4_2, X5_2, X6_2, X7_2, X8_2, X9_2, C4_2, C5_2, C6_2, C7_2, C8_2, C9_2, D1_2, D2_2, D3_2, D4_2, D5_2, D6_2, D7_2, D8, D9, E1, E2, E3, E4, E5, E6) | state(A1_2, A2_2, A3_2, A4_2, A5_2, A6_2, A7_2, A8_2, A9_2, B1_2, B2_2, B3_2, B4_2, B5_2, B6_2, B7_2, B8_2, B9_2, C1_2, C2_2, C3_2, X1_2, X2_2, X3_2, X4_2, X5_2, X6_2, X7_2, X8_2, X9_2, Y1_2, Y2_2, Y3_2, C4_2, C5_2, C6_2, C7_2, C8_2, C9_2, D1_2, D2_2, D3_2, D4_2, D5_2, D6_2, D7_2, D8, D9, E1, E2, E3, E4, E5, E6))).
% 3.54/0.87 fof(rzx, axiom, ![W7_2, W6_2, W5_2, W8_2, A1_2, W4_2, W1_2, W2_2, W3_2, Y1_2, Y2_2, Y3_2, X1_2, X2_2, X3_2, X4_2, X5_2, X6_2, X7_2, X8_2, X9_2, A2_2, A3_2, A4_2, A5_2, A6_2, A7_2, A8_2, A9_2, B1_2, B2_2, B3_2, B4_2, B5_2, B6_2, B7_2, B8_2, B9_2, C1_2, C2_2, C3_2, C4_2, C5_2, C6_2, C7_2, C8_2, C9_2, D1_2, D2_2, D3_2, D4_2, D5_2, D6_2, D7_2]: (~state(A1_2, A2_2, Y1_2, A3_2, A4_2, Y2_2, A5_2, A6_2, Y3_2, A7_2, A8_2, A9_2, B1_2, B2_2, X1_2, W1_2, W8_2, W7_2, X9_2, B3_2, B4_2, B5_2, B6_2, B7_2, B8_2, B9_2, X2_2, W2_2, C1_2, W6_2, X8_2, C2_2, C3_2, C4_2, C5_2, C6_2, C7_2, C8_2, X3_2, W3_2, W4_2, W5_2, X7_2, C9_2, D1_2, D2_2, D3_2, X4_2, D4_2, D5_2, X5_2, D6_2, D7_2, X6_2) | state(A1_2, A2_2, X1_2, A3_2, A4_2, X2_2, A5_2, A6_2, X3_2, A7_2, A8_2, A9_2, B1_2, B2_2, X4_2, W3_2, W2_2, W1_2, Y3_2, B3_2, B4_2, B5_2, B6_2, B7_2, B8_2, B9_2, X5_2, W4_2, C1_2, W8_2, Y2_2, C2_2, C3_2, C4_2, C5_2, C6_2, C7_2, C8_2, X6_2, W5_2, W6_2, W7_2, Y1_2, C9_2, D1_2, D2_2, D3_2, X7_2, D4_2, D5_2, X8_2, D6_2, D7_2, X9_2))).
% 3.54/0.87 fof(start_with_this, hypothesis, state(y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, w, y, w, r, r, r, b, g, b, o, o, o, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g)).
% 3.54/0.87
% 3.54/0.87 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.54/0.87 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.54/0.87 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.54/0.87 fresh(y, y, x1...xn) = u
% 3.54/0.87 C => fresh(s, t, x1...xn) = v
% 3.54/0.87 where fresh is a fresh function symbol and x1..xn are the free
% 3.54/0.87 variables of u and v.
% 3.54/0.87 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.54/0.87 input problem has no model of domain size 1).
% 3.54/0.87
% 3.54/0.87 The encoding turns the above axioms into the following unit equations and goals:
% 3.54/0.87
% 3.54/0.87 Axiom 1 (start_with_this): state(y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, w, y, w, r, r, r, b, g, b, o, o, o, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g) = true.
