TSTP Solution File: COM002_1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COM002_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n005.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 : Wed Aug 30 18:45:17 EDT 2023
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COM002_1 : TPTP v8.1.2. Released v5.0.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 12:59:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.41 Command-line arguments: --no-flatten-goal
% 0.21/0.41
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Take the following subset of the input axioms:
% 0.21/0.42 fof(direct_success, axiom, ![Start_state, Goal_state]: (follows(Goal_state, Start_state) => succeeds(Goal_state, Start_state))).
% 0.21/0.42 fof(goto_success, axiom, ![Label, Start_state2, Goal_state2]: ((has(Start_state2, goto(Label)) & labels(Label, Goal_state2)) => succeeds(Goal_state2, Start_state2))).
% 0.21/0.42 fof(label_state_3, hypothesis, labels(loop, p3)).
% 0.21/0.42 fof(prove_there_is_a_loop_through_p3, conjecture, succeeds(p3, p3)).
% 0.21/0.42 fof(state_8, hypothesis, has(p8, goto(loop))).
% 0.21/0.42 fof(transition_3_to_6, hypothesis, follows(p6, p3)).
% 0.21/0.42 fof(transition_6_to_7, hypothesis, follows(p7, p6)).
% 0.21/0.42 fof(transition_7_to_8, hypothesis, follows(p8, p7)).
% 0.21/0.42 fof(transitivity_of_success, axiom, ![Intermediate_state, Start_state2, Goal_state2]: ((succeeds(Goal_state2, Intermediate_state) & succeeds(Intermediate_state, Start_state2)) => succeeds(Goal_state2, Start_state2))).
% 0.21/0.42
% 0.21/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.42 fresh(y, y, x1...xn) = u
% 0.21/0.42 C => fresh(s, t, x1...xn) = v
% 0.21/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.42 variables of u and v.
% 0.21/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.42 input problem has no model of domain size 1).
% 0.21/0.42
% 0.21/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.42
% 0.21/0.42 Axiom 1 (label_state_3): labels(loop, p3) = true.
% 0.21/0.42 Axiom 2 (transition_7_to_8): follows(p8, p7) = true.
% 0.21/0.42 Axiom 3 (transition_3_to_6): follows(p6, p3) = true.
% 0.21/0.42 Axiom 4 (transition_6_to_7): follows(p7, p6) = true.
% 0.21/0.42 Axiom 5 (state_8): has(p8, goto(loop)) = true.
% 0.21/0.42 Axiom 6 (direct_success): fresh(X, X, Y, Z) = true.
% 0.21/0.42 Axiom 7 (transitivity_of_success): fresh5(X, X, Y, Z) = true.
% 0.21/0.42 Axiom 8 (goto_success): fresh3(X, X, Y, Z) = true.
% 0.21/0.42 Axiom 9 (transitivity_of_success): fresh6(X, X, Y, Z, W) = succeeds(W, Y).
% 0.21/0.42 Axiom 10 (goto_success): fresh4(X, X, Y, Z, W) = succeeds(Y, W).
% 0.21/0.42 Axiom 11 (direct_success): fresh(follows(X, Y), true, Y, X) = succeeds(X, Y).
% 0.21/0.42 Axiom 12 (transitivity_of_success): fresh6(succeeds(X, Y), true, Z, Y, X) = fresh5(succeeds(Y, Z), true, Z, X).
% 0.21/0.42 Axiom 13 (goto_success): fresh4(has(X, goto(Y)), true, Z, Y, X) = fresh3(labels(Y, Z), true, Z, X).
% 0.21/0.42
% 0.21/0.42 Goal 1 (prove_there_is_a_loop_through_p3): succeeds(p3, p3) = true.
% 0.21/0.42 Proof:
% 0.21/0.42 succeeds(p3, p3)
% 0.21/0.42 = { by axiom 9 (transitivity_of_success) R->L }
% 0.21/0.42 fresh6(true, true, p3, p8, p3)
% 0.21/0.42 = { by axiom 8 (goto_success) R->L }
% 0.21/0.42 fresh6(fresh3(true, true, p3, p8), true, p3, p8, p3)
% 0.21/0.42 = { by axiom 1 (label_state_3) R->L }
% 0.21/0.42 fresh6(fresh3(labels(loop, p3), true, p3, p8), true, p3, p8, p3)
% 0.21/0.42 = { by axiom 13 (goto_success) R->L }
% 0.21/0.42 fresh6(fresh4(has(p8, goto(loop)), true, p3, loop, p8), true, p3, p8, p3)
% 0.21/0.42 = { by axiom 5 (state_8) }
% 0.21/0.42 fresh6(fresh4(true, true, p3, loop, p8), true, p3, p8, p3)
% 0.21/0.42 = { by axiom 10 (goto_success) }
% 0.21/0.42 fresh6(succeeds(p3, p8), true, p3, p8, p3)
% 0.21/0.42 = { by axiom 12 (transitivity_of_success) }
% 0.21/0.42 fresh5(succeeds(p8, p3), true, p3, p3)
% 0.21/0.42 = { by axiom 9 (transitivity_of_success) R->L }
% 0.21/0.42 fresh5(fresh6(true, true, p3, p7, p8), true, p3, p3)
% 0.21/0.42 = { by axiom 6 (direct_success) R->L }
% 0.21/0.42 fresh5(fresh6(fresh(true, true, p7, p8), true, p3, p7, p8), true, p3, p3)
% 0.21/0.42 = { by axiom 2 (transition_7_to_8) R->L }
% 0.21/0.42 fresh5(fresh6(fresh(follows(p8, p7), true, p7, p8), true, p3, p7, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 11 (direct_success) }
% 0.21/0.43 fresh5(fresh6(succeeds(p8, p7), true, p3, p7, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 12 (transitivity_of_success) }
% 0.21/0.43 fresh5(fresh5(succeeds(p7, p3), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 9 (transitivity_of_success) R->L }
% 0.21/0.43 fresh5(fresh5(fresh6(true, true, p3, p6, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 6 (direct_success) R->L }
% 0.21/0.43 fresh5(fresh5(fresh6(fresh(true, true, p6, p7), true, p3, p6, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 4 (transition_6_to_7) R->L }
% 0.21/0.43 fresh5(fresh5(fresh6(fresh(follows(p7, p6), true, p6, p7), true, p3, p6, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 11 (direct_success) }
% 0.21/0.43 fresh5(fresh5(fresh6(succeeds(p7, p6), true, p3, p6, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 12 (transitivity_of_success) }
% 0.21/0.43 fresh5(fresh5(fresh5(succeeds(p6, p3), true, p3, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 11 (direct_success) R->L }
% 0.21/0.43 fresh5(fresh5(fresh5(fresh(follows(p6, p3), true, p3, p6), true, p3, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 3 (transition_3_to_6) }
% 0.21/0.43 fresh5(fresh5(fresh5(fresh(true, true, p3, p6), true, p3, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 6 (direct_success) }
% 0.21/0.43 fresh5(fresh5(fresh5(true, true, p3, p7), true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 7 (transitivity_of_success) }
% 0.21/0.43 fresh5(fresh5(true, true, p3, p8), true, p3, p3)
% 0.21/0.43 = { by axiom 7 (transitivity_of_success) }
% 0.21/0.43 fresh5(true, true, p3, p3)
% 0.21/0.43 = { by axiom 7 (transitivity_of_success) }
% 0.21/0.43 true
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------