TSTP Solution File: COL098-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL098-1 : TPTP v8.1.2. Released v2.7.0.
% 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 : n005.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 : Wed Aug 30 18:32:07 EDT 2023
% Result : Unsatisfiable 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL098-1 : TPTP v8.1.2. Released v2.7.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 04:35:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.51 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.51
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Take the following subset of the input axioms:
% 0.19/0.52 fof(diamond_strip_lemmaD_2c1, negated_conjecture, member(pair(x, sk3), r)).
% 0.19/0.52 fof(diamond_strip_lemmaD_2c2, negated_conjecture, ![ZA]: (~member(pair(sk3, ZA), trancl(r)) | ~member(pair(z, ZA), r))).
% 0.19/0.52 fof(diamond_strip_lemmaD_2h1, hypothesis, ![X, Y, YP]: (~member(pair(X, Y), r) | (~member(pair(X, YP), r) | member(pair(Y, sk1(X, Y, YP)), r)))).
% 0.19/0.52 fof(diamond_strip_lemmaD_2h2, hypothesis, ![YP2, X2, Y2]: (~member(pair(X2, Y2), r) | (~member(pair(X2, YP2), r) | member(pair(YP2, sk1(X2, Y2, YP2)), r)))).
% 0.19/0.52 fof(diamond_strip_lemmaD_2h4, hypothesis, member(pair(y, z), r)).
% 0.19/0.52 fof(diamond_strip_lemmaD_2h5, hypothesis, ![YP2]: (~member(pair(x, YP2), r) | member(pair(YP2, sk2(YP2)), trancl(r)))).
% 0.19/0.52 fof(diamond_strip_lemmaD_2h6, hypothesis, ![YP2]: (~member(pair(x, YP2), r) | member(pair(y, sk2(YP2)), r))).
% 0.19/0.52 fof(k_app, axiom, ![P, Q]: combK!=comb_app(P, Q)).
% 0.19/0.52 fof(r_into_trancl, axiom, ![B, R, A2]: (~member(pair(A2, B), R) | member(pair(A2, B), trancl(R)))).
% 0.19/0.52 fof(s_app, axiom, ![P2, Q2]: combS!=comb_app(P2, Q2)).
% 0.19/0.52 fof(transD, axiom, ![C, R2, B2, A2_2]: (~trans(R2) | (~member(pair(A2_2, B2), R2) | (~member(pair(B2, C), R2) | member(pair(A2_2, C), R2))))).
% 0.19/0.52 fof(trans_trancl, axiom, ![R2]: trans(trancl(R2))).
% 0.19/0.52
% 0.19/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.52 fresh(y, y, x1...xn) = u
% 0.19/0.52 C => fresh(s, t, x1...xn) = v
% 0.19/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.52 variables of u and v.
% 0.19/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.52 input problem has no model of domain size 1).
% 0.19/0.52
% 0.19/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.52
% 0.19/0.52 Axiom 1 (trans_trancl): trans(trancl(X)) = true2.
% 0.19/0.52 Axiom 2 (diamond_strip_lemmaD_2h5): fresh6(X, X, Y) = true2.
% 0.19/0.52 Axiom 3 (diamond_strip_lemmaD_2h6): fresh5(X, X, Y) = true2.
% 0.19/0.52 Axiom 4 (diamond_strip_lemmaD_2c1): member(pair(x, sk3), r) = true2.
% 0.19/0.52 Axiom 5 (diamond_strip_lemmaD_2h4): member(pair(y, z), r) = true2.
% 0.19/0.52 Axiom 6 (transD): fresh12(X, X, Y, Z, W) = true2.
% 0.19/0.52 Axiom 7 (diamond_strip_lemmaD_2h1): fresh10(X, X, Y, Z, W) = true2.
% 0.19/0.52 Axiom 8 (diamond_strip_lemmaD_2h2): fresh7(X, X, Y, Z, W) = true2.
% 0.19/0.52 Axiom 9 (r_into_trancl): fresh4(X, X, Y, Z, W) = true2.
% 0.19/0.52 Axiom 10 (transD): fresh3(X, X, Y, Z, W, V) = member(pair(Z, V), Y).
% 0.19/0.52 Axiom 11 (diamond_strip_lemmaD_2h1): fresh9(X, X, Y, Z, W) = member(pair(Z, sk1(Y, Z, W)), r).
% 0.19/0.52 Axiom 12 (diamond_strip_lemmaD_2h2): fresh8(X, X, Y, Z, W) = member(pair(W, sk1(Y, Z, W)), r).
% 0.19/0.52 Axiom 13 (diamond_strip_lemmaD_2h5): fresh6(member(pair(x, X), r), true2, X) = member(pair(X, sk2(X)), trancl(r)).
% 0.19/0.52 Axiom 14 (diamond_strip_lemmaD_2h6): fresh5(member(pair(x, X), r), true2, X) = member(pair(y, sk2(X)), r).
% 0.19/0.52 Axiom 15 (transD): fresh11(X, X, Y, Z, W, V) = fresh12(member(pair(Z, W), Y), true2, Y, Z, V).
% 0.19/0.52 Axiom 16 (diamond_strip_lemmaD_2h1): fresh9(member(pair(X, Y), r), true2, X, Z, Y) = fresh10(member(pair(X, Z), r), true2, X, Z, Y).
