TSTP Solution File: HWC002-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HWC002-1 : TPTP v8.1.2. Released v1.1.0.
% 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 01:58:12 EDT 2023
% Result : Unsatisfiable 2.05s 0.66s
% Output : Proof 2.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : HWC002-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 06:55:40 EDT 2023
% 0.15/0.36 % CPUTime :
% 2.05/0.66 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.05/0.66
% 2.05/0.66 % SZS status Unsatisfiable
% 2.05/0.66
% 2.05/0.67 % SZS output start Proof
% 2.05/0.67 Take the following subset of the input axioms:
% 2.05/0.67 fof(and_definition1, axiom, and(n0, n0)=n0).
% 2.05/0.67 fof(and_definition2, axiom, and(n0, n1)=n0).
% 2.05/0.67 fof(and_definition5, axiom, ![X]: and(nil, X)=X).
% 2.05/0.67 fof(and_table_definition, axiom, ![X1, X2, Y1, Y2, X3, X4, Y3, Y4]: and(table(X1, X2, X3, X4), table(Y1, Y2, Y3, Y4))=table(and(X1, Y1), and(X2, Y2), and(X3, Y3), and(X4, Y4))).
% 2.05/0.67 fof(connect_definition1, axiom, ![X5]: connect(nil, X5)=X5).
% 2.05/0.67 fof(empty_table, axiom, table(n0, n0, n0, n0)=nil).
% 2.05/0.67 fof(full_table, axiom, table(n1, n1, n1, n1)=nil).
% 2.05/0.67 fof(not_definition1, axiom, not(n0)=n1).
% 2.05/0.67 fof(not_definition2, axiom, not(n1)=n0).
% 2.05/0.67 fof(not_definition3, axiom, not(nil)=nil).
% 2.05/0.67 fof(not_table_definition, axiom, ![X1_2, X2_2, X3_2, X4_2]: not(table(X1_2, X2_2, X3_2, X4_2))=table(not(X1_2), not(X2_2), not(X3_2), not(X4_2))).
% 2.05/0.67 fof(prove_output_configuration, negated_conjecture, ~circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, n1, n1), nil)))).
% 2.05/0.67 fof(subsume_symmetric, axiom, ![Y, X5]: circuit(top(X5), Y, bottom(X5))).
% 2.05/0.67
% 2.05/0.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.05/0.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.05/0.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.05/0.67 fresh(y, y, x1...xn) = u
% 2.05/0.67 C => fresh(s, t, x1...xn) = v
% 2.05/0.67 where fresh is a fresh function symbol and x1..xn are the free
% 2.05/0.67 variables of u and v.
% 2.05/0.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.05/0.67 input problem has no model of domain size 1).
% 2.05/0.67
% 2.05/0.67 The encoding turns the above axioms into the following unit equations and goals:
% 2.05/0.67
% 2.05/0.67 Axiom 1 (not_definition3): not(nil) = nil.
% 2.05/0.67 Axiom 2 (not_definition1): not(n0) = n1.
% 2.05/0.67 Axiom 3 (not_definition2): not(n1) = n0.
% 2.05/0.67 Axiom 4 (and_definition5): and(nil, X) = X.
% 2.05/0.67 Axiom 5 (and_definition1): and(n0, n0) = n0.
% 2.05/0.67 Axiom 6 (and_definition2): and(n0, n1) = n0.
% 2.05/0.67 Axiom 7 (connect_definition1): connect(nil, X) = X.
% 2.05/0.67 Axiom 8 (empty_table): table(n0, n0, n0, n0) = nil.
% 2.05/0.67 Axiom 9 (full_table): table(n1, n1, n1, n1) = nil.
% 2.05/0.67 Axiom 10 (subsume_symmetric): circuit(top(X), Y, bottom(X)) = true.
% 2.05/0.67 Axiom 11 (not_table_definition): not(table(X, Y, Z, W)) = table(not(X), not(Y), not(Z), not(W)).
% 2.05/0.67 Axiom 12 (and_table_definition): and(table(X, Y, Z, W), table(V, U, T, S)) = table(and(X, V), and(Y, U), and(Z, T), and(W, S)).
% 2.05/0.67
% 2.05/0.67 Lemma 13: and(table(nil, X, Y, Z), table(W, V, U, T)) = table(W, and(X, V), and(Y, U), and(Z, T)).
% 2.05/0.67 Proof:
% 2.05/0.67 and(table(nil, X, Y, Z), table(W, V, U, T))
% 2.05/0.67 = { by axiom 12 (and_table_definition) }
% 2.05/0.67 table(and(nil, W), and(X, V), and(Y, U), and(Z, T))
% 2.05/0.67 = { by axiom 4 (and_definition5) }
% 2.05/0.67 table(W, and(X, V), and(Y, U), and(Z, T))
% 2.05/0.67
% 2.05/0.67 Lemma 14: table(n0, and(X, n0), and(Y, n0), and(Z, n0)) = and(table(nil, X, Y, Z), nil).
% 2.05/0.67 Proof:
% 2.05/0.67 table(n0, and(X, n0), and(Y, n0), and(Z, n0))
% 2.05/0.67 = { by lemma 13 R->L }
% 2.05/0.67 and(table(nil, X, Y, Z), table(n0, n0, n0, n0))
% 2.05/0.67 = { by axiom 8 (empty_table) }
% 2.05/0.67 and(table(nil, X, Y, Z), nil)
% 2.05/0.67
% 2.05/0.67 Lemma 15: table(n1, and(X, n1), and(Y, n1), and(Z, n1)) = and(table(nil, X, Y, Z), nil).
