TSTP Solution File: COL099-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL099-1 : 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 : 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 : Wed Aug 30 18:32:07 EDT 2023
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL099-1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 04:38:49 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Take the following subset of the input axioms:
% 0.20/0.46 fof(diamond_strip_lemmaD1, axiom, ![R, X, Y, YP]: (~diamond(R) | (~member(pair(X, Y), trancl(R)) | (~member(pair(X, YP), R) | member(pair(YP, diamond_strip_lemmaD_sk1(X, Y, YP, R)), trancl(R)))))).
% 0.20/0.46 fof(diamond_strip_lemmaD2, axiom, ![R2, X2, Y2, YP2]: (~diamond(R2) | (~member(pair(X2, Y2), trancl(R2)) | (~member(pair(X2, YP2), R2) | member(pair(Y2, diamond_strip_lemmaD_sk1(X2, Y2, YP2, R2)), R2))))).
% 0.20/0.46 fof(diamond_trancl_1c1, negated_conjecture, member(pair(y, yp), trancl(r))).
% 0.20/0.46 fof(diamond_trancl_1c2, negated_conjecture, ![Z]: (~member(pair(ya, Z), trancl(r)) | ~member(pair(yp, Z), trancl(r)))).
% 0.20/0.46 fof(diamond_trancl_1h1, hypothesis, diamond(r)).
% 0.20/0.46 fof(diamond_trancl_1h2, hypothesis, member(pair(y, ya), r)).
% 0.20/0.46 fof(k_app, axiom, ![P, Q]: combK!=comb_app(P, Q)).
% 0.20/0.46 fof(r_into_trancl, axiom, ![B, A2, R2]: (~member(pair(A2, B), R2) | member(pair(A2, B), trancl(R2)))).
% 0.20/0.46 fof(s_app, axiom, ![P2, Q2]: combS!=comb_app(P2, Q2)).
% 0.20/0.46
% 0.20/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.46 fresh(y, y, x1...xn) = u
% 0.20/0.46 C => fresh(s, t, x1...xn) = v
% 0.20/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.46 variables of u and v.
% 0.20/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.46 input problem has no model of domain size 1).
% 0.20/0.46
% 0.20/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.46
% 0.20/0.46 Axiom 1 (diamond_trancl_1h1): diamond(r) = true2.
% 0.20/0.46 Axiom 2 (diamond_trancl_1h2): member(pair(y, ya), r) = true2.
% 0.20/0.46 Axiom 3 (diamond_trancl_1c1): member(pair(y, yp), trancl(r)) = true2.
% 0.20/0.46 Axiom 4 (r_into_trancl): fresh4(X, X, Y, Z, W) = true2.
% 0.20/0.46 Axiom 5 (diamond_strip_lemmaD1): fresh6(X, X, Y, Z, W, V) = true2.
% 0.20/0.46 Axiom 6 (diamond_strip_lemmaD2): fresh5(X, X, Y, Z, W, V) = true2.
% 0.20/0.46 Axiom 7 (diamond_strip_lemmaD2): fresh8(X, X, Y, Z, W, V) = member(pair(W, diamond_strip_lemmaD_sk1(Z, W, V, Y)), Y).
% 0.20/0.46 Axiom 8 (diamond_strip_lemmaD1): fresh10(X, X, Y, Z, W, V) = member(pair(V, diamond_strip_lemmaD_sk1(Z, W, V, Y)), trancl(Y)).
% 0.20/0.46 Axiom 9 (r_into_trancl): fresh4(member(pair(X, Y), Z), true2, X, Y, Z) = member(pair(X, Y), trancl(Z)).
% 0.20/0.46 Axiom 10 (diamond_strip_lemmaD1): fresh9(X, X, Y, Z, W, V) = fresh10(member(pair(Z, V), Y), true2, Y, Z, W, V).
% 0.20/0.46 Axiom 11 (diamond_strip_lemmaD2): fresh7(X, X, Y, Z, W, V) = fresh8(member(pair(Z, V), Y), true2, Y, Z, W, V).
% 0.20/0.46 Axiom 12 (diamond_strip_lemmaD1): fresh9(diamond(X), true2, X, Y, Z, W) = fresh6(member(pair(Y, Z), trancl(X)), true2, X, Y, Z, W).
% 0.20/0.46 Axiom 13 (diamond_strip_lemmaD2): fresh7(diamond(X), true2, X, Y, Z, W) = fresh5(member(pair(Y, Z), trancl(X)), true2, X, Y, Z, W).
% 0.20/0.46
% 0.20/0.46 Goal 1 (diamond_trancl_1c2): tuple(member(pair(ya, X), trancl(r)), member(pair(yp, X), trancl(r))) = tuple(true2, true2).
% 0.20/0.46 The goal is true when:
% 0.20/0.46 X = diamond_strip_lemmaD_sk1(y, yp, ya, r)
% 0.20/0.46
% 0.20/0.46 Proof:
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), member(pair(yp, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)))
% 0.20/0.46 = { by axiom 9 (r_into_trancl) R->L }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(member(pair(yp, diamond_strip_lemmaD_sk1(y, yp, ya, r)), r), true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 7 (diamond_strip_lemmaD2) R->L }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(fresh8(true2, true2, r, y, yp, ya), true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 2 (diamond_trancl_1h2) R->L }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(fresh8(member(pair(y, ya), r), true2, r, y, yp, ya), true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 11 (diamond_strip_lemmaD2) R->L }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(fresh7(true2, true2, r, y, yp, ya), true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 1 (diamond_trancl_1h1) R->L }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(fresh7(diamond(r), true2, r, y, yp, ya), true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 13 (diamond_strip_lemmaD2) }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(fresh5(member(pair(y, yp), trancl(r)), true2, r, y, yp, ya), true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 3 (diamond_trancl_1c1) }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(fresh5(true2, true2, r, y, yp, ya), true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 6 (diamond_strip_lemmaD2) }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), fresh4(true2, true2, yp, diamond_strip_lemmaD_sk1(y, yp, ya, r), r))
% 0.20/0.46 = { by axiom 4 (r_into_trancl) }
% 0.20/0.46 tuple(member(pair(ya, diamond_strip_lemmaD_sk1(y, yp, ya, r)), trancl(r)), true2)
% 0.20/0.46 = { by axiom 8 (diamond_strip_lemmaD1) R->L }
% 0.20/0.46 tuple(fresh10(true2, true2, r, y, yp, ya), true2)
% 0.20/0.46 = { by axiom 2 (diamond_trancl_1h2) R->L }
% 0.20/0.46 tuple(fresh10(member(pair(y, ya), r), true2, r, y, yp, ya), true2)
% 0.20/0.46 = { by axiom 10 (diamond_strip_lemmaD1) R->L }
% 0.20/0.46 tuple(fresh9(true2, true2, r, y, yp, ya), true2)
% 0.20/0.46 = { by axiom 1 (diamond_trancl_1h1) R->L }
% 0.20/0.46 tuple(fresh9(diamond(r), true2, r, y, yp, ya), true2)
% 0.20/0.46 = { by axiom 12 (diamond_strip_lemmaD1) }
% 0.20/0.46 tuple(fresh6(member(pair(y, yp), trancl(r)), true2, r, y, yp, ya), true2)
% 0.20/0.46 = { by axiom 3 (diamond_trancl_1c1) }
% 0.20/0.46 tuple(fresh6(true2, true2, r, y, yp, ya), true2)
% 0.20/0.46 = { by axiom 5 (diamond_strip_lemmaD1) }
% 0.20/0.46 tuple(true2, true2)
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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