TSTP Solution File: AGT016+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : AGT016+2 : 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 : n003.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 15:55:44 EDT 2023
% Result : Theorem 11.46s 1.89s
% Output : Proof 12.05s
% 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 : AGT016+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n003.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 : Sun Aug 27 17:14:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 11.46/1.89 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 11.46/1.89
% 11.46/1.89 % SZS status Theorem
% 11.46/1.89
% 12.05/1.89 % SZS output start Proof
% 12.05/1.89 Take the following subset of the input axioms:
% 12.05/1.89 fof(a2_9, axiom, ![A2]: ((accept_population(A2, atheist, n75) & (accept_population(A2, christian, n24) & (accept_population(A2, muslim, n1) & (accept_population(A2, native, n0) & accept_population(A2, other, n0))))) <=> accept_city(A2, towna))).
% 12.05/1.89 fof(deduced_366, axiom, ~accept_city(muslimcountrybhumanitarianorganization, towna)).
% 12.05/1.89 fof(query_16, conjecture, ?[X, Y]: ~accept_population(muslimcountrybhumanitarianorganization, X, Y)).
% 12.05/1.89
% 12.05/1.89 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.05/1.89 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.05/1.89 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.05/1.89 fresh(y, y, x1...xn) = u
% 12.05/1.89 C => fresh(s, t, x1...xn) = v
% 12.05/1.89 where fresh is a fresh function symbol and x1..xn are the free
% 12.05/1.89 variables of u and v.
% 12.05/1.89 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.05/1.89 input problem has no model of domain size 1).
% 12.05/1.89
% 12.05/1.89 The encoding turns the above axioms into the following unit equations and goals:
% 12.05/1.89
% 12.05/1.89 Axiom 1 (query_16): accept_population(muslimcountrybhumanitarianorganization, X, Y) = true2.
% 12.05/1.89 Axiom 2 (a2_9_5): fresh121(X, X, Y) = true2.
% 12.05/1.89 Axiom 3 (a2_9_5): fresh119(X, X, Y) = accept_city(Y, towna).
% 12.05/1.89 Axiom 4 (a2_9_5): fresh120(X, X, Y) = fresh121(accept_population(Y, atheist, n75), true2, Y).
% 12.05/1.89 Axiom 5 (a2_9_5): fresh117(X, X, Y) = fresh120(accept_population(Y, muslim, n1), true2, Y).
% 12.05/1.89 Axiom 6 (a2_9_5): fresh118(X, X, Y) = fresh119(accept_population(Y, christian, n24), true2, Y).
% 12.05/1.89 Axiom 7 (a2_9_5): fresh117(accept_population(X, other, n0), true2, X) = fresh118(accept_population(X, native, n0), true2, X).
% 12.05/1.89
% 12.05/1.89 Goal 1 (deduced_366): accept_city(muslimcountrybhumanitarianorganization, towna) = true2.
% 12.05/1.89 Proof:
% 12.05/1.89 accept_city(muslimcountrybhumanitarianorganization, towna)
% 12.05/1.89 = { by axiom 3 (a2_9_5) R->L }
% 12.05/1.89 fresh119(true2, true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 1 (query_16) R->L }
% 12.05/1.89 fresh119(accept_population(muslimcountrybhumanitarianorganization, christian, n24), true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 6 (a2_9_5) R->L }
% 12.05/1.89 fresh118(true2, true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 1 (query_16) R->L }
% 12.05/1.89 fresh118(accept_population(muslimcountrybhumanitarianorganization, native, n0), true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 7 (a2_9_5) R->L }
% 12.05/1.89 fresh117(accept_population(muslimcountrybhumanitarianorganization, other, n0), true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 1 (query_16) }
% 12.05/1.89 fresh117(true2, true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 5 (a2_9_5) }
% 12.05/1.89 fresh120(accept_population(muslimcountrybhumanitarianorganization, muslim, n1), true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 1 (query_16) }
% 12.05/1.89 fresh120(true2, true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 4 (a2_9_5) }
% 12.05/1.89 fresh121(accept_population(muslimcountrybhumanitarianorganization, atheist, n75), true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 1 (query_16) }
% 12.05/1.89 fresh121(true2, true2, muslimcountrybhumanitarianorganization)
% 12.05/1.89 = { by axiom 2 (a2_9_5) }
% 12.05/1.89 true2
% 12.05/1.89 % SZS output end Proof
% 12.05/1.89
% 12.05/1.89 RESULT: Theorem (the conjecture is true).
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