TSTP Solution File: SEU032+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU032+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 : 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 17:50:50 EDT 2023
% Result : Theorem 5.92s 1.16s
% Output : Proof 5.92s
% 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 : SEU032+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
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 12:38:01 EDT 2023
% 0.14/0.34 % CPUTime :
% 5.92/1.16 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 5.92/1.16
% 5.92/1.16 % SZS status Theorem
% 5.92/1.16
% 5.92/1.17 % SZS output start Proof
% 5.92/1.17 Take the following subset of the input axioms:
% 5.92/1.18 fof(dt_k2_funct_1, axiom, ![A2]: ((relation(A2) & function(A2)) => (relation(function_inverse(A2)) & function(function_inverse(A2))))).
% 5.92/1.18 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)))))).
% 5.92/1.18 fof(t61_funct_1, axiom, ![A2_2]: ((relation(A2_2) & function(A2_2)) => (one_to_one(A2_2) => (relation_composition(A2_2, function_inverse(A2_2))=identity_relation(relation_dom(A2_2)) & relation_composition(function_inverse(A2_2), A2_2)=identity_relation(relation_rng(A2_2)))))).
% 5.92/1.18 fof(t62_funct_1, axiom, ![A2_2]: ((relation(A2_2) & function(A2_2)) => (one_to_one(A2_2) => one_to_one(function_inverse(A2_2))))).
% 5.92/1.18 fof(t63_funct_1, axiom, ![A2_2]: ((relation(A2_2) & function(A2_2)) => ![B]: ((relation(B) & function(B)) => ((one_to_one(A2_2) & (relation_rng(A2_2)=relation_dom(B) & relation_composition(A2_2, B)=identity_relation(relation_dom(A2_2)))) => B=function_inverse(A2_2))))).
% 5.92/1.18 fof(t65_funct_1, conjecture, ![A]: ((relation(A) & function(A)) => (one_to_one(A) => function_inverse(function_inverse(A))=A))).
% 5.92/1.18
% 5.92/1.18 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.92/1.18 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.92/1.18 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.92/1.18 fresh(y, y, x1...xn) = u
% 5.92/1.18 C => fresh(s, t, x1...xn) = v
% 5.92/1.18 where fresh is a fresh function symbol and x1..xn are the free
% 5.92/1.18 variables of u and v.
% 5.92/1.18 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.92/1.18 input problem has no model of domain size 1).
% 5.92/1.18
% 5.92/1.18 The encoding turns the above axioms into the following unit equations and goals:
% 5.92/1.18
% 5.92/1.18 Axiom 1 (t65_funct_1_1): relation(a) = true2.
% 5.92/1.18 Axiom 2 (t65_funct_1): function(a) = true2.
% 5.92/1.18 Axiom 3 (t65_funct_1_2): one_to_one(a) = true2.
% 5.92/1.18 Axiom 4 (t55_funct_1_1): fresh56(X, X, Y) = relation_rng(Y).
% 5.92/1.18 Axiom 5 (t55_funct_1): fresh54(X, X, Y) = relation_dom(Y).
% 5.92/1.18 Axiom 6 (t61_funct_1_1): fresh52(X, X, Y) = identity_relation(relation_rng(Y)).
% 5.92/1.18 Axiom 7 (t62_funct_1): fresh48(X, X, Y) = true2.
% 5.92/1.18 Axiom 8 (dt_k2_funct_1): fresh37(X, X, Y) = function(function_inverse(Y)).
% 5.92/1.18 Axiom 9 (dt_k2_funct_1): fresh36(X, X, Y) = true2.
% 5.92/1.18 Axiom 10 (dt_k2_funct_1_1): fresh35(X, X, Y) = relation(function_inverse(Y)).
% 5.92/1.18 Axiom 11 (dt_k2_funct_1_1): fresh34(X, X, Y) = true2.
% 5.92/1.18 Axiom 12 (t55_funct_1): fresh9(X, X, Y) = relation_rng(function_inverse(Y)).
% 5.92/1.18 Axiom 13 (t55_funct_1_1): fresh8(X, X, Y) = relation_dom(function_inverse(Y)).
% 5.92/1.18 Axiom 14 (t61_funct_1_1): fresh6(X, X, Y) = relation_composition(function_inverse(Y), Y).
% 5.92/1.18 Axiom 15 (t62_funct_1): fresh5(X, X, Y) = one_to_one(function_inverse(Y)).
% 5.92/1.18 Axiom 16 (t55_funct_1_1): fresh55(X, X, Y) = fresh56(function(Y), true2, Y).
% 5.92/1.18 Axiom 17 (t55_funct_1): fresh53(X, X, Y) = fresh54(function(Y), true2, Y).
