TSTP Solution File: PLA006-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PLA006-1 : 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 : 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 13:03:13 EDT 2023
% Result : Unsatisfiable 16.93s 2.52s
% Output : Proof 16.93s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : PLA006-1 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 06:37:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 16.93/2.52 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 16.93/2.52
% 16.93/2.52 % SZS status Unsatisfiable
% 16.93/2.52
% 16.93/2.52 % SZS output start Proof
% 16.93/2.52 Take the following subset of the input axioms:
% 16.93/2.52 fof(clear_table, axiom, ![State]: holds(clear(table), State)).
% 16.93/2.52 fof(differ_c_table, axiom, differ(c, table)).
% 16.93/2.52 fof(initial_state7, axiom, holds(clear(c), s0)).
% 16.93/2.52 fof(initial_state8, axiom, holds(empty, s0)).
% 16.93/2.52 fof(pickup_1, axiom, ![X, State2]: (holds(holding(X), do(pickup(X), State2)) | (~holds(empty, State2) | (~holds(clear(X), State2) | ~differ(X, table))))).
% 16.93/2.52 fof(prove_CTable, negated_conjecture, ![State2]: ~holds(on(c, table), State2)).
% 16.93/2.52 fof(putdown_2, axiom, ![Y, X2, State2]: (holds(on(X2, Y), do(putdown(X2, Y), State2)) | (~holds(holding(X2), State2) | ~holds(clear(Y), State2)))).
% 16.93/2.52
% 16.93/2.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.93/2.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.93/2.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.93/2.52 fresh(y, y, x1...xn) = u
% 16.93/2.52 C => fresh(s, t, x1...xn) = v
% 16.93/2.52 where fresh is a fresh function symbol and x1..xn are the free
% 16.93/2.52 variables of u and v.
% 16.93/2.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.93/2.52 input problem has no model of domain size 1).
% 16.93/2.52
% 16.93/2.52 The encoding turns the above axioms into the following unit equations and goals:
% 16.93/2.52
% 16.93/2.52 Axiom 1 (initial_state8): holds(empty, s0) = true2.
% 16.93/2.52 Axiom 2 (differ_c_table): differ(c, table) = true2.
% 16.93/2.52 Axiom 3 (clear_table): holds(clear(table), X) = true2.
% 16.93/2.52 Axiom 4 (initial_state7): holds(clear(c), s0) = true2.
% 16.93/2.52 Axiom 5 (pickup_1): fresh22(X, X, Y, Z) = true2.
% 16.93/2.52 Axiom 6 (putdown_2): fresh7(X, X, Y, Z, W) = true2.
% 16.93/2.52 Axiom 7 (pickup_1): fresh16(X, X, Y, Z) = holds(holding(Y), do(pickup(Y), Z)).
% 16.93/2.52 Axiom 8 (pickup_1): fresh21(X, X, Y, Z) = fresh22(holds(empty, Z), true2, Y, Z).
% 16.93/2.52 Axiom 9 (pickup_1): fresh21(differ(X, table), true2, X, Y) = fresh16(holds(clear(X), Y), true2, X, Y).
% 16.93/2.52 Axiom 10 (putdown_2): fresh8(X, X, Y, Z, W) = holds(on(Y, Z), do(putdown(Y, Z), W)).
% 16.93/2.52 Axiom 11 (putdown_2): fresh8(holds(clear(X), Y), true2, Z, X, Y) = fresh7(holds(holding(Z), Y), true2, Z, X, Y).
% 16.93/2.52
% 16.93/2.52 Goal 1 (prove_CTable): holds(on(c, table), X) = true2.
% 16.93/2.52 The goal is true when:
% 16.93/2.52 X = do(putdown(c, table), do(pickup(c), s0))
% 16.93/2.52
% 16.93/2.52 Proof:
% 16.93/2.52 holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))
% 16.93/2.52 = { by axiom 10 (putdown_2) R->L }
% 16.93/2.52 fresh8(true2, true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 3 (clear_table) R->L }
% 16.93/2.52 fresh8(holds(clear(table), do(pickup(c), s0)), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 11 (putdown_2) }
% 16.93/2.52 fresh7(holds(holding(c), do(pickup(c), s0)), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 7 (pickup_1) R->L }
% 16.93/2.52 fresh7(fresh16(true2, true2, c, s0), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 4 (initial_state7) R->L }
% 16.93/2.52 fresh7(fresh16(holds(clear(c), s0), true2, c, s0), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 9 (pickup_1) R->L }
% 16.93/2.52 fresh7(fresh21(differ(c, table), true2, c, s0), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 2 (differ_c_table) }
% 16.93/2.52 fresh7(fresh21(true2, true2, c, s0), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 8 (pickup_1) }
% 16.93/2.52 fresh7(fresh22(holds(empty, s0), true2, c, s0), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 1 (initial_state8) }
% 16.93/2.52 fresh7(fresh22(true2, true2, c, s0), true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 5 (pickup_1) }
% 16.93/2.52 fresh7(true2, true2, c, table, do(pickup(c), s0))
% 16.93/2.52 = { by axiom 6 (putdown_2) }
% 16.93/2.52 true2
% 16.93/2.52 % SZS output end Proof
% 16.93/2.52
% 16.93/2.52 RESULT: Unsatisfiable (the axioms are contradictory).
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