TSTP Solution File: SEU025+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU025+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 : n031.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 17:50:49 EDT 2023
% Result : Theorem 9.27s 1.59s
% Output : Proof 9.63s
% 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 : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.36 % Computer : n031.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Aug 23 17:49:20 EDT 2023
% 0.13/0.36 % CPUTime :
% 9.27/1.59 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 9.27/1.59
% 9.27/1.59 % SZS status Theorem
% 9.27/1.59
% 9.63/1.60 % SZS output start Proof
% 9.63/1.60 Take the following subset of the input axioms:
% 9.63/1.60 fof(dt_k2_funct_1, axiom, ![A2]: ((relation(A2) & function(A2)) => (relation(function_inverse(A2)) & function(function_inverse(A2))))).
% 9.63/1.60 fof(reflexivity_r1_tarski, axiom, ![A, B]: subset(A, A)).
% 9.63/1.60 fof(t46_relat_1, axiom, ![A2_2]: (relation(A2_2) => ![B2]: (relation(B2) => (subset(relation_rng(A2_2), relation_dom(B2)) => relation_dom(relation_composition(A2_2, B2))=relation_dom(A2_2))))).
% 9.63/1.60 fof(t47_relat_1, axiom, ![A2_2]: (relation(A2_2) => ![B2]: (relation(B2) => (subset(relation_dom(A2_2), relation_rng(B2)) => relation_rng(relation_composition(B2, A2_2))=relation_rng(A2_2))))).
% 9.63/1.60 fof(t55_funct_1, axiom, ![A2_2]: ((relation(A2_2) & function(A2_2)) => (one_to_one(A2_2) => (relation_rng(A2_2)=relation_dom(function_inverse(A2_2)) & relation_dom(A2_2)=relation_rng(function_inverse(A2_2)))))).
% 9.63/1.60 fof(t58_funct_1, conjecture, ![A3]: ((relation(A3) & function(A3)) => (one_to_one(A3) => (relation_dom(relation_composition(A3, function_inverse(A3)))=relation_dom(A3) & relation_rng(relation_composition(A3, function_inverse(A3)))=relation_dom(A3))))).
% 9.63/1.60
% 9.63/1.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.63/1.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.63/1.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.63/1.60 fresh(y, y, x1...xn) = u
% 9.63/1.60 C => fresh(s, t, x1...xn) = v
% 9.63/1.60 where fresh is a fresh function symbol and x1..xn are the free
% 9.63/1.60 variables of u and v.
% 9.63/1.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.63/1.60 input problem has no model of domain size 1).
% 9.63/1.60
% 9.63/1.60 The encoding turns the above axioms into the following unit equations and goals:
% 9.63/1.60
% 9.63/1.60 Axiom 1 (t58_funct_1_1): relation(a) = true2.
% 9.63/1.60 Axiom 2 (t58_funct_1): function(a) = true2.
% 9.63/1.60 Axiom 3 (t58_funct_1_2): one_to_one(a) = true2.
% 9.63/1.60 Axiom 4 (reflexivity_r1_tarski): subset(X, X) = true2.
% 9.63/1.60 Axiom 5 (t55_funct_1_1): fresh42(X, X, Y) = relation_rng(Y).
% 9.63/1.60 Axiom 6 (t55_funct_1): fresh40(X, X, Y) = relation_dom(Y).
% 9.63/1.60 Axiom 7 (dt_k2_funct_1_1): fresh33(X, X, Y) = relation(function_inverse(Y)).
% 9.63/1.60 Axiom 8 (dt_k2_funct_1_1): fresh32(X, X, Y) = true2.
% 9.63/1.60 Axiom 9 (t55_funct_1): fresh5(X, X, Y) = relation_rng(function_inverse(Y)).
% 9.63/1.60 Axiom 10 (t55_funct_1_1): fresh4(X, X, Y) = relation_dom(function_inverse(Y)).
% 9.63/1.60 Axiom 11 (t46_relat_1): fresh46(X, X, Y, Z) = relation_dom(Y).
% 9.63/1.60 Axiom 12 (t47_relat_1): fresh44(X, X, Y, Z) = relation_rng(Y).
% 9.63/1.60 Axiom 13 (t55_funct_1_1): fresh41(X, X, Y) = fresh42(function(Y), true2, Y).
