TSTP Solution File: PLA017-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PLA017-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n022.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 13:03:16 EDT 2023
% Result : Unsatisfiable 0.19s 0.75s
% Output : Proof 0.19s
% 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 : PLA017-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 06:11:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.75 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.75
% 0.19/0.75 % SZS status Unsatisfiable
% 0.19/0.75
% 0.19/0.76 % SZS output start Proof
% 0.19/0.76 Take the following subset of the input axioms:
% 0.19/0.76 fof(differ_a_c, axiom, differ(a, c)).
% 0.19/0.76 fof(differ_a_table, axiom, differ(a, table)).
% 0.19/0.76 fof(initial_state5, axiom, holds(clear(a), s0)).
% 0.19/0.76 fof(initial_state7, axiom, holds(clear(c), s0)).
% 0.19/0.76 fof(initial_state8, axiom, holds(empty, s0)).
% 0.19/0.76 fof(pickup_1, axiom, ![X, State]: (holds(holding(X), do(pickup(X), State)) | (~holds(empty, State) | (~holds(clear(X), State) | ~differ(X, table))))).
% 0.19/0.76 fof(pickup_4, axiom, ![Z, X2, State2]: (holds(clear(X2), do(pickup(Z), State2)) | (~holds(clear(X2), State2) | ~differ(X2, Z)))).
% 0.19/0.76 fof(prove_AC, negated_conjecture, ![State2]: ~holds(on(a, c), State2)).
% 0.19/0.76 fof(putdown_2, axiom, ![Y, X2, State2]: (holds(on(X2, Y), do(putdown(X2, Y), State2)) | (~holds(holding(X2), State2) | ~holds(clear(Y), State2)))).
% 0.19/0.76 fof(symmetry_of_differ, axiom, ![X2, Y2]: (differ(X2, Y2) | ~differ(Y2, X2))).
% 0.19/0.76
% 0.19/0.76 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.76 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.76 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.76 fresh(y, y, x1...xn) = u
% 0.19/0.76 C => fresh(s, t, x1...xn) = v
% 0.19/0.76 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.76 variables of u and v.
% 0.19/0.76 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.76 input problem has no model of domain size 1).
% 0.19/0.76
% 0.19/0.76 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.76
% 0.19/0.76 Axiom 1 (initial_state8): holds(empty, s0) = true2.
% 0.19/0.76 Axiom 2 (differ_a_table): differ(a, table) = true2.
% 0.19/0.76 Axiom 3 (differ_a_c): differ(a, c) = true2.
% 0.19/0.76 Axiom 4 (initial_state5): holds(clear(a), s0) = true2.
% 0.19/0.76 Axiom 5 (initial_state7): holds(clear(c), s0) = true2.
% 0.19/0.76 Axiom 6 (symmetry_of_differ): fresh(X, X, Y, Z) = true2.
% 0.19/0.76 Axiom 7 (pickup_1): fresh22(X, X, Y, Z) = true2.
% 0.19/0.76 Axiom 8 (pickup_4): fresh11(X, X, Y, Z, W) = true2.
% 0.19/0.76 Axiom 9 (putdown_2): fresh7(X, X, Y, Z, W) = true2.
% 0.19/0.76 Axiom 10 (pickup_4): fresh12(X, X, Y, Z, W) = holds(clear(Y), do(pickup(Z), W)).
% 0.19/0.76 Axiom 11 (pickup_1): fresh16(X, X, Y, Z) = holds(holding(Y), do(pickup(Y), Z)).
% 0.19/0.76 Axiom 12 (symmetry_of_differ): fresh(differ(X, Y), true2, Y, X) = differ(Y, X).
% 0.19/0.76 Axiom 13 (pickup_1): fresh21(X, X, Y, Z) = fresh22(holds(empty, Z), true2, Y, Z).
% 0.19/0.76 Axiom 14 (pickup_1): fresh21(differ(X, table), true2, X, Y) = fresh16(holds(clear(X), Y), true2, X, Y).
% 0.19/0.76 Axiom 15 (putdown_2): fresh8(X, X, Y, Z, W) = holds(on(Y, Z), do(putdown(Y, Z), W)).
% 0.19/0.76 Axiom 16 (pickup_4): fresh12(differ(X, Y), true2, X, Y, Z) = fresh11(holds(clear(X), Z), true2, X, Y, Z).
% 0.19/0.76 Axiom 17 (putdown_2): fresh8(holds(clear(X), Y), true2, Z, X, Y) = fresh7(holds(holding(Z), Y), true2, Z, X, Y).
% 0.19/0.76
% 0.19/0.76 Goal 1 (prove_AC): holds(on(a, c), X) = true2.
% 0.19/0.76 The goal is true when:
% 0.19/0.76 X = do(putdown(a, c), do(pickup(a), s0))
% 0.19/0.76
% 0.19/0.76 Proof:
% 0.19/0.76 holds(on(a, c), do(putdown(a, c), do(pickup(a), s0)))
% 0.19/0.76 = { by axiom 15 (putdown_2) R->L }
% 0.19/0.76 fresh8(true2, true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 8 (pickup_4) R->L }
% 0.19/0.76 fresh8(fresh11(true2, true2, c, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 5 (initial_state7) R->L }
% 0.19/0.76 fresh8(fresh11(holds(clear(c), s0), true2, c, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 16 (pickup_4) R->L }
% 0.19/0.76 fresh8(fresh12(differ(c, a), true2, c, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 12 (symmetry_of_differ) R->L }
% 0.19/0.76 fresh8(fresh12(fresh(differ(a, c), true2, c, a), true2, c, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 3 (differ_a_c) }
% 0.19/0.76 fresh8(fresh12(fresh(true2, true2, c, a), true2, c, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 6 (symmetry_of_differ) }
% 0.19/0.76 fresh8(fresh12(true2, true2, c, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 10 (pickup_4) }
% 0.19/0.76 fresh8(holds(clear(c), do(pickup(a), s0)), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 17 (putdown_2) }
% 0.19/0.76 fresh7(holds(holding(a), do(pickup(a), s0)), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 11 (pickup_1) R->L }
% 0.19/0.76 fresh7(fresh16(true2, true2, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 4 (initial_state5) R->L }
% 0.19/0.76 fresh7(fresh16(holds(clear(a), s0), true2, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 14 (pickup_1) R->L }
% 0.19/0.76 fresh7(fresh21(differ(a, table), true2, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 2 (differ_a_table) }
% 0.19/0.76 fresh7(fresh21(true2, true2, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 13 (pickup_1) }
% 0.19/0.76 fresh7(fresh22(holds(empty, s0), true2, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 1 (initial_state8) }
% 0.19/0.76 fresh7(fresh22(true2, true2, a, s0), true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 7 (pickup_1) }
% 0.19/0.76 fresh7(true2, true2, a, c, do(pickup(a), s0))
% 0.19/0.76 = { by axiom 9 (putdown_2) }
% 0.19/0.76 true2
% 0.19/0.76 % SZS output end Proof
% 0.19/0.76
% 0.19/0.76 RESULT: Unsatisfiable (the axioms are contradictory).
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