% 5.92/1.18 Axiom 18 (t61_funct_1_1): fresh51(X, X, Y) = fresh52(function(Y), true2, Y).
% 5.92/1.18 Axiom 19 (t62_funct_1): fresh47(X, X, Y) = fresh48(function(Y), true2, Y).
% 5.92/1.18 Axiom 20 (t63_funct_1): fresh46(X, X, Y, Z) = function_inverse(Y).
% 5.92/1.18 Axiom 21 (dt_k2_funct_1): fresh37(relation(X), true2, X) = fresh36(function(X), true2, X).
% 5.92/1.18 Axiom 22 (dt_k2_funct_1_1): fresh35(relation(X), true2, X) = fresh34(function(X), true2, X).
% 5.92/1.18 Axiom 23 (t55_funct_1): fresh53(one_to_one(X), true2, X) = fresh9(relation(X), true2, X).
% 5.92/1.18 Axiom 24 (t55_funct_1_1): fresh55(one_to_one(X), true2, X) = fresh8(relation(X), true2, X).
% 5.92/1.18 Axiom 25 (t61_funct_1_1): fresh51(one_to_one(X), true2, X) = fresh6(relation(X), true2, X).
% 5.92/1.18 Axiom 26 (t62_funct_1): fresh47(one_to_one(X), true2, X) = fresh5(relation(X), true2, X).
% 5.92/1.18 Axiom 27 (t63_funct_1): fresh3(X, X, Y, Z) = Z.
% 5.92/1.18 Axiom 28 (t63_funct_1): fresh44(X, X, Y, Z) = fresh45(function(Y), true2, Y, Z).
% 5.92/1.18 Axiom 29 (t63_funct_1): fresh43(X, X, Y, Z) = fresh44(function(Z), true2, Y, Z).
% 5.92/1.18 Axiom 30 (t63_funct_1): fresh42(X, X, Y, Z) = fresh43(relation(Y), true2, Y, Z).
% 5.92/1.18 Axiom 31 (t63_funct_1): fresh41(X, X, Y, Z) = fresh42(relation(Z), true2, Y, Z).
% 5.92/1.18 Axiom 32 (t63_funct_1): fresh45(X, X, Y, Z) = fresh46(relation_rng(Y), relation_dom(Z), Y, Z).
% 5.92/1.18 Axiom 33 (t63_funct_1): fresh41(one_to_one(X), true2, X, Y) = fresh3(relation_composition(X, Y), identity_relation(relation_dom(X)), X, Y).
% 5.92/1.18
% 5.92/1.18 Goal 1 (t65_funct_1_3): function_inverse(function_inverse(a)) = a.
% 5.92/1.18 Proof:
% 5.92/1.18 function_inverse(function_inverse(a))
% 5.92/1.18 = { by axiom 20 (t63_funct_1) R->L }
% 5.92/1.18 fresh46(relation_dom(a), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 5 (t55_funct_1) R->L }
% 5.92/1.18 fresh46(fresh54(true2, true2, a), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 2 (t65_funct_1) R->L }
% 5.92/1.18 fresh46(fresh54(function(a), true2, a), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 17 (t55_funct_1) R->L }
% 5.92/1.18 fresh46(fresh53(true2, true2, a), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 3 (t65_funct_1_2) R->L }
% 5.92/1.18 fresh46(fresh53(one_to_one(a), true2, a), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 23 (t55_funct_1) }
% 5.92/1.18 fresh46(fresh9(relation(a), true2, a), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 1 (t65_funct_1_1) }
% 5.92/1.18 fresh46(fresh9(true2, true2, a), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 12 (t55_funct_1) }
% 5.92/1.18 fresh46(relation_rng(function_inverse(a)), relation_dom(a), function_inverse(a), a)
% 5.92/1.18 = { by axiom 32 (t63_funct_1) R->L }
% 5.92/1.18 fresh45(true2, true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 9 (dt_k2_funct_1) R->L }
% 5.92/1.18 fresh45(fresh36(true2, true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 2 (t65_funct_1) R->L }
% 5.92/1.18 fresh45(fresh36(function(a), true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 21 (dt_k2_funct_1) R->L }
% 5.92/1.18 fresh45(fresh37(relation(a), true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 1 (t65_funct_1_1) }
% 5.92/1.18 fresh45(fresh37(true2, true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 8 (dt_k2_funct_1) }
% 5.92/1.18 fresh45(function(function_inverse(a)), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 28 (t63_funct_1) R->L }
% 5.92/1.18 fresh44(true2, true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 2 (t65_funct_1) R->L }
% 5.92/1.18 fresh44(function(a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 29 (t63_funct_1) R->L }
% 5.92/1.18 fresh43(true2, true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 11 (dt_k2_funct_1_1) R->L }
% 5.92/1.18 fresh43(fresh34(true2, true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 2 (t65_funct_1) R->L }
% 5.92/1.18 fresh43(fresh34(function(a), true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 22 (dt_k2_funct_1_1) R->L }
% 5.92/1.18 fresh43(fresh35(relation(a), true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 1 (t65_funct_1_1) }
