TSTP Solution File: SWV416+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV416+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 : n011.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 23:04:10 EDT 2023
% Result : Theorem 0.22s 0.51s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV416+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % 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 : n011.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 : Tue Aug 29 03:09:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.51 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.51
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51
% 0.22/0.52 % SZS output start Proof
% 0.22/0.52 Take the following subset of the input axioms:
% 0.22/0.52 fof(ax56, axiom, ![U, V]: (pi_sharp_remove(U, V) <=> contains_pq(U, V))).
% 0.22/0.52 fof(ax57, axiom, ![U2, V2]: (pi_remove(U2, V2) <=> pi_sharp_remove(i(U2), V2))).
% 0.22/0.52 fof(co3, conjecture, ![W, X, U2, V2]: (pi_remove(triple(U2, V2, W), X) => (phi(remove_cpq(triple(U2, V2, W), X)) => (pi_sharp_remove(i(triple(U2, V2, W)), X) & i(remove_cpq(triple(U2, V2, W), X))=remove_pq(i(triple(U2, V2, W)), X))))).
% 0.22/0.52 fof(main3_li12, lemma, ![Y, U2, V2, W2, X2]: i(triple(U2, W2, X2))=i(triple(V2, W2, Y))).
% 0.22/0.52 fof(main3_li34, lemma, ![U2, V2, W2, X2]: (contains_pq(i(triple(U2, V2, W2)), X2) => i(remove_cpq(triple(U2, V2, W2), X2))=remove_pq(i(triple(U2, V2, W2)), X2))).
% 0.22/0.52
% 0.22/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.52 fresh(y, y, x1...xn) = u
% 0.22/0.52 C => fresh(s, t, x1...xn) = v
% 0.22/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.52 variables of u and v.
% 0.22/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.52 input problem has no model of domain size 1).
% 0.22/0.52
% 0.22/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.52
% 0.22/0.52 Axiom 1 (ax56_1): fresh27(X, X, Y, Z) = true2.
% 0.22/0.52 Axiom 2 (ax57_1): fresh25(X, X, Y, Z) = true2.
% 0.22/0.52 Axiom 3 (main3_li12): i(triple(X, Y, Z)) = i(triple(W, Y, V)).
% 0.22/0.52 Axiom 4 (co3): pi_remove(triple(u, v, w), x) = true2.
% 0.22/0.52 Axiom 5 (ax56_1): fresh27(pi_sharp_remove(X, Y), true2, X, Y) = contains_pq(X, Y).
% 0.22/0.52 Axiom 6 (ax57_1): fresh25(pi_remove(X, Y), true2, X, Y) = pi_sharp_remove(i(X), Y).
% 0.22/0.52 Axiom 7 (main3_li34): fresh7(X, X, Y, Z, W, V) = remove_pq(i(triple(Y, Z, W)), V).
% 0.22/0.52 Axiom 8 (main3_li34): fresh7(contains_pq(i(triple(X, Y, Z)), W), true2, X, Y, Z, W) = i(remove_cpq(triple(X, Y, Z), W)).
% 0.22/0.52
% 0.22/0.52 Lemma 9: pi_sharp_remove(i(triple(X, v, Y)), x) = true2.
% 0.22/0.52 Proof:
% 0.22/0.52 pi_sharp_remove(i(triple(X, v, Y)), x)
% 0.22/0.52 = { by axiom 3 (main3_li12) R->L }
% 0.22/0.52 pi_sharp_remove(i(triple(u, v, w)), x)
% 0.22/0.52 = { by axiom 6 (ax57_1) R->L }
% 0.22/0.52 fresh25(pi_remove(triple(u, v, w), x), true2, triple(u, v, w), x)
% 0.22/0.52 = { by axiom 4 (co3) }
% 0.22/0.52 fresh25(true2, true2, triple(u, v, w), x)
% 0.22/0.52 = { by axiom 2 (ax57_1) }
% 0.22/0.52 true2
% 0.22/0.52
% 0.22/0.52 Goal 1 (co3_2): tuple2(i(remove_cpq(triple(u, v, w), x)), pi_sharp_remove(i(triple(u, v, w)), x)) = tuple2(remove_pq(i(triple(u, v, w)), x), true2).
% 0.22/0.52 Proof:
% 0.22/0.52 tuple2(i(remove_cpq(triple(u, v, w), x)), pi_sharp_remove(i(triple(u, v, w)), x))
% 0.22/0.52 = { by lemma 9 }
% 0.22/0.52 tuple2(i(remove_cpq(triple(u, v, w), x)), true2)
% 0.22/0.52 = { by axiom 8 (main3_li34) R->L }
% 0.22/0.52 tuple2(fresh7(contains_pq(i(triple(u, v, w)), x), true2, u, v, w, x), true2)
% 0.22/0.52 = { by axiom 5 (ax56_1) R->L }
% 0.22/0.52 tuple2(fresh7(fresh27(pi_sharp_remove(i(triple(u, v, w)), x), true2, i(triple(u, v, w)), x), true2, u, v, w, x), true2)
% 0.22/0.52 = { by lemma 9 }
% 0.22/0.52 tuple2(fresh7(fresh27(true2, true2, i(triple(u, v, w)), x), true2, u, v, w, x), true2)
% 0.22/0.52 = { by axiom 1 (ax56_1) }
% 0.22/0.52 tuple2(fresh7(true2, true2, u, v, w, x), true2)
% 0.22/0.52 = { by axiom 7 (main3_li34) }
% 0.22/0.52 tuple2(remove_pq(i(triple(u, v, w)), x), true2)
% 0.22/0.52 % SZS output end Proof
% 0.22/0.52
% 0.22/0.52 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------