TSTP Solution File: COL100-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL100-1 : 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 : n008.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 0.67s
% Output : Proof 0.19s
% 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 : COL100-1 : 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 : n008.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 04:14:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.67 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.19/0.67
% 0.19/0.67 % SZS status Unsatisfiable
% 0.19/0.67
% 0.19/0.68 % SZS output start Proof
% 0.19/0.68 Take the following subset of the input axioms:
% 0.19/0.69 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)))))).
% 0.19/0.69 fof(diamond_strip_lemmaD2, axiom, ![R2, YP2, X2, Y2]: (~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))))).
% 0.19/0.69 fof(diamond_trancl_2c1, negated_conjecture, member(pair(y, yp), trancl(r))).
% 0.19/0.69 fof(diamond_trancl_2c2, negated_conjecture, ![ZA]: (~member(pair(z, ZA), trancl(r)) | ~member(pair(yp, ZA), trancl(r)))).
% 0.19/0.69 fof(diamond_trancl_2h1, hypothesis, diamond(r)).
% 0.19/0.69 fof(diamond_trancl_2h3, hypothesis, member(pair(ya, z), r)).
% 0.19/0.69 fof(diamond_trancl_2h4, hypothesis, ![YP2]: (~member(pair(y, YP2), trancl(r)) | member(pair(ya, sk1(YP2)), trancl(r)))).
% 0.19/0.69 fof(diamond_trancl_2h5, hypothesis, ![YP2]: (~member(pair(y, YP2), trancl(r)) | member(pair(YP2, sk1(YP2)), trancl(r)))).
% 0.19/0.69 fof(k_app, axiom, ![P, Q]: combK!=comb_app(P, Q)).
% 0.19/0.69 fof(r_into_trancl, axiom, ![B, A2, R2]: (~member(pair(A2, B), R2) | member(pair(A2, B), trancl(R2)))).
% 0.19/0.69 fof(s_app, axiom, ![P2, Q2]: combS!=comb_app(P2, Q2)).
% 0.19/0.69 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))))).
% 0.19/0.69 fof(trans_trancl, axiom, ![R2]: trans(trancl(R2))).
% 0.19/0.69
% 0.19/0.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.69 fresh(y, y, x1...xn) = u
% 0.19/0.69 C => fresh(s, t, x1...xn) = v
% 0.19/0.69 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.69 variables of u and v.
% 0.19/0.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.69 input problem has no model of domain size 1).
% 0.19/0.69
% 0.19/0.69 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.69
% 0.19/0.69 Axiom 1 (diamond_trancl_2h1): diamond(r) = true2.
% 0.19/0.69 Axiom 2 (trans_trancl): trans(trancl(X)) = true2.
% 0.19/0.69 Axiom 3 (diamond_trancl_2h4): fresh6(X, X, Y) = true2.
% 0.19/0.69 Axiom 4 (diamond_trancl_2h5): fresh5(X, X, Y) = true2.
% 0.19/0.69 Axiom 5 (diamond_trancl_2h3): member(pair(ya, z), r) = true2.
% 0.19/0.69 Axiom 6 (diamond_trancl_2c1): member(pair(y, yp), trancl(r)) = true2.
% 0.19/0.69 Axiom 7 (transD): fresh14(X, X, Y, Z, W) = true2.
% 0.19/0.69 Axiom 8 (r_into_trancl): fresh4(X, X, Y, Z, W) = true2.
% 0.19/0.69 Axiom 9 (diamond_strip_lemmaD1): fresh8(X, X, Y, Z, W, V) = true2.
% 0.19/0.69 Axiom 10 (diamond_strip_lemmaD2): fresh7(X, X, Y, Z, W, V) = true2.
% 0.19/0.69 Axiom 11 (transD): fresh3(X, X, Y, Z, W, V) = member(pair(Z, V), Y).
% 0.19/0.69 Axiom 12 (diamond_strip_lemmaD2): fresh10(X, X, Y, Z, W, V) = member(pair(W, diamond_strip_lemmaD_sk1(Z, W, V, Y)), Y).
% 0.19/0.69 Axiom 13 (diamond_trancl_2h4): fresh6(member(pair(y, X), trancl(r)), true2, X) = member(pair(ya, sk1(X)), trancl(r)).
% 0.19/0.69 Axiom 14 (diamond_trancl_2h5): fresh5(member(pair(y, X), trancl(r)), true2, X) = member(pair(X, sk1(X)), trancl(r)).
% 0.19/0.69 Axiom 15 (diamond_strip_lemmaD1): fresh12(X, X, Y, Z, W, V) = member(pair(V, diamond_strip_lemmaD_sk1(Z, W, V, Y)), trancl(Y)).
% 0.19/0.69 Axiom 16 (transD): fresh13(X, X, Y, Z, W, V) = fresh14(member(pair(Z, W), Y), true2, Y, Z, V).
% 0.19/0.69 Axiom 17 (r_into_trancl): fresh4(member(pair(X, Y), Z), true2, X, Y, Z) = member(pair(X, Y), trancl(Z)).
% 0.19/0.69 Axiom 18 (diamond_strip_lemmaD1): fresh11(X, X, Y, Z, W, V) = fresh12(member(pair(Z, V), Y), true2, Y, Z, W, V).
