TSTP Solution File: SEU382+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU382+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n013.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 17:52:29 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU382+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 12:40:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.61
% 0.21/0.61 % SZS status Theorem
% 0.21/0.61
% 0.21/0.61 % SZS output start Proof
% 0.21/0.61 Take the following subset of the input axioms:
% 0.21/0.62 fof(abstractness_v1_orders_2, axiom, ![A2]: (rel_str(A2) => (strict_rel_str(A2) => A2=rel_str_of(the_carrier(A2), the_InternalRel(A2))))).
% 0.21/0.62 fof(d1_yellow_1, axiom, ![A]: incl_POSet(A)=rel_str_of(A, inclusion_order(A))).
% 0.21/0.62 fof(dt_k3_yellow_1, axiom, ![A3]: (strict_rel_str(boole_POSet(A3)) & rel_str(boole_POSet(A3)))).
% 0.21/0.62 fof(dt_u1_orders_2, axiom, ![A2_2]: (rel_str(A2_2) => relation_of2_as_subset(the_InternalRel(A2_2), the_carrier(A2_2), the_carrier(A2_2)))).
% 0.21/0.62 fof(free_g1_orders_2, axiom, ![B, A2_2]: (relation_of2(B, A2_2, A2_2) => ![C, D]: (rel_str_of(A2_2, B)=rel_str_of(C, D) => (A2_2=C & B=D)))).
% 0.21/0.62 fof(redefinition_m2_relset_1, axiom, ![B2, C2, A2_2]: (relation_of2_as_subset(C2, A2_2, B2) <=> relation_of2(C2, A2_2, B2))).
% 0.21/0.62 fof(t4_waybel_7, conjecture, ![A3]: the_carrier(boole_POSet(A3))=powerset(A3)).
% 0.21/0.62 fof(t4_yellow_1, axiom, ![A3]: boole_POSet(A3)=incl_POSet(powerset(A3))).
% 0.21/0.62
% 0.21/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.62 fresh(y, y, x1...xn) = u
% 0.21/0.62 C => fresh(s, t, x1...xn) = v
% 0.21/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.62 variables of u and v.
% 0.21/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.62 input problem has no model of domain size 1).
% 0.21/0.62
% 0.21/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.62
% 0.21/0.62 Axiom 1 (dt_k3_yellow_1): rel_str(boole_POSet(X)) = true2.
% 0.21/0.62 Axiom 2 (dt_k3_yellow_1_1): strict_rel_str(boole_POSet(X)) = true2.
% 0.21/0.62 Axiom 3 (t4_yellow_1): boole_POSet(X) = incl_POSet(powerset(X)).
% 0.21/0.62 Axiom 4 (d1_yellow_1): incl_POSet(X) = rel_str_of(X, inclusion_order(X)).
% 0.21/0.62 Axiom 5 (dt_u1_orders_2): fresh28(X, X, Y) = true2.
% 0.21/0.62 Axiom 6 (abstractness_v1_orders_2): fresh7(X, X, Y) = Y.
% 0.21/0.62 Axiom 7 (abstractness_v1_orders_2): fresh45(X, X, Y) = rel_str_of(the_carrier(Y), the_InternalRel(Y)).
% 0.21/0.62 Axiom 8 (abstractness_v1_orders_2): fresh45(strict_rel_str(X), true2, X) = fresh7(rel_str(X), true2, X).
% 0.21/0.62 Axiom 9 (free_g1_orders_2): fresh3(X, X, Y, Z) = Z.
% 0.21/0.62 Axiom 10 (redefinition_m2_relset_1_1): fresh14(X, X, Y, Z, W) = true2.
% 0.21/0.62 Axiom 11 (dt_u1_orders_2): fresh28(rel_str(X), true2, X) = relation_of2_as_subset(the_InternalRel(X), the_carrier(X), the_carrier(X)).
% 0.21/0.62 Axiom 12 (free_g1_orders_2): fresh4(X, X, Y, Z, W, V) = Y.
% 0.21/0.62 Axiom 13 (redefinition_m2_relset_1_1): fresh14(relation_of2_as_subset(X, Y, Z), true2, Y, Z, X) = relation_of2(X, Y, Z).
