TSTP Solution File: COM001-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COM001-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n025.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 18:45:16 EDT 2023
% Result : Unsatisfiable 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 12:59:10 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.40 Command-line arguments: --no-flatten-goal
% 0.22/0.40
% 0.22/0.40 % SZS status Unsatisfiable
% 0.22/0.40
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 Take the following subset of the input axioms:
% 0.22/0.40 fof(direct_success, axiom, ![Goal_state, Start_state]: (succeeds(Goal_state, Start_state) | ~follows(Goal_state, Start_state))).
% 0.22/0.40 fof(goto_success, axiom, ![Label, Goal_state2, Start_state2]: (succeeds(Goal_state2, Start_state2) | (~has(Start_state2, goto(Label)) | ~labels(Label, Goal_state2)))).
% 0.22/0.40 fof(label_state_3, hypothesis, labels(loop, p3)).
% 0.22/0.40 fof(prove_there_is_a_loop_through_p3, negated_conjecture, ~succeeds(p3, p3)).
% 0.22/0.40 fof(state_8, hypothesis, has(p8, goto(loop))).
% 0.22/0.40 fof(transition_3_to_8, hypothesis, follows(p8, p3)).
% 0.22/0.40 fof(transitivity_of_success, axiom, ![Intermediate_state, Goal_state2, Start_state2]: (succeeds(Goal_state2, Start_state2) | (~succeeds(Goal_state2, Intermediate_state) | ~succeeds(Intermediate_state, Start_state2)))).
% 0.22/0.40
% 0.22/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.40 fresh(y, y, x1...xn) = u
% 0.22/0.40 C => fresh(s, t, x1...xn) = v
% 0.22/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.40 variables of u and v.
% 0.22/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.40 input problem has no model of domain size 1).
% 0.22/0.40
% 0.22/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.40
% 0.22/0.40 Axiom 1 (label_state_3): labels(loop, p3) = true.
% 0.22/0.40 Axiom 2 (transition_3_to_8): follows(p8, p3) = true.
% 0.22/0.40 Axiom 3 (state_8): has(p8, goto(loop)) = true.
% 0.22/0.40 Axiom 4 (transitivity_of_success): fresh(X, X, Y, Z) = true.
% 0.22/0.40 Axiom 5 (direct_success): fresh6(X, X, Y, Z) = true.
% 0.22/0.40 Axiom 6 (goto_success): fresh3(X, X, Y, Z) = true.
% 0.22/0.40 Axiom 7 (goto_success): fresh4(X, X, Y, Z, W) = succeeds(Y, Z).
% 0.22/0.40 Axiom 8 (transitivity_of_success): fresh2(X, X, Y, Z, W) = succeeds(Y, Z).
% 0.22/0.40 Axiom 9 (direct_success): fresh6(follows(X, Y), true, X, Y) = succeeds(X, Y).
% 0.22/0.40 Axiom 10 (goto_success): fresh4(labels(X, Y), true, Y, Z, X) = fresh3(has(Z, goto(X)), true, Y, Z).
% 0.22/0.40 Axiom 11 (transitivity_of_success): fresh2(succeeds(X, Y), true, Z, Y, X) = fresh(succeeds(Z, X), true, Z, Y).
% 0.22/0.40
% 0.22/0.40 Goal 1 (prove_there_is_a_loop_through_p3): succeeds(p3, p3) = true.
% 0.22/0.40 Proof:
% 0.22/0.40 succeeds(p3, p3)
% 0.22/0.40 = { by axiom 8 (transitivity_of_success) R->L }
% 0.22/0.40 fresh2(true, true, p3, p3, p8)
% 0.22/0.40 = { by axiom 5 (direct_success) R->L }
% 0.22/0.40 fresh2(fresh6(true, true, p8, p3), true, p3, p3, p8)
% 0.22/0.40 = { by axiom 2 (transition_3_to_8) R->L }
% 0.22/0.40 fresh2(fresh6(follows(p8, p3), true, p8, p3), true, p3, p3, p8)
% 0.22/0.40 = { by axiom 9 (direct_success) }
% 0.22/0.40 fresh2(succeeds(p8, p3), true, p3, p3, p8)
% 0.22/0.40 = { by axiom 11 (transitivity_of_success) }
% 0.22/0.40 fresh(succeeds(p3, p8), true, p3, p3)
% 0.22/0.40 = { by axiom 7 (goto_success) R->L }
% 0.22/0.40 fresh(fresh4(true, true, p3, p8, loop), true, p3, p3)
% 0.22/0.40 = { by axiom 1 (label_state_3) R->L }
% 0.22/0.40 fresh(fresh4(labels(loop, p3), true, p3, p8, loop), true, p3, p3)
% 0.22/0.40 = { by axiom 10 (goto_success) }
% 0.22/0.40 fresh(fresh3(has(p8, goto(loop)), true, p3, p8), true, p3, p3)
% 0.22/0.40 = { by axiom 3 (state_8) }
% 0.22/0.40 fresh(fresh3(true, true, p3, p8), true, p3, p3)
% 0.22/0.40 = { by axiom 6 (goto_success) }
% 0.22/0.40 fresh(true, true, p3, p3)
% 0.22/0.40 = { by axiom 4 (transitivity_of_success) }
% 0.22/0.40 true
% 0.22/0.40 % SZS output end Proof
% 0.22/0.40
% 0.22/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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