TSTP Solution File: SEU096+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n029.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 17:50:59 EDT 2023
% Result : Theorem 0.19s 0.58s
% 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 : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 18:21:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 Command-line arguments: --no-flatten-goal
% 0.19/0.58
% 0.19/0.58 % SZS status Theorem
% 0.19/0.58
% 0.19/0.59 % SZS output start Proof
% 0.19/0.59 Take the following subset of the input axioms:
% 0.19/0.59 fof(fc13_finset_1, axiom, ![B, A2]: ((relation(A2) & (function(A2) & finite(B))) => finite(relation_image(A2, B)))).
% 0.19/0.59 fof(t147_funct_1, axiom, ![B2, A2_2]: ((relation(B2) & function(B2)) => (subset(A2_2, relation_rng(B2)) => relation_image(B2, relation_inverse_image(B2, A2_2))=A2_2))).
% 0.19/0.59 fof(t27_finset_1, conjecture, ![A, B2]: ((relation(B2) & function(B2)) => ((subset(A, relation_rng(B2)) & finite(relation_inverse_image(B2, A))) => finite(A)))).
% 0.19/0.59
% 0.19/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.59 fresh(y, y, x1...xn) = u
% 0.19/0.59 C => fresh(s, t, x1...xn) = v
% 0.19/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.59 variables of u and v.
% 0.19/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.59 input problem has no model of domain size 1).
% 0.19/0.59
% 0.19/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.59
% 0.19/0.59 Axiom 1 (t27_finset_1_1): function(b) = true2.
% 0.19/0.59 Axiom 2 (t27_finset_1_2): relation(b) = true2.
% 0.19/0.59 Axiom 3 (t27_finset_1_3): subset(a, relation_rng(b)) = true2.
% 0.19/0.59 Axiom 4 (t27_finset_1): finite(relation_inverse_image(b, a)) = true2.
% 0.19/0.59 Axiom 5 (fc13_finset_1): fresh57(X, X, Y, Z) = true2.
% 0.19/0.59 Axiom 6 (t147_funct_1): fresh53(X, X, Y, Z) = Y.
% 0.19/0.59 Axiom 7 (fc13_finset_1): fresh18(X, X, Y, Z) = finite(relation_image(Y, Z)).
% 0.19/0.59 Axiom 8 (t147_funct_1): fresh10(X, X, Y, Z) = relation_image(Z, relation_inverse_image(Z, Y)).
% 0.19/0.59 Axiom 9 (fc13_finset_1): fresh56(X, X, Y, Z) = fresh57(finite(Z), true2, Y, Z).
% 0.19/0.59 Axiom 10 (t147_funct_1): fresh52(X, X, Y, Z) = fresh53(function(Z), true2, Y, Z).
% 0.19/0.59 Axiom 11 (fc13_finset_1): fresh56(relation(X), true2, X, Y) = fresh18(function(X), true2, X, Y).
% 0.19/0.59 Axiom 12 (t147_funct_1): fresh52(subset(X, relation_rng(Y)), true2, X, Y) = fresh10(relation(Y), true2, X, Y).
% 0.19/0.59
% 0.19/0.59 Goal 1 (t27_finset_1_4): finite(a) = true2.
% 0.19/0.59 Proof:
% 0.19/0.59 finite(a)
% 0.19/0.59 = { by axiom 6 (t147_funct_1) R->L }
% 0.19/0.59 finite(fresh53(true2, true2, a, b))
% 0.19/0.59 = { by axiom 1 (t27_finset_1_1) R->L }
% 0.19/0.59 finite(fresh53(function(b), true2, a, b))
% 0.19/0.59 = { by axiom 10 (t147_funct_1) R->L }
% 0.19/0.59 finite(fresh52(true2, true2, a, b))
% 0.19/0.59 = { by axiom 3 (t27_finset_1_3) R->L }
% 0.19/0.59 finite(fresh52(subset(a, relation_rng(b)), true2, a, b))
% 0.19/0.59 = { by axiom 12 (t147_funct_1) }
% 0.19/0.59 finite(fresh10(relation(b), true2, a, b))
% 0.19/0.59 = { by axiom 2 (t27_finset_1_2) }
% 0.19/0.59 finite(fresh10(true2, true2, a, b))
% 0.19/0.59 = { by axiom 8 (t147_funct_1) }
% 0.19/0.59 finite(relation_image(b, relation_inverse_image(b, a)))
% 0.19/0.59 = { by axiom 7 (fc13_finset_1) R->L }
% 0.19/0.59 fresh18(true2, true2, b, relation_inverse_image(b, a))
% 0.19/0.59 = { by axiom 1 (t27_finset_1_1) R->L }
% 0.19/0.59 fresh18(function(b), true2, b, relation_inverse_image(b, a))
% 0.19/0.59 = { by axiom 11 (fc13_finset_1) R->L }
% 0.19/0.59 fresh56(relation(b), true2, b, relation_inverse_image(b, a))
% 0.19/0.59 = { by axiom 2 (t27_finset_1_2) }
% 0.19/0.59 fresh56(true2, true2, b, relation_inverse_image(b, a))
% 0.19/0.59 = { by axiom 9 (fc13_finset_1) }
% 0.19/0.59 fresh57(finite(relation_inverse_image(b, a)), true2, b, relation_inverse_image(b, a))
% 0.19/0.59 = { by axiom 4 (t27_finset_1) }
% 0.19/0.59 fresh57(true2, true2, b, relation_inverse_image(b, a))
% 0.19/0.59 = { by axiom 5 (fc13_finset_1) }
% 0.19/0.59 true2
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59
% 0.19/0.59 RESULT: Theorem (the conjecture is true).
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