% 5.92/1.18 fresh43(fresh35(true2, true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 10 (dt_k2_funct_1_1) }
% 5.92/1.18 fresh43(relation(function_inverse(a)), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 30 (t63_funct_1) R->L }
% 5.92/1.18 fresh42(true2, true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 1 (t65_funct_1_1) R->L }
% 5.92/1.18 fresh42(relation(a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 31 (t63_funct_1) R->L }
% 5.92/1.18 fresh41(true2, true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 7 (t62_funct_1) R->L }
% 5.92/1.18 fresh41(fresh48(true2, true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 2 (t65_funct_1) R->L }
% 5.92/1.18 fresh41(fresh48(function(a), true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 19 (t62_funct_1) R->L }
% 5.92/1.18 fresh41(fresh47(true2, true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 3 (t65_funct_1_2) R->L }
% 5.92/1.18 fresh41(fresh47(one_to_one(a), true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 26 (t62_funct_1) }
% 5.92/1.18 fresh41(fresh5(relation(a), true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 1 (t65_funct_1_1) }
% 5.92/1.18 fresh41(fresh5(true2, true2, a), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 15 (t62_funct_1) }
% 5.92/1.18 fresh41(one_to_one(function_inverse(a)), true2, function_inverse(a), a)
% 5.92/1.18 = { by axiom 33 (t63_funct_1) }
% 5.92/1.18 fresh3(relation_composition(function_inverse(a), a), identity_relation(relation_dom(function_inverse(a))), function_inverse(a), a)
% 5.92/1.18 = { by axiom 13 (t55_funct_1_1) R->L }
% 5.92/1.18 fresh3(relation_composition(function_inverse(a), a), identity_relation(fresh8(true2, true2, a)), function_inverse(a), a)
% 5.92/1.18 = { by axiom 1 (t65_funct_1_1) R->L }
% 5.92/1.18 fresh3(relation_composition(function_inverse(a), a), identity_relation(fresh8(relation(a), true2, a)), function_inverse(a), a)
% 5.92/1.18 = { by axiom 24 (t55_funct_1_1) R->L }
% 5.92/1.18 fresh3(relation_composition(function_inverse(a), a), identity_relation(fresh55(one_to_one(a), true2, a)), function_inverse(a), a)
% 5.92/1.18 = { by axiom 3 (t65_funct_1_2) }
% 5.92/1.18 fresh3(relation_composition(function_inverse(a), a), identity_relation(fresh55(true2, true2, a)), function_inverse(a), a)
% 5.92/1.18 = { by axiom 16 (t55_funct_1_1) }
% 5.92/1.18 fresh3(relation_composition(function_inverse(a), a), identity_relation(fresh56(function(a), true2, a)), function_inverse(a), a)
% 5.92/1.18 = { by axiom 2 (t65_funct_1) }
% 5.92/1.18 fresh3(relation_composition(function_inverse(a), a), identity_relation(fresh56(true2, true2, a)), function_inverse(a), a)
% 5.92/1.19 = { by axiom 4 (t55_funct_1_1) }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), identity_relation(relation_rng(a)), function_inverse(a), a)
% 5.92/1.19 = { by axiom 6 (t61_funct_1_1) R->L }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), fresh52(true2, true2, a), function_inverse(a), a)
% 5.92/1.19 = { by axiom 2 (t65_funct_1) R->L }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), fresh52(function(a), true2, a), function_inverse(a), a)
% 5.92/1.19 = { by axiom 18 (t61_funct_1_1) R->L }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), fresh51(true2, true2, a), function_inverse(a), a)
% 5.92/1.19 = { by axiom 3 (t65_funct_1_2) R->L }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), fresh51(one_to_one(a), true2, a), function_inverse(a), a)
% 5.92/1.19 = { by axiom 25 (t61_funct_1_1) }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), fresh6(relation(a), true2, a), function_inverse(a), a)
% 5.92/1.19 = { by axiom 1 (t65_funct_1_1) }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), fresh6(true2, true2, a), function_inverse(a), a)
% 5.92/1.19 = { by axiom 14 (t61_funct_1_1) }
% 5.92/1.19 fresh3(relation_composition(function_inverse(a), a), relation_composition(function_inverse(a), a), function_inverse(a), a)
% 5.92/1.19 = { by axiom 27 (t63_funct_1) }
% 5.92/1.19 a
% 5.92/1.19 % SZS output end Proof
% 5.92/1.19
% 5.92/1.19 RESULT: Theorem (the conjecture is true).
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