TSTP Solution File: SEU177+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU177+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 : n032.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 17:51:24 EDT 2023
% Result : Theorem 0.09s 0.34s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU177+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 23 15:12:10 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.34 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.09/0.34
% 0.09/0.34 % SZS status Theorem
% 0.09/0.34
% 0.09/0.34 % SZS output start Proof
% 0.09/0.34 Take the following subset of the input axioms:
% 0.09/0.34 fof(d4_relat_1, axiom, ![A2]: (relation(A2) => ![B]: (B=relation_dom(A2) <=> ![C]: (in(C, B) <=> ?[D]: in(ordered_pair(C, D), A2))))).
% 0.09/0.34 fof(d5_relat_1, axiom, ![A2_2]: (relation(A2_2) => ![B2]: (B2=relation_rng(A2_2) <=> ![C2]: (in(C2, B2) <=> ?[D2]: in(ordered_pair(D2, C2), A2_2))))).
% 0.09/0.34 fof(t20_relat_1, conjecture, ![A, B2, C2]: (relation(C2) => (in(ordered_pair(A, B2), C2) => (in(A, relation_dom(C2)) & in(B2, relation_rng(C2)))))).
% 0.09/0.34
% 0.09/0.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.09/0.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.09/0.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.09/0.34 fresh(y, y, x1...xn) = u
% 0.09/0.34 C => fresh(s, t, x1...xn) = v
% 0.09/0.34 where fresh is a fresh function symbol and x1..xn are the free
% 0.09/0.34 variables of u and v.
% 0.09/0.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.09/0.34 input problem has no model of domain size 1).
% 0.09/0.34
% 0.09/0.34 The encoding turns the above axioms into the following unit equations and goals:
% 0.09/0.34
% 0.09/0.34 Axiom 1 (t20_relat_1): relation(c3) = true2.
% 0.09/0.34 Axiom 2 (d4_relat_1_1): fresh20(X, X, Y, Z) = true2.
% 0.09/0.35 Axiom 3 (d5_relat_1_1): fresh14(X, X, Y, Z) = true2.
% 0.09/0.35 Axiom 4 (t20_relat_1_1): in(ordered_pair(a, b), c3) = true2.
% 0.09/0.35 Axiom 5 (d4_relat_1_1): fresh19(X, X, Y, Z, W) = fresh20(Z, relation_dom(Y), Z, W).
% 0.09/0.35 Axiom 6 (d5_relat_1_1): fresh13(X, X, Y, Z, W) = fresh14(Z, relation_rng(Y), Z, W).
% 0.09/0.35 Axiom 7 (d4_relat_1_1): fresh9(X, X, Y, Z, W) = in(W, Z).
% 0.09/0.35 Axiom 8 (d5_relat_1_1): fresh6(X, X, Y, Z, W) = in(W, Z).
% 0.09/0.35 Axiom 9 (d4_relat_1_1): fresh19(in(ordered_pair(X, Y), Z), true2, Z, W, X) = fresh9(relation(Z), true2, Z, W, X).
% 0.09/0.35 Axiom 10 (d5_relat_1_1): fresh13(in(ordered_pair(X, Y), Z), true2, Z, W, Y) = fresh6(relation(Z), true2, Z, W, Y).
% 0.09/0.35
% 0.09/0.35 Goal 1 (t20_relat_1_2): tuple(in(a, relation_dom(c3)), in(b, relation_rng(c3))) = tuple(true2, true2).
% 0.09/0.35 Proof:
% 0.09/0.35 tuple(in(a, relation_dom(c3)), in(b, relation_rng(c3)))
% 0.09/0.35 = { by axiom 7 (d4_relat_1_1) R->L }
% 0.09/0.35 tuple(fresh9(true2, true2, c3, relation_dom(c3), a), in(b, relation_rng(c3)))
% 0.09/0.35 = { by axiom 1 (t20_relat_1) R->L }
% 0.09/0.35 tuple(fresh9(relation(c3), true2, c3, relation_dom(c3), a), in(b, relation_rng(c3)))
% 0.09/0.35 = { by axiom 9 (d4_relat_1_1) R->L }
% 0.09/0.35 tuple(fresh19(in(ordered_pair(a, b), c3), true2, c3, relation_dom(c3), a), in(b, relation_rng(c3)))
% 0.09/0.35 = { by axiom 4 (t20_relat_1_1) }
% 0.09/0.35 tuple(fresh19(true2, true2, c3, relation_dom(c3), a), in(b, relation_rng(c3)))
% 0.09/0.35 = { by axiom 5 (d4_relat_1_1) }
% 0.09/0.35 tuple(fresh20(relation_dom(c3), relation_dom(c3), relation_dom(c3), a), in(b, relation_rng(c3)))
% 0.09/0.35 = { by axiom 2 (d4_relat_1_1) }
% 0.09/0.35 tuple(true2, in(b, relation_rng(c3)))
% 0.09/0.35 = { by axiom 8 (d5_relat_1_1) R->L }
% 0.09/0.35 tuple(true2, fresh6(true2, true2, c3, relation_rng(c3), b))
% 0.09/0.35 = { by axiom 1 (t20_relat_1) R->L }
% 0.09/0.35 tuple(true2, fresh6(relation(c3), true2, c3, relation_rng(c3), b))
% 0.09/0.35 = { by axiom 10 (d5_relat_1_1) R->L }
% 0.09/0.35 tuple(true2, fresh13(in(ordered_pair(a, b), c3), true2, c3, relation_rng(c3), b))
% 0.09/0.35 = { by axiom 4 (t20_relat_1_1) }
% 0.09/0.35 tuple(true2, fresh13(true2, true2, c3, relation_rng(c3), b))
% 0.09/0.35 = { by axiom 6 (d5_relat_1_1) }
% 0.09/0.35 tuple(true2, fresh14(relation_rng(c3), relation_rng(c3), relation_rng(c3), b))
% 0.09/0.35 = { by axiom 3 (d5_relat_1_1) }
% 0.09/0.35 tuple(true2, true2)
% 0.09/0.35 % SZS output end Proof
% 0.09/0.35
% 0.09/0.35 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------