% 0.21/0.62 Axiom 14 (free_g1_orders_2): fresh4(relation_of2(X, Y, Y), true2, Y, X, Z, W) = fresh3(rel_str_of(Y, X), rel_str_of(Z, W), Y, Z).
% 0.21/0.62
% 0.21/0.62 Goal 1 (t4_waybel_7): the_carrier(boole_POSet(a)) = powerset(a).
% 0.21/0.62 Proof:
% 0.21/0.62 the_carrier(boole_POSet(a))
% 0.21/0.62 = { by axiom 12 (free_g1_orders_2) R->L }
% 0.21/0.62 fresh4(true2, true2, the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a)), powerset(a), inclusion_order(powerset(a)))
% 0.21/0.62 = { by axiom 10 (redefinition_m2_relset_1_1) R->L }
% 0.21/0.62 fresh4(fresh14(true2, true2, the_carrier(boole_POSet(a)), the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a))), true2, the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a)), powerset(a), inclusion_order(powerset(a)))
% 0.21/0.62 = { by axiom 5 (dt_u1_orders_2) R->L }
% 0.21/0.62 fresh4(fresh14(fresh28(true2, true2, boole_POSet(a)), true2, the_carrier(boole_POSet(a)), the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a))), true2, the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a)), powerset(a), inclusion_order(powerset(a)))
% 0.21/0.62 = { by axiom 1 (dt_k3_yellow_1) R->L }
% 0.21/0.62 fresh4(fresh14(fresh28(rel_str(boole_POSet(a)), true2, boole_POSet(a)), true2, the_carrier(boole_POSet(a)), the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a))), true2, the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a)), powerset(a), inclusion_order(powerset(a)))
% 0.21/0.62 = { by axiom 11 (dt_u1_orders_2) }
% 0.21/0.62 fresh4(fresh14(relation_of2_as_subset(the_InternalRel(boole_POSet(a)), the_carrier(boole_POSet(a)), the_carrier(boole_POSet(a))), true2, the_carrier(boole_POSet(a)), the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a))), true2, the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a)), powerset(a), inclusion_order(powerset(a)))
% 0.21/0.62 = { by axiom 13 (redefinition_m2_relset_1_1) }
% 0.21/0.62 fresh4(relation_of2(the_InternalRel(boole_POSet(a)), the_carrier(boole_POSet(a)), the_carrier(boole_POSet(a))), true2, the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a)), powerset(a), inclusion_order(powerset(a)))
% 0.21/0.62 = { by axiom 14 (free_g1_orders_2) }
% 0.21/0.62 fresh3(rel_str_of(the_carrier(boole_POSet(a)), the_InternalRel(boole_POSet(a))), rel_str_of(powerset(a), inclusion_order(powerset(a))), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 7 (abstractness_v1_orders_2) R->L }
% 0.21/0.62 fresh3(fresh45(true2, true2, boole_POSet(a)), rel_str_of(powerset(a), inclusion_order(powerset(a))), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 2 (dt_k3_yellow_1_1) R->L }
% 0.21/0.62 fresh3(fresh45(strict_rel_str(boole_POSet(a)), true2, boole_POSet(a)), rel_str_of(powerset(a), inclusion_order(powerset(a))), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 8 (abstractness_v1_orders_2) }
% 0.21/0.62 fresh3(fresh7(rel_str(boole_POSet(a)), true2, boole_POSet(a)), rel_str_of(powerset(a), inclusion_order(powerset(a))), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 1 (dt_k3_yellow_1) }
% 0.21/0.62 fresh3(fresh7(true2, true2, boole_POSet(a)), rel_str_of(powerset(a), inclusion_order(powerset(a))), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 6 (abstractness_v1_orders_2) }
% 0.21/0.62 fresh3(boole_POSet(a), rel_str_of(powerset(a), inclusion_order(powerset(a))), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 4 (d1_yellow_1) R->L }
% 0.21/0.62 fresh3(boole_POSet(a), incl_POSet(powerset(a)), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 3 (t4_yellow_1) R->L }
% 0.21/0.62 fresh3(boole_POSet(a), boole_POSet(a), the_carrier(boole_POSet(a)), powerset(a))
% 0.21/0.62 = { by axiom 9 (free_g1_orders_2) }
% 0.21/0.62 powerset(a)
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62
% 0.21/0.62 RESULT: Theorem (the conjecture is true).
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