% 3.54/0.87 Axiom 2 (lzx): fresh11(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7, T7) = true.
% 3.54/0.87 Axiom 3 (mxy): fresh10(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7, T7) = true.
% 3.54/0.87 Axiom 4 (rzx): fresh3(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7, T7) = true.
% 3.54/0.87 Axiom 5 (lzx): fresh11(state(X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7), true, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7) = state(V2, Y, Z, X4, V, U, V5, S, X2, W2, S3, W5, U6, U2, T2, S2, X3, Y3, Z3, W3, T, Z2, T3, Z5, X7, Y4, Z4, W4, V4, U4, T4, S4, W, Y2, U3, Y5, W7, U5, T5, S5, X6, Y6, Z6, W6, X, V6, T6, S6, X5, Y7, Z7, V3, V7, U7).
% 3.54/0.87 Axiom 6 (mxy): fresh10(state(X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7), true, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7) = state(X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, U3, T3, S3, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7).
% 3.54/0.87 Axiom 7 (rzx): fresh3(state(X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7), true, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2, U2, T2, S2, X3, Y3, Z3, W3, V3, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, T4, S4, X5, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7) = state(X, Y, T2, W, V, Z4, T, S, T5, Y2, Z2, W2, V2, U2, S6, S5, W4, S2, X2, W3, V3, U3, T3, S3, X4, Y4, Z7, X6, V4, X3, U, S4, X5, Y5, Z5, W5, V5, U5, U7, Y6, U4, Y3, Z, W6, V6, U6, T6, Z6, X7, Y7, T4, W7, V7, Z3).
% 3.54/0.87
% 3.54/0.87 Goal 1 (make_like_this): state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) = true.
% 3.54/0.87 Proof:
% 3.54/0.87 state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w)
% 3.54/0.87 = { by axiom 7 (rzx) R->L }
% 3.54/0.87 fresh3(state(b, b, y, b, b, y, b, b, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, w, w, g, w, w, g, w, w, g), true, b, b, y, b, b, y, b, b, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, w, w, g, w, w, g, w, w, g)
% 3.54/0.87 = { by axiom 5 (lzx) R->L }
% 3.54/0.87 fresh3(fresh11(state(y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, b, b, y, b, b, y, b, b, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, w, w, g, w, w, g, w, w, g)
% 3.54/0.87 = { by axiom 6 (mxy) R->L }
% 3.54/0.87 fresh3(fresh11(fresh10(state(y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, w, y, w, r, r, r, b, g, b, o, o, o, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, w, y, w, r, r, r, b, g, b, o, o, o, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, b, b, y, b, b, y, b, b, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, w, w, g, w, w, g, w, w, g)
% 3.54/0.87 = { by axiom 1 (start_with_this) }
% 3.54/0.87 fresh3(fresh11(fresh10(true, true, y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, w, y, w, r, r, r, b, g, b, o, o, o, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, b, b, y, b, b, y, b, b, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, w, w, g, w, w, g, w, w, g)
% 3.54/0.87 = { by axiom 3 (mxy) }
% 3.54/0.87 fresh3(fresh11(true, true, y, b, y, y, b, y, y, b, y, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, r, r, r, b, g, b, o, o, o, w, y, w, g, w, g, g, w, g, g, w, g), true, b, b, y, b, b, y, b, b, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, w, w, g, w, w, g, w, w, g)
% 3.54/0.87 = { by axiom 2 (lzx) }
% 3.54/0.88 fresh3(true, true, b, b, y, b, b, y, b, b, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, r, r, r, g, g, b, o, o, o, w, y, y, w, w, g, w, w, g, w, w, g)
% 3.54/0.88 = { by axiom 4 (rzx) }
% 3.54/0.88 true
% 3.54/0.88 % SZS output end Proof
% 3.54/0.88
% 3.54/0.88 RESULT: Unsatisfiable (the axioms are contradictory).
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