% 9.63/1.60 Axiom 14 (t55_funct_1): fresh39(X, X, Y) = fresh40(function(Y), true2, Y).
% 9.63/1.60 Axiom 15 (dt_k2_funct_1_1): fresh33(relation(X), true2, X) = fresh32(function(X), true2, X).
% 9.63/1.60 Axiom 16 (t46_relat_1): fresh9(X, X, Y, Z) = relation_dom(relation_composition(Y, Z)).
% 9.63/1.60 Axiom 17 (t47_relat_1): fresh8(X, X, Y, Z) = relation_rng(relation_composition(Z, Y)).
% 9.63/1.60 Axiom 18 (t55_funct_1): fresh39(one_to_one(X), true2, X) = fresh5(relation(X), true2, X).
% 9.63/1.60 Axiom 19 (t55_funct_1_1): fresh41(one_to_one(X), true2, X) = fresh4(relation(X), true2, X).
% 9.63/1.60 Axiom 20 (t46_relat_1): fresh45(X, X, Y, Z) = fresh46(relation(Y), true2, Y, Z).
% 9.63/1.60 Axiom 21 (t47_relat_1): fresh43(X, X, Y, Z) = fresh44(relation(Y), true2, Y, Z).
% 9.63/1.60 Axiom 22 (t46_relat_1): fresh45(subset(relation_rng(X), relation_dom(Y)), true2, X, Y) = fresh9(relation(Y), true2, X, Y).
% 9.63/1.60 Axiom 23 (t47_relat_1): fresh43(subset(relation_dom(X), relation_rng(Y)), true2, X, Y) = fresh8(relation(Y), true2, X, Y).
% 9.63/1.60
% 9.63/1.60 Lemma 24: relation(function_inverse(a)) = true2.
% 9.63/1.60 Proof:
% 9.63/1.60 relation(function_inverse(a))
% 9.63/1.60 = { by axiom 7 (dt_k2_funct_1_1) R->L }
% 9.63/1.60 fresh33(true2, true2, a)
% 9.63/1.60 = { by axiom 1 (t58_funct_1_1) R->L }
% 9.63/1.60 fresh33(relation(a), true2, a)
% 9.63/1.60 = { by axiom 15 (dt_k2_funct_1_1) }
% 9.63/1.60 fresh32(function(a), true2, a)
% 9.63/1.60 = { by axiom 2 (t58_funct_1) }
% 9.63/1.60 fresh32(true2, true2, a)
% 9.63/1.60 = { by axiom 8 (dt_k2_funct_1_1) }
% 9.63/1.60 true2
% 9.63/1.60
% 9.63/1.60 Lemma 25: relation_dom(function_inverse(a)) = relation_rng(a).
% 9.63/1.60 Proof:
% 9.63/1.60 relation_dom(function_inverse(a))
% 9.63/1.60 = { by axiom 10 (t55_funct_1_1) R->L }
% 9.63/1.60 fresh4(true2, true2, a)
% 9.63/1.60 = { by axiom 1 (t58_funct_1_1) R->L }
% 9.63/1.60 fresh4(relation(a), true2, a)
% 9.63/1.60 = { by axiom 19 (t55_funct_1_1) R->L }
% 9.63/1.60 fresh41(one_to_one(a), true2, a)
% 9.63/1.60 = { by axiom 3 (t58_funct_1_2) }
% 9.63/1.60 fresh41(true2, true2, a)
% 9.63/1.60 = { by axiom 13 (t55_funct_1_1) }
% 9.63/1.60 fresh42(function(a), true2, a)
% 9.63/1.60 = { by axiom 2 (t58_funct_1) }
% 9.63/1.60 fresh42(true2, true2, a)
% 9.63/1.60 = { by axiom 5 (t55_funct_1_1) }
% 9.63/1.60 relation_rng(a)
% 9.63/1.60
% 9.63/1.60 Lemma 26: relation_dom(relation_composition(a, function_inverse(a))) = relation_dom(a).
