TSTP Solution File: LCL106-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL106-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n020.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 08:17:26 EDT 2023
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL106-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n020.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 : Fri Aug 25 04:46:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.38 Command-line arguments: --no-flatten-goal
% 0.20/0.38
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 Take the following subset of the input axioms:
% 0.20/0.40 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.40 fof(prove_q_2, negated_conjecture, ~is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))).
% 0.20/0.40 fof(q_1, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(X2, equivalent(equivalent(Y2, Z), equivalent(equivalent(Z, Y2), X2))))).
% 0.20/0.40 fof(q_4, axiom, ![X2, Y2, Z2]: is_a_theorem(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)))).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.40 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.40 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.40 Axiom 4 (q_1): is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, Y), X)))) = true.
% 0.20/0.40 Axiom 5 (q_4): is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))) = true.
% 0.20/0.40
% 0.20/0.40 Lemma 6: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z)) = is_a_theorem(equivalent(Y, Z)).
% 0.20/0.40 Proof:
% 0.20/0.40 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z))
% 0.20/0.40 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.40 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 0.20/0.40 = { by axiom 5 (q_4) }
% 0.20/0.40 fresh(true, true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 0.20/0.40 = { by axiom 2 (condensed_detachment) }
% 0.20/0.40 is_a_theorem(equivalent(Y, Z))
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_q_2): is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))) = true.
% 0.20/0.40 Proof:
% 0.20/0.40 is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by lemma 6 R->L }
% 0.20/0.40 fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by lemma 6 R->L }
% 0.20/0.40 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.40 fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.40 fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by axiom 4 (q_1) R->L }
% 0.20/0.40 fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.40 fresh2(fresh2(fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))))), true, equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by axiom 4 (q_1) }
% 0.20/0.40 fresh2(fresh2(fresh(fresh(true, true, equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by axiom 2 (condensed_detachment) }
% 0.20/0.40 fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.40 = { by axiom 3 (condensed_detachment) }
% 0.20/0.41 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b))), true, equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.41 = { by axiom 5 (q_4) }
% 0.20/0.41 fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.41 = { by axiom 1 (condensed_detachment) }
% 0.20/0.41 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.41 = { by axiom 1 (condensed_detachment) }
% 0.20/0.41 fresh2(true, true, equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.20/0.41 = { by axiom 1 (condensed_detachment) }
% 0.20/0.41 true
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------