TSTP Solution File: PUZ056-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ056-1 : 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 : n023.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 13:24:06 EDT 2023
% Result : Unsatisfiable 15.55s 2.30s
% Output : Proof 15.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : PUZ056-1 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 23:12:26 EDT 2023
% 0.13/0.33 % CPUTime :
% 15.55/2.30 Command-line arguments: --ground-connectedness --complete-subsets
% 15.55/2.30
% 15.55/2.30 % SZS status Unsatisfiable
% 15.55/2.30
% 15.87/2.33 % SZS output start Proof
% 15.87/2.33 Take the following subset of the input axioms:
% 15.87/2.33 fof(a_move, axiom, ![X, B, A2]: (nextto(on(X, A2), B)=nextto(A2, on(X, B)) | (~fits(X, B) | ~fits(X, A2)))).
% 15.87/2.33 fof(final_state, negated_conjecture, ~state(nextto(pin(n1), nextto(pin(n2), on(small, on(medium, on(large, pin(n3)))))))).
% 15.87/2.33 fof(fits_1, axiom, ![N]: fits(small, pin(N))).
% 15.87/2.33 fof(fits_2, axiom, ![N2]: fits(medium, pin(N2))).
% 15.87/2.33 fof(fits_3, axiom, ![N2]: fits(large, pin(N2))).
% 15.87/2.33 fof(fits_4, axiom, ![A]: fits(small, on(medium, A))).
% 15.87/2.33 fof(fits_5, axiom, ![A3]: fits(medium, on(large, A3))).
% 15.87/2.33 fof(fits_6, axiom, ![A3]: fits(small, on(large, A3))).
% 15.87/2.33 fof(initial_state, axiom, state(nextto(on(small, on(medium, on(large, pin(n1)))), nextto(pin(n2), pin(n3))))).
% 15.87/2.33 fof(nextto_associative, axiom, ![Y, Z, X2]: nextto(X2, nextto(Y, Z))=nextto(nextto(X2, Y), Z)).
% 15.87/2.33 fof(nextto_commutative, axiom, ![X2, Y2]: nextto(X2, Y2)=nextto(Y2, X2)).
% 15.87/2.33
% 15.87/2.33 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.87/2.33 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.87/2.33 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.87/2.33 fresh(y, y, x1...xn) = u
% 15.87/2.33 C => fresh(s, t, x1...xn) = v
% 15.87/2.33 where fresh is a fresh function symbol and x1..xn are the free
% 15.87/2.33 variables of u and v.
% 15.87/2.33 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.87/2.33 input problem has no model of domain size 1).
% 15.87/2.33
% 15.87/2.33 The encoding turns the above axioms into the following unit equations and goals:
% 15.87/2.33
% 15.87/2.33 Axiom 1 (nextto_commutative): nextto(X, Y) = nextto(Y, X).
% 15.87/2.33 Axiom 2 (fits_1): fits(small, pin(X)) = true.
% 15.87/2.33 Axiom 3 (fits_2): fits(medium, pin(X)) = true.
% 15.87/2.33 Axiom 4 (fits_3): fits(large, pin(X)) = true.
% 15.87/2.33 Axiom 5 (fits_4): fits(small, on(medium, X)) = true.
% 15.87/2.33 Axiom 6 (fits_6): fits(small, on(large, X)) = true.
% 15.87/2.33 Axiom 7 (fits_5): fits(medium, on(large, X)) = true.
% 15.87/2.33 Axiom 8 (nextto_associative): nextto(X, nextto(Y, Z)) = nextto(nextto(X, Y), Z).
% 15.87/2.33 Axiom 9 (a_move): fresh(X, X, Y, Z, W) = nextto(Z, on(Y, W)).
% 15.87/2.33 Axiom 10 (a_move): fresh2(X, X, Y, Z, W) = nextto(on(Y, Z), W).
% 15.87/2.33 Axiom 11 (a_move): fresh2(fits(X, Y), true, X, Z, Y) = fresh(fits(X, Z), true, X, Z, Y).
% 15.87/2.33 Axiom 12 (initial_state): state(nextto(on(small, on(medium, on(large, pin(n1)))), nextto(pin(n2), pin(n3)))) = true.
% 15.87/2.33
% 15.87/2.33 Lemma 13: fresh(fits(small, X), true, small, X, pin(Y)) = nextto(pin(Y), on(small, X)).