% 9.63/1.60 Proof:
% 9.63/1.60 relation_dom(relation_composition(a, function_inverse(a)))
% 9.63/1.60 = { by axiom 16 (t46_relat_1) R->L }
% 9.63/1.60 fresh9(true2, true2, a, function_inverse(a))
% 9.63/1.60 = { by lemma 24 R->L }
% 9.63/1.60 fresh9(relation(function_inverse(a)), true2, a, function_inverse(a))
% 9.63/1.60 = { by axiom 22 (t46_relat_1) R->L }
% 9.63/1.60 fresh45(subset(relation_rng(a), relation_dom(function_inverse(a))), true2, a, function_inverse(a))
% 9.63/1.60 = { by lemma 25 R->L }
% 9.63/1.60 fresh45(subset(relation_dom(function_inverse(a)), relation_dom(function_inverse(a))), true2, a, function_inverse(a))
% 9.63/1.60 = { by axiom 4 (reflexivity_r1_tarski) }
% 9.63/1.60 fresh45(true2, true2, a, function_inverse(a))
% 9.63/1.60 = { by axiom 20 (t46_relat_1) }
% 9.63/1.60 fresh46(relation(a), true2, a, function_inverse(a))
% 9.63/1.60 = { by axiom 1 (t58_funct_1_1) }
% 9.63/1.60 fresh46(true2, true2, a, function_inverse(a))
% 9.63/1.60 = { by axiom 11 (t46_relat_1) }
% 9.63/1.60 relation_dom(a)
% 9.63/1.60
% 9.63/1.60 Goal 1 (t58_funct_1_3): tuple3(relation_dom(relation_composition(a, function_inverse(a))), relation_rng(relation_composition(a, function_inverse(a)))) = tuple3(relation_dom(a), relation_dom(a)).
% 9.63/1.60 Proof:
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), relation_rng(relation_composition(a, function_inverse(a))))
% 9.63/1.60 = { by axiom 17 (t47_relat_1) R->L }
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh8(true2, true2, function_inverse(a), a))
% 9.63/1.60 = { by axiom 1 (t58_funct_1_1) R->L }
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh8(relation(a), true2, function_inverse(a), a))
% 9.63/1.60 = { by axiom 23 (t47_relat_1) R->L }
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh43(subset(relation_dom(function_inverse(a)), relation_rng(a)), true2, function_inverse(a), a))
% 9.63/1.60 = { by lemma 25 R->L }
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh43(subset(relation_dom(function_inverse(a)), relation_dom(function_inverse(a))), true2, function_inverse(a), a))
% 9.63/1.60 = { by axiom 4 (reflexivity_r1_tarski) }
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh43(true2, true2, function_inverse(a), a))
% 9.63/1.60 = { by axiom 21 (t47_relat_1) }
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh44(relation(function_inverse(a)), true2, function_inverse(a), a))
% 9.63/1.60 = { by lemma 24 }
% 9.63/1.60 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh44(true2, true2, function_inverse(a), a))
% 9.63/1.60 = { by axiom 12 (t47_relat_1) }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), relation_rng(function_inverse(a)))
% 9.63/1.61 = { by axiom 9 (t55_funct_1) R->L }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh5(true2, true2, a))
% 9.63/1.61 = { by axiom 1 (t58_funct_1_1) R->L }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh5(relation(a), true2, a))
% 9.63/1.61 = { by axiom 18 (t55_funct_1) R->L }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh39(one_to_one(a), true2, a))
% 9.63/1.61 = { by axiom 3 (t58_funct_1_2) }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh39(true2, true2, a))
% 9.63/1.61 = { by axiom 14 (t55_funct_1) }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh40(function(a), true2, a))
% 9.63/1.61 = { by axiom 2 (t58_funct_1) }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), fresh40(true2, true2, a))
% 9.63/1.61 = { by axiom 6 (t55_funct_1) }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), relation_dom(a))
% 9.63/1.61 = { by lemma 26 R->L }
% 9.63/1.61 tuple3(relation_dom(relation_composition(a, function_inverse(a))), relation_dom(relation_composition(a, function_inverse(a))))
% 9.63/1.61 = { by lemma 26 }
% 9.63/1.61 tuple3(relation_dom(a), relation_dom(relation_composition(a, function_inverse(a))))
% 9.63/1.61 = { by lemma 26 }
% 9.63/1.61 tuple3(relation_dom(a), relation_dom(a))
% 9.63/1.61 % SZS output end Proof
% 9.63/1.61
% 9.63/1.61 RESULT: Theorem (the conjecture is true).
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