TSTP Solution File: PUZ037-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ037-1 : 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 : n031.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 0.20s 0.62s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ037-1 : TPTP v8.1.2. Released v2.3.0.
% 0.13/0.13 % 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 : n031.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 22:23:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 Command-line arguments: --no-flatten-goal
% 0.20/0.62
% 0.20/0.62 % SZS status Unsatisfiable
% 0.20/0.62
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 Take the following subset of the input axioms:
% 0.20/0.63 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)).
% 0.20/0.63 fof(myx, axiom, ![A1, 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, D8, D9, E1, E2, E3, E4, E5, E6]: (~state(A1, A2, A3, A4, A5, A6, A7, A8, A9, B1, B2, B3, B4, B5, B6, B7, B8, B9, C1, C2, C3, X1, X2, X3, X4, X5, X6, X7, X8, X9, Y1, Y2, Y3, C4, C5, C6, C7, C8, C9, D1, D2, D3, D4, D5, D6, D7, D8, D9, E1, E2, E3, E4, E5, E6) | state(A1, A2, A3, A4, A5, A6, A7, A8, A9, B1, B2, B3, B4, B5, B6, B7, B8, B9, C1, C2, C3, Y1, Y2, Y3, X1, X2, X3, X4, X5, X6, X7, X8, X9, C4, C5, C6, C7, C8, C9, D1, D2, D3, D4, D5, D6, D7, D8, D9, E1, E2, E3, E4, E5, E6))).
% 0.20/0.63 fof(start_with_this, hypothesis, state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w)).
% 0.20/0.63
% 0.20/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.63 fresh(y, y, x1...xn) = u
% 0.20/0.63 C => fresh(s, t, x1...xn) = v
% 0.20/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.63 variables of u and v.
% 0.20/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.63 input problem has no model of domain size 1).
% 0.20/0.63
% 0.20/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.63
% 0.20/0.63 Axiom 1 (start_with_this): state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w) = true.
% 0.20/0.63 Axiom 2 (myx): fresh8(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.
% 0.20/0.63 Axiom 3 (myx): fresh8(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, T4, S4, X5, U3, T3, S3, X4, Y4, Z4, W4, V4, U4, Y5, Z5, W5, V5, U5, T5, S5, X6, Y6, Z6, W6, V6, U6, T6, S6, X7, Y7, Z7, W7, V7, U7).
% 0.20/0.63
% 0.20/0.63 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.
% 0.20/0.63 Proof:
% 0.20/0.63 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)
% 0.20/0.63 = { by axiom 3 (myx) R->L }
% 0.20/0.63 fresh8(state(b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w), true, b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w)
% 0.20/0.63 = { by axiom 1 (start_with_this) }
% 0.20/0.63 fresh8(true, true, b, b, b, b, b, b, b, b, b, r, r, r, g, g, g, o, o, o, y, y, y, g, g, g, o, o, o, y, y, y, r, r, r, r, r, r, g, g, g, o, o, o, y, y, y, w, w, w, w, w, w, w, w, w)
% 0.20/0.63 = { by axiom 2 (myx) }
% 0.20/0.63 true
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63
% 0.20/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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