% 15.87/2.33 Proof:
% 15.87/2.33 fresh(fits(small, X), true, small, X, pin(Y))
% 15.87/2.33 = { by axiom 11 (a_move) R->L }
% 15.87/2.33 fresh2(fits(small, pin(Y)), true, small, X, pin(Y))
% 15.87/2.33 = { by axiom 2 (fits_1) }
% 15.87/2.33 fresh2(true, true, small, X, pin(Y))
% 15.87/2.33 = { by axiom 10 (a_move) }
% 15.87/2.33 nextto(on(small, X), pin(Y))
% 15.87/2.33 = { by axiom 1 (nextto_commutative) }
% 15.87/2.33 nextto(pin(Y), on(small, X))
% 15.87/2.33
% 15.87/2.33 Lemma 14: nextto(on(small, pin(X)), on(medium, Y)) = nextto(pin(X), on(small, on(medium, Y))).
% 15.87/2.33 Proof:
% 15.87/2.33 nextto(on(small, pin(X)), on(medium, Y))
% 15.87/2.33 = { by axiom 1 (nextto_commutative) R->L }
% 15.87/2.33 nextto(on(medium, Y), on(small, pin(X)))
% 15.87/2.33 = { by axiom 9 (a_move) R->L }
% 15.87/2.33 fresh(true, true, small, on(medium, Y), pin(X))
% 15.87/2.33 = { by axiom 5 (fits_4) R->L }
% 15.87/2.33 fresh(fits(small, on(medium, Y)), true, small, on(medium, Y), pin(X))
% 15.87/2.33 = { by lemma 13 }
% 15.87/2.33 nextto(pin(X), on(small, on(medium, Y)))
% 15.87/2.33
% 15.87/2.33 Lemma 15: fresh(fits(medium, X), true, medium, X, pin(Y)) = nextto(pin(Y), on(medium, X)).
% 15.87/2.33 Proof:
% 15.87/2.33 fresh(fits(medium, X), true, medium, X, pin(Y))
% 15.87/2.33 = { by axiom 11 (a_move) R->L }
% 15.87/2.33 fresh2(fits(medium, pin(Y)), true, medium, X, pin(Y))
% 15.87/2.33 = { by axiom 3 (fits_2) }
% 15.87/2.33 fresh2(true, true, medium, X, pin(Y))
% 15.87/2.33 = { by axiom 10 (a_move) }
% 15.87/2.33 nextto(on(medium, X), pin(Y))
% 15.87/2.33 = { by axiom 1 (nextto_commutative) }
% 15.87/2.33 nextto(pin(Y), on(medium, X))
% 15.87/2.33
% 15.87/2.33 Goal 1 (final_state): state(nextto(pin(n1), nextto(pin(n2), on(small, on(medium, on(large, pin(n3))))))) = true.
% 15.87/2.33 Proof:
% 15.87/2.33 state(nextto(pin(n1), nextto(pin(n2), on(small, on(medium, on(large, pin(n3)))))))
% 15.87/2.33 = { by axiom 1 (nextto_commutative) R->L }
% 15.87/2.33 state(nextto(nextto(pin(n2), on(small, on(medium, on(large, pin(n3))))), pin(n1)))
% 15.87/2.33 = { by axiom 1 (nextto_commutative) }
% 15.87/2.33 state(nextto(nextto(on(small, on(medium, on(large, pin(n3)))), pin(n2)), pin(n1)))
% 15.87/2.33 = { by axiom 8 (nextto_associative) R->L }
% 15.87/2.33 state(nextto(on(small, on(medium, on(large, pin(n3)))), nextto(pin(n2), pin(n1))))
% 15.87/2.33 = { by axiom 1 (nextto_commutative) R->L }
% 15.87/2.33 state(nextto(on(small, on(medium, on(large, pin(n3)))), nextto(pin(n1), pin(n2))))
% 15.87/2.33 = { by axiom 8 (nextto_associative) }
% 15.87/2.33 state(nextto(nextto(on(small, on(medium, on(large, pin(n3)))), pin(n1)), pin(n2)))
% 15.90/2.33 = { by axiom 1 (nextto_commutative) R->L }
% 15.90/2.33 state(nextto(nextto(pin(n1), on(small, on(medium, on(large, pin(n3))))), pin(n2)))
% 15.90/2.33 = { by lemma 13 R->L }
% 15.90/2.33 state(nextto(fresh(fits(small, on(medium, on(large, pin(n3)))), true, small, on(medium, on(large, pin(n3))), pin(n1)), pin(n2)))
% 15.90/2.34 = { by axiom 5 (fits_4) }
% 15.90/2.34 state(nextto(fresh(true, true, small, on(medium, on(large, pin(n3))), pin(n1)), pin(n2)))
% 15.90/2.34 = { by axiom 9 (a_move) }
% 15.90/2.34 state(nextto(nextto(on(medium, on(large, pin(n3))), on(small, pin(n1))), pin(n2)))
% 15.90/2.34 = { by axiom 8 (nextto_associative) R->L }
% 15.90/2.34 state(nextto(on(medium, on(large, pin(n3))), nextto(on(small, pin(n1)), pin(n2))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) R->L }