% 2.05/0.67 Proof:
% 2.05/0.67 table(n1, and(X, n1), and(Y, n1), and(Z, n1))
% 2.05/0.67 = { by lemma 13 R->L }
% 2.05/0.67 and(table(nil, X, Y, Z), table(n1, n1, n1, n1))
% 2.05/0.67 = { by axiom 9 (full_table) }
% 2.05/0.67 and(table(nil, X, Y, Z), nil)
% 2.05/0.67
% 2.05/0.67 Goal 1 (prove_output_configuration): circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, n1, n1), nil))) = true.
% 2.05/0.67 Proof:
% 2.05/0.67 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, n1, n1), nil)))
% 2.05/0.67 = { by axiom 3 (not_definition2) R->L }
% 2.05/0.67 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, not(n1), n1, n1), nil)))
% 2.05/0.67 = { by axiom 3 (not_definition2) R->L }
% 2.05/0.67 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(not(n1), not(n1), n1, n1), nil)))
% 2.05/0.67 = { by axiom 2 (not_definition1) R->L }
% 2.05/0.67 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(not(n1), not(n1), n1, not(n0)), nil)))
% 2.05/0.67 = { by axiom 2 (not_definition1) R->L }
% 2.05/0.67 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(not(n1), not(n1), not(n0), not(n0)), nil)))
% 2.05/0.67 = { by axiom 11 (not_table_definition) R->L }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n1, n1, n0, n0)), nil)))
% 2.05/0.68 = { by axiom 6 (and_definition2) R->L }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n1, n1, n0, and(n0, n1))), nil)))
% 2.05/0.68 = { by axiom 6 (and_definition2) R->L }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n1, n1, and(n0, n1), and(n0, n1))), nil)))
% 2.05/0.68 = { by axiom 4 (and_definition5) R->L }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n1, and(nil, n1), and(n0, n1), and(n0, n1))), nil)))
% 2.05/0.68 = { by lemma 15 }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(and(table(nil, nil, n0, n0), nil)), nil)))
% 2.05/0.68 = { by lemma 14 R->L }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n0, and(nil, n0), and(n0, n0), and(n0, n0))), nil)))
% 2.05/0.68 = { by axiom 4 (and_definition5) }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n0, n0, and(n0, n0), and(n0, n0))), nil)))
% 2.05/0.68 = { by axiom 5 (and_definition1) }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n0, n0, n0, and(n0, n0))), nil)))
% 2.05/0.68 = { by axiom 5 (and_definition1) }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(table(n0, n0, n0, n0)), nil)))
% 2.05/0.68 = { by axiom 8 (empty_table) }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(not(nil), nil)))
% 2.05/0.68 = { by axiom 1 (not_definition3) }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(nil, nil)))
% 2.05/0.68 = { by axiom 7 (connect_definition1) }
% 2.05/0.68 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 3 (not_definition2) R->L }
% 2.05/0.68 circuit(top(connect(table(n0, n1, not(n1), n1), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 3 (not_definition2) R->L }
% 2.05/0.68 circuit(top(connect(table(not(n1), n1, not(n1), n1), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 2 (not_definition1) R->L }
% 2.05/0.68 circuit(top(connect(table(not(n1), n1, not(n1), not(n0)), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 2 (not_definition1) R->L }
% 2.05/0.68 circuit(top(connect(table(not(n1), not(n0), not(n1), not(n0)), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 11 (not_table_definition) R->L }
% 2.05/0.68 circuit(top(connect(not(table(n1, n0, n1, n0)), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 6 (and_definition2) R->L }
% 2.05/0.68 circuit(top(connect(not(table(n1, n0, n1, and(n0, n1))), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 6 (and_definition2) R->L }
% 2.05/0.68 circuit(top(connect(not(table(n1, and(n0, n1), n1, and(n0, n1))), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 4 (and_definition5) R->L }
% 2.05/0.68 circuit(top(connect(not(table(n1, and(n0, n1), and(nil, n1), and(n0, n1))), nil)), nil, bottom(nil))
% 2.05/0.68 = { by lemma 15 }
% 2.05/0.68 circuit(top(connect(not(and(table(nil, n0, nil, n0), nil)), nil)), nil, bottom(nil))
% 2.05/0.68 = { by lemma 14 R->L }
% 2.05/0.68 circuit(top(connect(not(table(n0, and(n0, n0), and(nil, n0), and(n0, n0))), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 4 (and_definition5) }
% 2.05/0.68 circuit(top(connect(not(table(n0, and(n0, n0), n0, and(n0, n0))), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 5 (and_definition1) }
% 2.05/0.68 circuit(top(connect(not(table(n0, n0, n0, and(n0, n0))), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 5 (and_definition1) }
% 2.05/0.68 circuit(top(connect(not(table(n0, n0, n0, n0)), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 8 (empty_table) }
% 2.05/0.68 circuit(top(connect(not(nil), nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 1 (not_definition3) }
% 2.05/0.68 circuit(top(connect(nil, nil)), nil, bottom(nil))
% 2.05/0.68 = { by axiom 7 (connect_definition1) }
% 2.05/0.68 circuit(top(nil), nil, bottom(nil))
% 2.05/0.68 = { by axiom 10 (subsume_symmetric) }
% 2.05/0.68 true
% 2.05/0.68 % SZS output end Proof
% 2.05/0.68
% 2.05/0.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------