TSTP Solution File: MGT059+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : MGT059+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n017.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 09:17:16 EDT 2023
% Result : Theorem 0.22s 0.41s
% 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
% 0.08/0.13 % Problem : MGT059+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 05:41:12 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.41 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.22/0.41
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 Take the following subset of the input axioms:
% 0.22/0.41 fof(assumption_17, axiom, ![X, T]: (organization(X) => ((has_immunity(X, T) => hazard_of_mortality(X, T)=very_low) & (~has_immunity(X, T) => (((is_aligned(X, T) & positional_advantage(X, T)) => hazard_of_mortality(X, T)=low) & (((~is_aligned(X, T) & positional_advantage(X, T)) => hazard_of_mortality(X, T)=mod1) & (((is_aligned(X, T) & ~positional_advantage(X, T)) => hazard_of_mortality(X, T)=mod2) & ((~is_aligned(X, T) & ~positional_advantage(X, T)) => hazard_of_mortality(X, T)=high)))))))).
% 0.22/0.41 fof(assumption_2, conjecture, ![T0, X2, T2]: ((organization(X2) & (has_immunity(X2, T0) & has_immunity(X2, T2))) => hazard_of_mortality(X2, T0)=hazard_of_mortality(X2, T2))).
% 0.22/0.41
% 0.22/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.41 fresh(y, y, x1...xn) = u
% 0.22/0.41 C => fresh(s, t, x1...xn) = v
% 0.22/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.41 variables of u and v.
% 0.22/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.41 input problem has no model of domain size 1).
% 0.22/0.41
% 0.22/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.41
% 0.22/0.41 Axiom 1 (assumption_2): organization(x) = true2.
% 0.22/0.41 Axiom 2 (assumption_2_1): has_immunity(x, t) = true2.
% 0.22/0.41 Axiom 3 (assumption_2_2): has_immunity(x, t0) = true2.
% 0.22/0.41 Axiom 4 (assumption_17_1): fresh8(X, X, Y, Z) = very_low.
% 0.22/0.41 Axiom 5 (assumption_17_1): fresh7(X, X, Y, Z) = hazard_of_mortality(Y, Z).
% 0.22/0.41 Axiom 6 (assumption_17_1): fresh7(has_immunity(X, Y), true2, X, Y) = fresh8(organization(X), true2, X, Y).
% 0.22/0.41
% 0.22/0.41 Goal 1 (assumption_2_3): hazard_of_mortality(x, t0) = hazard_of_mortality(x, t).
% 0.22/0.41 Proof:
% 0.22/0.41 hazard_of_mortality(x, t0)
% 0.22/0.41 = { by axiom 5 (assumption_17_1) R->L }
% 0.22/0.41 fresh7(true2, true2, x, t0)
% 0.22/0.41 = { by axiom 3 (assumption_2_2) R->L }
% 0.22/0.41 fresh7(has_immunity(x, t0), true2, x, t0)
% 0.22/0.41 = { by axiom 6 (assumption_17_1) }
% 0.22/0.41 fresh8(organization(x), true2, x, t0)
% 0.22/0.41 = { by axiom 1 (assumption_2) }
% 0.22/0.41 fresh8(true2, true2, x, t0)
% 0.22/0.41 = { by axiom 4 (assumption_17_1) }
% 0.22/0.41 very_low
% 0.22/0.41 = { by axiom 4 (assumption_17_1) R->L }
% 0.22/0.41 fresh8(true2, true2, x, t)
% 0.22/0.41 = { by axiom 1 (assumption_2) R->L }
% 0.22/0.41 fresh8(organization(x), true2, x, t)
% 0.22/0.41 = { by axiom 6 (assumption_17_1) R->L }
% 0.22/0.41 fresh7(has_immunity(x, t), true2, x, t)
% 0.22/0.41 = { by axiom 2 (assumption_2_1) }
% 0.22/0.41 fresh7(true2, true2, x, t)
% 0.22/0.41 = { by axiom 5 (assumption_17_1) }
% 0.22/0.41 hazard_of_mortality(x, t)
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41
% 0.22/0.41 RESULT: Theorem (the conjecture is true).
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