% 15.90/2.34 state(nextto(on(medium, on(large, pin(n3))), nextto(pin(n2), on(small, pin(n1)))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) }
% 15.90/2.34 state(nextto(nextto(on(medium, on(large, pin(n3))), pin(n2)), on(small, pin(n1))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) R->L }
% 15.90/2.34 state(nextto(nextto(pin(n2), on(medium, on(large, pin(n3)))), on(small, pin(n1))))
% 15.90/2.34 = { by lemma 15 R->L }
% 15.90/2.34 state(nextto(fresh(fits(medium, on(large, pin(n3))), true, medium, on(large, pin(n3)), pin(n2)), on(small, pin(n1))))
% 15.90/2.34 = { by axiom 7 (fits_5) }
% 15.90/2.34 state(nextto(fresh(true, true, medium, on(large, pin(n3)), pin(n2)), on(small, pin(n1))))
% 15.90/2.34 = { by axiom 9 (a_move) }
% 15.90/2.34 state(nextto(nextto(on(large, pin(n3)), on(medium, pin(n2))), on(small, pin(n1))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) R->L }
% 15.90/2.34 state(nextto(on(large, pin(n3)), nextto(on(medium, pin(n2)), on(small, pin(n1)))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) }
% 15.90/2.34 state(nextto(on(large, pin(n3)), nextto(on(small, pin(n1)), on(medium, pin(n2)))))
% 15.90/2.34 = { by lemma 14 }
% 15.90/2.34 state(nextto(on(large, pin(n3)), nextto(pin(n1), on(small, on(medium, pin(n2))))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) }
% 15.90/2.34 state(nextto(nextto(on(large, pin(n3)), pin(n1)), on(small, on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 10 (a_move) R->L }
% 15.90/2.34 state(nextto(fresh2(true, true, large, pin(n3), pin(n1)), on(small, on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 4 (fits_3) R->L }
% 15.90/2.34 state(nextto(fresh2(fits(large, pin(n1)), true, large, pin(n3), pin(n1)), on(small, on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 11 (a_move) }
% 15.90/2.34 state(nextto(fresh(fits(large, pin(n3)), true, large, pin(n3), pin(n1)), on(small, on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 4 (fits_3) }
% 15.90/2.34 state(nextto(fresh(true, true, large, pin(n3), pin(n1)), on(small, on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 9 (a_move) }
% 15.90/2.34 state(nextto(nextto(pin(n3), on(large, pin(n1))), on(small, on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) R->L }
% 15.90/2.34 state(nextto(pin(n3), nextto(on(large, pin(n1)), on(small, on(medium, pin(n2))))))
% 15.90/2.34 = { by axiom 9 (a_move) R->L }
% 15.90/2.34 state(nextto(pin(n3), fresh(true, true, small, on(large, pin(n1)), on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 6 (fits_6) R->L }
% 15.90/2.34 state(nextto(pin(n3), fresh(fits(small, on(large, pin(n1))), true, small, on(large, pin(n1)), on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 11 (a_move) R->L }
% 15.90/2.34 state(nextto(pin(n3), fresh2(fits(small, on(medium, pin(n2))), true, small, on(large, pin(n1)), on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 5 (fits_4) }
% 15.90/2.34 state(nextto(pin(n3), fresh2(true, true, small, on(large, pin(n1)), on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 10 (a_move) }
% 15.90/2.34 state(nextto(pin(n3), nextto(on(small, on(large, pin(n1))), on(medium, pin(n2)))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) }
% 15.90/2.34 state(nextto(pin(n3), nextto(on(medium, pin(n2)), on(small, on(large, pin(n1))))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) }
