TSTP Solution File: AGT016+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : AGT016+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 : n026.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 15:55:43 EDT 2023
% Result : Theorem 9.69s 1.65s
% Output : Proof 9.69s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : AGT016+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 17:47:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 9.69/1.65 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 9.69/1.65
% 9.69/1.65 % SZS status Theorem
% 9.69/1.65
% 9.69/1.65 % SZS output start Proof
% 9.69/1.65 Take the following subset of the input axioms:
% 9.69/1.65 fof(a1_5, axiom, ![C, L, A2]: (any_agent_in_all_proposed_teams(A2, L, C) => accept_leader(A2, L))).
% 9.69/1.65 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)))).
% 9.69/1.65 fof(a2_9, axiom, ![A2_2]: ((accept_population(A2_2, atheist, n75) & (accept_population(A2_2, christian, n24) & (accept_population(A2_2, muslim, n1) & (accept_population(A2_2, native, n0) & accept_population(A2_2, other, n0))))) <=> accept_city(A2_2, towna))).
% 9.69/1.65 fof(event_11, axiom, the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)).
% 9.69/1.65 fof(event_12, axiom, any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna)).
% 9.69/1.65 fof(less_property, axiom, ![X, Y]: (less(X, Y) <=> (~less(Y, X) & Y!=X))).
% 9.69/1.65 fof(query_16, conjecture, ?[X2, Y2]: ~accept_population(muslimcountrybhumanitarianorganization, X2, Y2)).
% 9.69/1.65
% 9.69/1.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.69/1.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.69/1.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.69/1.65 fresh(y, y, x1...xn) = u
% 9.69/1.65 C => fresh(s, t, x1...xn) = v
% 9.69/1.65 where fresh is a fresh function symbol and x1..xn are the free
% 9.69/1.65 variables of u and v.
% 9.69/1.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.69/1.65 input problem has no model of domain size 1).
% 9.69/1.65
% 9.69/1.65 The encoding turns the above axioms into the following unit equations and goals:
% 9.69/1.65
% 9.69/1.65 Axiom 1 (query_16): accept_population(muslimcountrybhumanitarianorganization, X, Y) = true2.
% 9.69/1.65 Axiom 2 (event_12): any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna) = true2.
% 9.69/1.65 Axiom 3 (event_11): the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna) = true2.
% 9.69/1.65 Axiom 4 (a2_9_5): fresh121(X, X, Y) = true2.
% 9.69/1.65 Axiom 5 (a2_9_5): fresh119(X, X, Y) = accept_city(Y, towna).
% 9.69/1.65 Axiom 6 (a1_5): fresh82(X, X, Y, Z) = true2.
% 9.69/1.65 Axiom 7 (a2_9_5): fresh120(X, X, Y) = fresh121(accept_population(Y, atheist, n75), true2, Y).
% 9.69/1.65 Axiom 8 (a2_9_5): fresh117(X, X, Y) = fresh120(accept_population(Y, muslim, n1), true2, Y).
% 9.69/1.65 Axiom 9 (a2_9_5): fresh118(X, X, Y) = fresh119(accept_population(Y, christian, n24), true2, Y).
% 9.69/1.65 Axiom 10 (a2_9_5): fresh117(accept_population(X, other, n0), true2, X) = fresh118(accept_population(X, native, n0), true2, X).
% 9.69/1.65 Axiom 11 (a1_5): fresh82(any_agent_in_all_proposed_teams(X, Y, Z), true2, X, Y) = accept_leader(X, Y).
% 9.69/1.65
% 9.69/1.65 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).
% 9.69/1.65 The goal is true when:
% 9.69/1.65 X = muslimcountrybhumanitarianorganization
% 9.69/1.65 Y = towna
% 9.69/1.65 Z = countryacivilorganization
% 9.69/1.65
% 9.69/1.65 Proof:
% 9.69/1.65 tuple(accept_city(muslimcountrybhumanitarianorganization, towna), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), the_agent_not_in_any_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna))
% 9.69/1.65 = { by axiom 3 (event_11) }
% 9.69/1.65 tuple(accept_city(muslimcountrybhumanitarianorganization, towna), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 5 (a2_9_5) R->L }
% 9.69/1.65 tuple(fresh119(true2, true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 1 (query_16) R->L }
% 9.69/1.65 tuple(fresh119(accept_population(muslimcountrybhumanitarianorganization, christian, n24), true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 9 (a2_9_5) R->L }
% 9.69/1.65 tuple(fresh118(true2, true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 1 (query_16) R->L }
% 9.69/1.65 tuple(fresh118(accept_population(muslimcountrybhumanitarianorganization, native, n0), true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 10 (a2_9_5) R->L }
% 9.69/1.65 tuple(fresh117(accept_population(muslimcountrybhumanitarianorganization, other, n0), true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 1 (query_16) }
% 9.69/1.65 tuple(fresh117(true2, true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 8 (a2_9_5) }
% 9.69/1.65 tuple(fresh120(accept_population(muslimcountrybhumanitarianorganization, muslim, n1), true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 1 (query_16) }
% 9.69/1.65 tuple(fresh120(true2, true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 7 (a2_9_5) }
% 9.69/1.65 tuple(fresh121(accept_population(muslimcountrybhumanitarianorganization, atheist, n75), true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 1 (query_16) }
% 9.69/1.65 tuple(fresh121(true2, true2, muslimcountrybhumanitarianorganization), accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 4 (a2_9_5) }
% 9.69/1.65 tuple(true2, accept_leader(muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.65 = { by axiom 11 (a1_5) R->L }
% 9.69/1.66 tuple(true2, fresh82(any_agent_in_all_proposed_teams(muslimcountrybhumanitarianorganization, countryacivilorganization, towna), true2, muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.66 = { by axiom 2 (event_12) }
% 9.69/1.66 tuple(true2, fresh82(true2, true2, muslimcountrybhumanitarianorganization, countryacivilorganization), true2)
% 9.69/1.66 = { by axiom 6 (a1_5) }
% 9.69/1.66 tuple(true2, true2, true2)
% 9.69/1.66 % SZS output end Proof
% 9.69/1.66
% 9.69/1.66 RESULT: Theorem (the conjecture is true).
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