% 0.19/0.52 Axiom 17 (diamond_strip_lemmaD_2h2): fresh8(member(pair(X, Y), r), true2, X, Z, Y) = fresh7(member(pair(X, Z), r), true2, X, Z, Y).
% 0.19/0.52 Axiom 18 (r_into_trancl): fresh4(member(pair(X, Y), Z), true2, X, Y, Z) = member(pair(X, Y), trancl(Z)).
% 0.19/0.52 Axiom 19 (transD): fresh11(trans(X), true2, X, Y, Z, W) = fresh3(member(pair(Z, W), X), true2, X, Y, Z, W).
% 0.19/0.52
% 0.19/0.52 Lemma 20: member(pair(y, sk2(sk3)), r) = true2.
% 0.19/0.52 Proof:
% 0.19/0.52 member(pair(y, sk2(sk3)), r)
% 0.19/0.52 = { by axiom 14 (diamond_strip_lemmaD_2h6) R->L }
% 0.19/0.52 fresh5(member(pair(x, sk3), r), true2, sk3)
% 0.19/0.52 = { by axiom 4 (diamond_strip_lemmaD_2c1) }
% 0.19/0.52 fresh5(true2, true2, sk3)
% 0.19/0.52 = { by axiom 3 (diamond_strip_lemmaD_2h6) }
% 0.19/0.52 true2
% 0.19/0.52
% 0.19/0.52 Goal 1 (diamond_strip_lemmaD_2c2): tuple(member(pair(z, X), r), member(pair(sk3, X), trancl(r))) = tuple(true2, true2).
% 0.19/0.52 The goal is true when:
% 0.19/0.52 X = sk1(y, sk2(sk3), z)
% 0.19/0.52
% 0.19/0.52 Proof:
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), member(pair(sk3, sk1(y, sk2(sk3), z)), trancl(r)))
% 0.19/0.52 = { by axiom 10 (transD) R->L }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(true2, true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 9 (r_into_trancl) R->L }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(fresh4(true2, true2, sk2(sk3), sk1(y, sk2(sk3), z), r), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 7 (diamond_strip_lemmaD_2h1) R->L }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(fresh4(fresh10(true2, true2, y, sk2(sk3), z), true2, sk2(sk3), sk1(y, sk2(sk3), z), r), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by lemma 20 R->L }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(fresh4(fresh10(member(pair(y, sk2(sk3)), r), true2, y, sk2(sk3), z), true2, sk2(sk3), sk1(y, sk2(sk3), z), r), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 16 (diamond_strip_lemmaD_2h1) R->L }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(fresh4(fresh9(member(pair(y, z), r), true2, y, sk2(sk3), z), true2, sk2(sk3), sk1(y, sk2(sk3), z), r), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 5 (diamond_strip_lemmaD_2h4) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(fresh4(fresh9(true2, true2, y, sk2(sk3), z), true2, sk2(sk3), sk1(y, sk2(sk3), z), r), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 11 (diamond_strip_lemmaD_2h1) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(fresh4(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), r), true2, sk2(sk3), sk1(y, sk2(sk3), z), r), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 18 (r_into_trancl) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh3(member(pair(sk2(sk3), sk1(y, sk2(sk3), z)), trancl(r)), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 19 (transD) R->L }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh11(trans(trancl(r)), true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 1 (trans_trancl) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh11(true2, true2, trancl(r), sk3, sk2(sk3), sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 15 (transD) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh12(member(pair(sk3, sk2(sk3)), trancl(r)), true2, trancl(r), sk3, sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 13 (diamond_strip_lemmaD_2h5) R->L }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh12(fresh6(member(pair(x, sk3), r), true2, sk3), true2, trancl(r), sk3, sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 4 (diamond_strip_lemmaD_2c1) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh12(fresh6(true2, true2, sk3), true2, trancl(r), sk3, sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 2 (diamond_strip_lemmaD_2h5) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), fresh12(true2, true2, trancl(r), sk3, sk1(y, sk2(sk3), z)))
% 0.19/0.52 = { by axiom 6 (transD) }
% 0.19/0.52 tuple(member(pair(z, sk1(y, sk2(sk3), z)), r), true2)
% 0.19/0.52 = { by axiom 12 (diamond_strip_lemmaD_2h2) R->L }
% 0.19/0.52 tuple(fresh8(true2, true2, y, sk2(sk3), z), true2)
% 0.19/0.52 = { by axiom 5 (diamond_strip_lemmaD_2h4) R->L }
% 0.19/0.52 tuple(fresh8(member(pair(y, z), r), true2, y, sk2(sk3), z), true2)
% 0.19/0.52 = { by axiom 17 (diamond_strip_lemmaD_2h2) }
% 0.19/0.52 tuple(fresh7(member(pair(y, sk2(sk3)), r), true2, y, sk2(sk3), z), true2)
% 0.19/0.52 = { by lemma 20 }
% 0.19/0.52 tuple(fresh7(true2, true2, y, sk2(sk3), z), true2)
% 0.19/0.52 = { by axiom 8 (diamond_strip_lemmaD_2h2) }
% 0.19/0.52 tuple(true2, true2)
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52
% 0.19/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------