TSTP Solution File: PHI022+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : PHI022+1 : TPTP v8.1.2. Released v7.4.0.
% 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 : n027.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 12:56:56 EDT 2023
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% 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 : PHI022+1 : TPTP v8.1.2. Released v7.4.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n027.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 09:18:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.46
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 Take the following subset of the input axioms:
% 0.19/0.46 fof(being_has_essense, axiom, ![X]: (being(X) => hasEssence(X))).
% 0.19/0.46 fof(essence_involves_existence_exists, axiom, ![X2]: ((essenceInvExistence(X2) & hasEssence(X2)) => exists(X2))).
% 0.19/0.46 fof(has_substance_being, axiom, ![X2]: (substance(X2) => being(X2))).
% 0.19/0.46 fof(has_substance_exists, conjecture, ![X2]: (substance(X2) => exists(X2))).
% 0.19/0.46 fof(is_in_itself_is_self_caused, axiom, ![X2]: (inItself(X2) => selfCaused(X2))).
% 0.19/0.46 fof(self_caused, axiom, ![X2]: (selfCaused(X2) <=> (essenceInvExistence(X2) & natureConcOnlyByExistence(X2)))).
% 0.19/0.46 fof(substance, axiom, ![X2]: (substance(X2) <=> (inItself(X2) & conceivedThruItself(X2)))).
% 0.19/0.46
% 0.19/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.46 fresh(y, y, x1...xn) = u
% 0.19/0.46 C => fresh(s, t, x1...xn) = v
% 0.19/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.46 variables of u and v.
% 0.19/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.46 input problem has no model of domain size 1).
% 0.19/0.46
% 0.19/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.46
% 0.19/0.46 Axiom 1 (has_substance_exists): substance(x) = true2.
% 0.19/0.46 Axiom 2 (being_has_essense): fresh41(X, X, Y) = true2.
% 0.19/0.46 Axiom 3 (essence_involves_existence_exists): fresh39(X, X, Y) = exists(Y).
% 0.19/0.46 Axiom 4 (essence_involves_existence_exists): fresh38(X, X, Y) = true2.
% 0.19/0.46 Axiom 5 (has_substance_being): fresh20(X, X, Y) = true2.
% 0.19/0.46 Axiom 6 (is_in_itself_is_self_caused): fresh19(X, X, Y) = true2.
% 0.19/0.46 Axiom 7 (self_caused): fresh9(X, X, Y) = true2.
% 0.19/0.46 Axiom 8 (substance): fresh5(X, X, Y) = true2.
% 0.19/0.46 Axiom 9 (being_has_essense): fresh41(being(X), true2, X) = hasEssence(X).
% 0.19/0.46 Axiom 10 (essence_involves_existence_exists): fresh39(hasEssence(X), true2, X) = fresh38(essenceInvExistence(X), true2, X).
% 0.19/0.46 Axiom 11 (has_substance_being): fresh20(substance(X), true2, X) = being(X).
% 0.19/0.46 Axiom 12 (is_in_itself_is_self_caused): fresh19(inItself(X), true2, X) = selfCaused(X).
% 0.19/0.46 Axiom 13 (self_caused): fresh9(selfCaused(X), true2, X) = essenceInvExistence(X).
% 0.19/0.46 Axiom 14 (substance): fresh5(substance(X), true2, X) = inItself(X).
% 0.19/0.46
% 0.19/0.46 Goal 1 (has_substance_exists_1): exists(x) = true2.
% 0.19/0.46 Proof:
% 0.19/0.46 exists(x)
% 0.19/0.46 = { by axiom 3 (essence_involves_existence_exists) R->L }
% 0.19/0.46 fresh39(true2, true2, x)
% 0.19/0.46 = { by axiom 2 (being_has_essense) R->L }
% 0.19/0.46 fresh39(fresh41(true2, true2, x), true2, x)
% 0.19/0.46 = { by axiom 5 (has_substance_being) R->L }
% 0.19/0.46 fresh39(fresh41(fresh20(true2, true2, x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 1 (has_substance_exists) R->L }
% 0.19/0.46 fresh39(fresh41(fresh20(substance(x), true2, x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 11 (has_substance_being) }
% 0.19/0.46 fresh39(fresh41(being(x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 9 (being_has_essense) }
% 0.19/0.46 fresh39(hasEssence(x), true2, x)
% 0.19/0.46 = { by axiom 10 (essence_involves_existence_exists) }
% 0.19/0.46 fresh38(essenceInvExistence(x), true2, x)
% 0.19/0.46 = { by axiom 13 (self_caused) R->L }
% 0.19/0.46 fresh38(fresh9(selfCaused(x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 12 (is_in_itself_is_self_caused) R->L }
% 0.19/0.46 fresh38(fresh9(fresh19(inItself(x), true2, x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 14 (substance) R->L }
% 0.19/0.46 fresh38(fresh9(fresh19(fresh5(substance(x), true2, x), true2, x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 1 (has_substance_exists) }
% 0.19/0.46 fresh38(fresh9(fresh19(fresh5(true2, true2, x), true2, x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 8 (substance) }
% 0.19/0.46 fresh38(fresh9(fresh19(true2, true2, x), true2, x), true2, x)
% 0.19/0.46 = { by axiom 6 (is_in_itself_is_self_caused) }
% 0.19/0.46 fresh38(fresh9(true2, true2, x), true2, x)
% 0.19/0.46 = { by axiom 7 (self_caused) }
% 0.19/0.46 fresh38(true2, true2, x)
% 0.19/0.46 = { by axiom 4 (essence_involves_existence_exists) }
% 0.19/0.46 true2
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46
% 0.19/0.46 RESULT: Theorem (the conjecture is true).
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