TSTP Solution File: SWV366+1 by Twee---2.5.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : SWV366+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n026.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 : Mon Jun 24 17:31:53 EDT 2024
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV366+1 : TPTP v8.2.0. Released v3.3.0.
% 0.00/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 16:35:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.47 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 Take the following subset of the input axioms:
% 0.19/0.47 fof(ax55, axiom, ![U, V, W, X, Y]: i(triple(U, insert_slb(V, pair(X, Y)), W))=insert_pq(i(triple(U, V, W)), X)).
% 0.19/0.47 fof(l2_co, conjecture, ![U2]: (![V2, W2, X6, Y2]: i(triple(V2, U2, X6))=i(triple(W2, U2, Y2)) => ![Z, X1, X2, X3, X4, X5]: i(triple(Z, insert_slb(U2, pair(X4, X5)), X2))=i(triple(X1, insert_slb(U2, pair(X4, X5)), X3)))).
% 0.19/0.47
% 0.19/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.47 fresh(y, y, x1...xn) = u
% 0.19/0.47 C => fresh(s, t, x1...xn) = v
% 0.19/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.47 variables of u and v.
% 0.19/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.47 input problem has no model of domain size 1).
% 0.19/0.47
% 0.19/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.47
% 0.19/0.47 Axiom 1 (l2_co): i(triple(X, u, Y)) = i(triple(Z, u, W)).
% 0.19/0.47 Axiom 2 (ax55): i(triple(X, insert_slb(Y, pair(Z, W)), V)) = insert_pq(i(triple(X, Y, V)), Z).
% 0.19/0.47
% 0.19/0.47 Goal 1 (l2_co_1): i(triple(z, insert_slb(u, pair(x4, x5)), x2)) = i(triple(x1, insert_slb(u, pair(x4, x5)), x3)).
% 0.19/0.47 Proof:
% 0.19/0.47 i(triple(z, insert_slb(u, pair(x4, x5)), x2))
% 0.19/0.47 = { by axiom 2 (ax55) }
% 0.19/0.47 insert_pq(i(triple(z, u, x2)), x4)
% 0.19/0.47 = { by axiom 1 (l2_co) R->L }
% 0.19/0.47 insert_pq(i(triple(x1, u, x3)), x4)
% 0.19/0.47 = { by axiom 2 (ax55) R->L }
% 0.19/0.47 i(triple(x1, insert_slb(u, pair(x4, x5)), x3))
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47
% 0.19/0.47 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------