TSTP Solution File: LCL190-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL190-1 : 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 : n022.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 08:17:53 EDT 2023
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL190-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n022.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 : Fri Aug 25 04:13:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.43 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Take the following subset of the input axioms:
% 0.20/0.43 fof(axiom_1_4, axiom, ![A, B]: axiom(or(not(or(A, B)), or(B, A)))).
% 0.20/0.43 fof(axiom_1_6, axiom, ![C, A2, B2]: axiom(or(not(or(not(A2), B2)), or(not(or(C, A2)), or(C, B2))))).
% 0.20/0.43 fof(prove_this, negated_conjecture, ~theorem(or(not(or(p, or(q, r))), or(p, or(r, q))))).
% 0.20/0.43 fof(rule_1, axiom, ![X]: (theorem(X) | ~axiom(X))).
% 0.20/0.43 fof(rule_2, axiom, ![Y, X2]: (theorem(X2) | (~axiom(or(not(Y), X2)) | ~theorem(Y)))).
% 0.20/0.43
% 0.20/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.43 fresh(y, y, x1...xn) = u
% 0.20/0.43 C => fresh(s, t, x1...xn) = v
% 0.20/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43 variables of u and v.
% 0.20/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43 input problem has no model of domain size 1).
% 0.20/0.43
% 0.20/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43
% 0.20/0.43 Axiom 1 (rule_1): fresh4(X, X, Y) = true.
% 0.20/0.43 Axiom 2 (rule_2): fresh3(X, X, Y) = true.
% 0.20/0.43 Axiom 3 (rule_2): fresh5(X, X, Y, Z) = theorem(Y).
% 0.20/0.43 Axiom 4 (rule_1): fresh4(axiom(X), true, X) = theorem(X).
% 0.20/0.43 Axiom 5 (rule_2): fresh5(theorem(X), true, Y, X) = fresh3(axiom(or(not(X), Y)), true, Y).
% 0.20/0.43 Axiom 6 (axiom_1_4): axiom(or(not(or(X, Y)), or(Y, X))) = true.
% 0.20/0.43 Axiom 7 (axiom_1_6): axiom(or(not(or(not(X), Y)), or(not(or(Z, X)), or(Z, Y)))) = true.
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_this): theorem(or(not(or(p, or(q, r))), or(p, or(r, q)))) = true.
% 0.20/0.43 Proof:
% 0.20/0.43 theorem(or(not(or(p, or(q, r))), or(p, or(r, q))))
% 0.20/0.43 = { by axiom 3 (rule_2) R->L }
% 0.20/0.43 fresh5(true, true, or(not(or(p, or(q, r))), or(p, or(r, q))), or(not(or(q, r)), or(r, q)))
% 0.20/0.43 = { by axiom 1 (rule_1) R->L }
% 0.20/0.43 fresh5(fresh4(true, true, or(not(or(q, r)), or(r, q))), true, or(not(or(p, or(q, r))), or(p, or(r, q))), or(not(or(q, r)), or(r, q)))
% 0.20/0.43 = { by axiom 6 (axiom_1_4) R->L }
% 0.20/0.43 fresh5(fresh4(axiom(or(not(or(q, r)), or(r, q))), true, or(not(or(q, r)), or(r, q))), true, or(not(or(p, or(q, r))), or(p, or(r, q))), or(not(or(q, r)), or(r, q)))
% 0.20/0.43 = { by axiom 4 (rule_1) }
% 0.20/0.43 fresh5(theorem(or(not(or(q, r)), or(r, q))), true, or(not(or(p, or(q, r))), or(p, or(r, q))), or(not(or(q, r)), or(r, q)))
% 0.20/0.43 = { by axiom 5 (rule_2) }
% 0.20/0.43 fresh3(axiom(or(not(or(not(or(q, r)), or(r, q))), or(not(or(p, or(q, r))), or(p, or(r, q))))), true, or(not(or(p, or(q, r))), or(p, or(r, q))))
% 0.20/0.44 = { by axiom 7 (axiom_1_6) }
% 0.20/0.44 fresh3(true, true, or(not(or(p, or(q, r))), or(p, or(r, q))))
% 0.20/0.44 = { by axiom 2 (rule_2) }
% 0.20/0.44 true
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------