% 0.19/0.69 Axiom 19 (diamond_strip_lemmaD2): fresh9(X, X, Y, Z, W, V) = fresh10(member(pair(Z, V), Y), true2, Y, Z, W, V).
% 0.19/0.69 Axiom 20 (transD): fresh13(trans(X), true2, X, Y, Z, W) = fresh3(member(pair(Z, W), X), true2, X, Y, Z, W).
% 0.19/0.69 Axiom 21 (diamond_strip_lemmaD1): fresh11(diamond(X), true2, X, Y, Z, W) = fresh8(member(pair(Y, Z), trancl(X)), true2, X, Y, Z, W).
% 0.19/0.69 Axiom 22 (diamond_strip_lemmaD2): fresh9(diamond(X), true2, X, Y, Z, W) = fresh7(member(pair(Y, Z), trancl(X)), true2, X, Y, Z, W).
% 0.19/0.69
% 0.19/0.69 Lemma 23: member(pair(ya, sk1(yp)), trancl(r)) = true2.
% 0.19/0.69 Proof:
% 0.19/0.69 member(pair(ya, sk1(yp)), trancl(r))
% 0.19/0.69 = { by axiom 13 (diamond_trancl_2h4) R->L }
% 0.19/0.69 fresh6(member(pair(y, yp), trancl(r)), true2, yp)
% 0.19/0.69 = { by axiom 6 (diamond_trancl_2c1) }
% 0.19/0.69 fresh6(true2, true2, yp)
% 0.19/0.69 = { by axiom 3 (diamond_trancl_2h4) }
% 0.19/0.69 true2
% 0.19/0.69
% 0.19/0.69 Goal 1 (diamond_trancl_2c2): tuple(member(pair(z, X), trancl(r)), member(pair(yp, X), trancl(r))) = tuple(true2, true2).
% 0.19/0.69 The goal is true when:
% 0.19/0.69 X = diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)
% 0.19/0.69
% 0.19/0.69 Proof:
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), member(pair(yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)))
% 0.19/0.69 = { by axiom 11 (transD) R->L }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(true2, true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 8 (r_into_trancl) R->L }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(true2, true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 10 (diamond_strip_lemmaD2) R->L }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(fresh7(true2, true2, r, ya, sk1(yp), z), true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by lemma 23 R->L }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(fresh7(member(pair(ya, sk1(yp)), trancl(r)), true2, r, ya, sk1(yp), z), true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 22 (diamond_strip_lemmaD2) R->L }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(fresh9(diamond(r), true2, r, ya, sk1(yp), z), true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 1 (diamond_trancl_2h1) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(fresh9(true2, true2, r, ya, sk1(yp), z), true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 19 (diamond_strip_lemmaD2) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(fresh10(member(pair(ya, z), r), true2, r, ya, sk1(yp), z), true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 5 (diamond_trancl_2h3) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(fresh10(true2, true2, r, ya, sk1(yp), z), true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 12 (diamond_strip_lemmaD2) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(fresh4(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), r), true2, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r), r), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 17 (r_into_trancl) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh3(member(pair(sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 20 (transD) R->L }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh13(trans(trancl(r)), true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 2 (trans_trancl) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh13(true2, true2, trancl(r), yp, sk1(yp), diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 16 (transD) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh14(member(pair(yp, sk1(yp)), trancl(r)), true2, trancl(r), yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 14 (diamond_trancl_2h5) R->L }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh14(fresh5(member(pair(y, yp), trancl(r)), true2, yp), true2, trancl(r), yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 6 (diamond_trancl_2c1) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh14(fresh5(true2, true2, yp), true2, trancl(r), yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 4 (diamond_trancl_2h5) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), fresh14(true2, true2, trancl(r), yp, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)))
% 0.19/0.69 = { by axiom 7 (transD) }
% 0.19/0.69 tuple(member(pair(z, diamond_strip_lemmaD_sk1(ya, sk1(yp), z, r)), trancl(r)), true2)
% 0.19/0.69 = { by axiom 15 (diamond_strip_lemmaD1) R->L }
% 0.19/0.69 tuple(fresh12(true2, true2, r, ya, sk1(yp), z), true2)
% 0.19/0.69 = { by axiom 5 (diamond_trancl_2h3) R->L }
% 0.19/0.69 tuple(fresh12(member(pair(ya, z), r), true2, r, ya, sk1(yp), z), true2)
% 0.19/0.69 = { by axiom 18 (diamond_strip_lemmaD1) R->L }
% 0.19/0.69 tuple(fresh11(true2, true2, r, ya, sk1(yp), z), true2)
% 0.19/0.69 = { by axiom 1 (diamond_trancl_2h1) R->L }
% 0.19/0.69 tuple(fresh11(diamond(r), true2, r, ya, sk1(yp), z), true2)
% 0.19/0.69 = { by axiom 21 (diamond_strip_lemmaD1) }
% 0.19/0.69 tuple(fresh8(member(pair(ya, sk1(yp)), trancl(r)), true2, r, ya, sk1(yp), z), true2)
% 0.19/0.69 = { by lemma 23 }
% 0.19/0.69 tuple(fresh8(true2, true2, r, ya, sk1(yp), z), true2)
% 0.19/0.69 = { by axiom 9 (diamond_strip_lemmaD1) }
% 0.19/0.69 tuple(true2, true2)
% 0.19/0.69 % SZS output end Proof
% 0.19/0.69
% 0.19/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
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