TSTP Solution File: AGT004+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : AGT004+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 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 : n012.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 15:55:39 EDT 2023
% Result : Theorem 8.34s 1.46s
% Output : Proof 8.34s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : AGT004+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 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 : n012.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 : Sun Aug 27 17:15:40 EDT 2023
% 0.15/0.35 % CPUTime :
% 8.34/1.46 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 8.34/1.46
% 8.34/1.46 % SZS status Theorem
% 8.34/1.46
% 8.34/1.46 % SZS output start Proof
% 8.34/1.46 Take the following subset of the input axioms:
% 8.34/1.46 fof(a1_1, axiom, ![C, N, L, A2]: (accept_team(A2, L, C, N) <=> (accept_city(A2, C) & (accept_leader(A2, L) & accept_number(A2, N))))).
% 8.34/1.46 fof(a1_5, axiom, ![C2, L2, A2_2]: (any_agent_in_all_proposed_teams(A2_2, L2, C2) => accept_leader(A2_2, L2))).
% 8.34/1.46 fof(a1_6, axiom, ![A, C2, L2]: (the_agent_not_in_any_proposed_teams(A, L2, C2) => ~(accept_city(A, C2) & accept_leader(A, L2)))).
% 8.34/1.46 fof(event_37, axiom, the_agent_not_in_any_proposed_teams(countryamedicalorganization, christiancountrychumanitarianorganization, coastvillage)).
% 8.34/1.46 fof(event_38, axiom, any_agent_in_all_proposed_teams(countryamedicalorganization, christiancountrychumanitarianorganization, coastvillage)).
% 8.34/1.46 fof(less_property, axiom, ![X, Y]: (less(X, Y) <=> (~less(Y, X) & Y!=X))).
% 8.34/1.46 fof(query_4, conjecture, ~accept_team(countryamedicalorganization, countryahumanitarianorganization, coastvillage, n5)).
% 8.34/1.46
% 8.34/1.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 8.34/1.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 8.34/1.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 8.34/1.46 fresh(y, y, x1...xn) = u
% 8.34/1.46 C => fresh(s, t, x1...xn) = v
% 8.34/1.46 where fresh is a fresh function symbol and x1..xn are the free
% 8.34/1.46 variables of u and v.
% 8.34/1.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 8.34/1.46 input problem has no model of domain size 1).
% 8.34/1.46
% 8.34/1.46 The encoding turns the above axioms into the following unit equations and goals:
% 8.34/1.46
% 8.34/1.46 Axiom 1 (event_38): any_agent_in_all_proposed_teams(countryamedicalorganization, christiancountrychumanitarianorganization, coastvillage) = true2.
% 8.34/1.46 Axiom 2 (event_37): the_agent_not_in_any_proposed_teams(countryamedicalorganization, christiancountrychumanitarianorganization, coastvillage) = true2.
% 8.34/1.46 Axiom 3 (query_4): accept_team(countryamedicalorganization, countryahumanitarianorganization, coastvillage, n5) = true2.
% 8.34/1.46 Axiom 4 (a1_1): fresh91(X, X, Y, Z) = true2.
% 8.34/1.46 Axiom 5 (a1_5): fresh82(X, X, Y, Z) = true2.
% 8.34/1.46 Axiom 6 (a1_5): fresh82(any_agent_in_all_proposed_teams(X, Y, Z), true2, X, Y) = accept_leader(X, Y).
% 8.34/1.46 Axiom 7 (a1_1): fresh91(accept_team(X, Y, Z, W), true2, X, Z) = accept_city(X, Z).
% 8.34/1.46
% 8.34/1.46 Goal 1 (a1_6): tuple(accept_city(X, Y), accept_leader(X, Z), the_agent_not_in_any_proposed_teams(X, Z, Y)) = tuple(true2, true2, true2).
% 8.34/1.46 The goal is true when:
% 8.34/1.46 X = countryamedicalorganization
% 8.34/1.46 Y = coastvillage
% 8.34/1.46 Z = christiancountrychumanitarianorganization
% 8.34/1.46
% 8.34/1.46 Proof:
% 8.34/1.46 tuple(accept_city(countryamedicalorganization, coastvillage), accept_leader(countryamedicalorganization, christiancountrychumanitarianorganization), the_agent_not_in_any_proposed_teams(countryamedicalorganization, christiancountrychumanitarianorganization, coastvillage))
% 8.34/1.46 = { by axiom 2 (event_37) }
% 8.34/1.46 tuple(accept_city(countryamedicalorganization, coastvillage), accept_leader(countryamedicalorganization, christiancountrychumanitarianorganization), true2)
% 8.34/1.46 = { by axiom 7 (a1_1) R->L }
% 8.34/1.46 tuple(fresh91(accept_team(countryamedicalorganization, countryahumanitarianorganization, coastvillage, n5), true2, countryamedicalorganization, coastvillage), accept_leader(countryamedicalorganization, christiancountrychumanitarianorganization), true2)
% 8.34/1.46 = { by axiom 3 (query_4) }
% 8.34/1.46 tuple(fresh91(true2, true2, countryamedicalorganization, coastvillage), accept_leader(countryamedicalorganization, christiancountrychumanitarianorganization), true2)
% 8.34/1.46 = { by axiom 4 (a1_1) }
% 8.34/1.46 tuple(true2, accept_leader(countryamedicalorganization, christiancountrychumanitarianorganization), true2)
% 8.34/1.46 = { by axiom 6 (a1_5) R->L }
% 8.34/1.46 tuple(true2, fresh82(any_agent_in_all_proposed_teams(countryamedicalorganization, christiancountrychumanitarianorganization, coastvillage), true2, countryamedicalorganization, christiancountrychumanitarianorganization), true2)
% 8.34/1.46 = { by axiom 1 (event_38) }
% 8.34/1.46 tuple(true2, fresh82(true2, true2, countryamedicalorganization, christiancountrychumanitarianorganization), true2)
% 8.34/1.46 = { by axiom 5 (a1_5) }
% 8.34/1.46 tuple(true2, true2, true2)
% 8.34/1.46 % SZS output end Proof
% 8.34/1.46
% 8.34/1.46 RESULT: Theorem (the conjecture is true).
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