% 15.90/2.34 state(nextto(nextto(pin(n3), on(medium, pin(n2))), on(small, on(large, pin(n1)))))
% 15.90/2.34 = { by axiom 9 (a_move) R->L }
% 15.90/2.34 state(nextto(fresh(true, true, medium, pin(n3), pin(n2)), on(small, on(large, pin(n1)))))
% 15.90/2.34 = { by axiom 3 (fits_2) R->L }
% 15.90/2.34 state(nextto(fresh(fits(medium, pin(n3)), true, medium, pin(n3), pin(n2)), on(small, on(large, pin(n1)))))
% 15.90/2.34 = { by lemma 15 }
% 15.90/2.34 state(nextto(nextto(pin(n2), on(medium, pin(n3))), on(small, on(large, pin(n1)))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) R->L }
% 15.90/2.34 state(nextto(pin(n2), nextto(on(medium, pin(n3)), on(small, on(large, pin(n1))))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) R->L }
% 15.90/2.34 state(nextto(pin(n2), nextto(on(small, on(large, pin(n1))), on(medium, pin(n3)))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) }
% 15.90/2.34 state(nextto(nextto(pin(n2), on(small, on(large, pin(n1)))), on(medium, pin(n3))))
% 15.90/2.34 = { by lemma 13 R->L }
% 15.90/2.34 state(nextto(fresh(fits(small, on(large, pin(n1))), true, small, on(large, pin(n1)), pin(n2)), on(medium, pin(n3))))
% 15.90/2.34 = { by axiom 6 (fits_6) }
% 15.90/2.34 state(nextto(fresh(true, true, small, on(large, pin(n1)), pin(n2)), on(medium, pin(n3))))
% 15.90/2.34 = { by axiom 9 (a_move) }
% 15.90/2.34 state(nextto(nextto(on(large, pin(n1)), on(small, pin(n2))), on(medium, pin(n3))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) }
% 15.90/2.34 state(nextto(nextto(on(small, pin(n2)), on(large, pin(n1))), on(medium, pin(n3))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) R->L }
% 15.90/2.34 state(nextto(on(small, pin(n2)), nextto(on(large, pin(n1)), on(medium, pin(n3)))))
% 15.90/2.34 = { by axiom 9 (a_move) R->L }
% 15.90/2.34 state(nextto(on(small, pin(n2)), fresh(true, true, medium, on(large, pin(n1)), pin(n3))))
% 15.90/2.34 = { by axiom 7 (fits_5) R->L }
% 15.90/2.34 state(nextto(on(small, pin(n2)), fresh(fits(medium, on(large, pin(n1))), true, medium, on(large, pin(n1)), pin(n3))))
% 15.90/2.34 = { by lemma 15 }
% 15.90/2.34 state(nextto(on(small, pin(n2)), nextto(pin(n3), on(medium, on(large, pin(n1))))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) R->L }
% 15.90/2.34 state(nextto(on(small, pin(n2)), nextto(on(medium, on(large, pin(n1))), pin(n3))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) }
% 15.90/2.34 state(nextto(nextto(on(small, pin(n2)), on(medium, on(large, pin(n1)))), pin(n3)))
% 15.90/2.34 = { by lemma 14 }
% 15.90/2.34 state(nextto(nextto(pin(n2), on(small, on(medium, on(large, pin(n1))))), pin(n3)))
% 15.90/2.34 = { by axiom 8 (nextto_associative) R->L }
% 15.90/2.34 state(nextto(pin(n2), nextto(on(small, on(medium, on(large, pin(n1)))), pin(n3))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) }
% 15.90/2.34 state(nextto(pin(n2), nextto(pin(n3), on(small, on(medium, on(large, pin(n1)))))))
% 15.90/2.34 = { by axiom 8 (nextto_associative) }
% 15.90/2.34 state(nextto(nextto(pin(n2), pin(n3)), on(small, on(medium, on(large, pin(n1))))))
% 15.90/2.34 = { by axiom 1 (nextto_commutative) R->L }
% 15.90/2.34 state(nextto(on(small, on(medium, on(large, pin(n1)))), nextto(pin(n2), pin(n3))))
% 15.90/2.34 = { by axiom 12 (initial_state) }
% 15.90/2.34 true
% 15.90/2.34 % SZS output end Proof
% 15.90/2.34
% 15.90/2.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------