TSTP Solution File: SWV006-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV006-1 : 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 : n032.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 23:02:09 EDT 2023
% Result : Unsatisfiable 0.11s 0.31s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWV006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.08 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.07/0.26 % Computer : n032.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Aug 29 03:51:46 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.11/0.31 Command-line arguments: --no-flatten-goal
% 0.11/0.31
% 0.11/0.31 % SZS status Unsatisfiable
% 0.11/0.31
% 0.11/0.31 % SZS output start Proof
% 0.11/0.31 Take the following subset of the input axioms:
% 0.11/0.31 fof(anti_symmetry_of_less_than, axiom, ![X, Y]: (~less_than(X, Y) | ~less_than(Y, X))).
% 0.11/0.31 fof(clause_3, negated_conjecture, less_than(i, n)).
% 0.11/0.31 fof(clause_5, negated_conjecture, less_than(a(i), a(m))).
% 0.11/0.31 fof(clause_6, negated_conjecture, ![X2]: (less_than(X2, i) | (~less_than(X2, successor(n)) | ~less_than(a(X2), a(m))))).
% 0.11/0.31 fof(clause_8, negated_conjecture, ![X2]: (~less_than(one, X2) | (~less_than(X2, i) | ~less_than(a(X2), a(predecessor(X2)))))).
% 0.11/0.31 fof(less_than_successor, axiom, ![X2]: less_than(X2, successor(X2))).
% 0.11/0.31 fof(transitivity_of_less_than, axiom, ![Z, X2, Y2]: (less_than(X2, Z) | (~less_than(X2, Y2) | ~less_than(Y2, Z)))).
% 0.11/0.31 fof(x_not_less_than_x, axiom, ![X2]: ~less_than(X2, X2)).
% 0.11/0.31
% 0.11/0.31 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.11/0.31 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.11/0.31 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.11/0.31 fresh(y, y, x1...xn) = u
% 0.11/0.31 C => fresh(s, t, x1...xn) = v
% 0.11/0.31 where fresh is a fresh function symbol and x1..xn are the free
% 0.11/0.31 variables of u and v.
% 0.11/0.31 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.11/0.31 input problem has no model of domain size 1).
% 0.11/0.31
% 0.11/0.31 The encoding turns the above axioms into the following unit equations and goals:
% 0.11/0.31
% 0.11/0.31 Axiom 1 (clause_3): less_than(i, n) = true2.
% 0.11/0.31 Axiom 2 (clause_6): fresh6(X, X, Y) = true2.
% 0.11/0.31 Axiom 3 (clause_6): fresh5(X, X, Y) = less_than(Y, i).
% 0.11/0.31 Axiom 4 (less_than_successor): less_than(X, successor(X)) = true2.
% 0.11/0.31 Axiom 5 (transitivity_of_less_than): fresh3(X, X, Y, Z) = true2.
% 0.11/0.31 Axiom 6 (clause_5): less_than(a(i), a(m)) = true2.
% 0.11/0.32 Axiom 7 (transitivity_of_less_than): fresh4(X, X, Y, Z, W) = less_than(Y, Z).
% 0.11/0.32 Axiom 8 (clause_6): fresh5(less_than(a(X), a(m)), true2, X) = fresh6(less_than(X, successor(n)), true2, X).
% 0.11/0.32 Axiom 9 (transitivity_of_less_than): fresh4(less_than(X, Y), true2, Z, Y, X) = fresh3(less_than(Z, X), true2, Z, Y).
% 0.11/0.32
% 0.11/0.32 Goal 1 (x_not_less_than_x): less_than(X, X) = true2.
% 0.11/0.32 The goal is true when:
% 0.11/0.32 X = i
% 0.11/0.32
% 0.11/0.32 Proof:
% 0.11/0.32 less_than(i, i)
% 0.11/0.32 = { by axiom 3 (clause_6) R->L }
% 0.11/0.32 fresh5(true2, true2, i)
% 0.11/0.32 = { by axiom 6 (clause_5) R->L }
% 0.11/0.32 fresh5(less_than(a(i), a(m)), true2, i)
% 0.11/0.32 = { by axiom 8 (clause_6) }
% 0.11/0.32 fresh6(less_than(i, successor(n)), true2, i)
% 0.11/0.32 = { by axiom 7 (transitivity_of_less_than) R->L }
% 0.11/0.32 fresh6(fresh4(true2, true2, i, successor(n), n), true2, i)
% 0.11/0.32 = { by axiom 4 (less_than_successor) R->L }
% 0.11/0.32 fresh6(fresh4(less_than(n, successor(n)), true2, i, successor(n), n), true2, i)
% 0.11/0.32 = { by axiom 9 (transitivity_of_less_than) }
% 0.11/0.32 fresh6(fresh3(less_than(i, n), true2, i, successor(n)), true2, i)
% 0.11/0.32 = { by axiom 1 (clause_3) }
% 0.11/0.32 fresh6(fresh3(true2, true2, i, successor(n)), true2, i)
% 0.11/0.32 = { by axiom 5 (transitivity_of_less_than) }
% 0.11/0.32 fresh6(true2, true2, i)
% 0.11/0.32 = { by axiom 2 (clause_6) }
% 0.11/0.32 true2
% 0.11/0.32 % SZS output end Proof
% 0.11/0.32
% 0.11/0.32 RESULT: Unsatisfiable (the axioms are contradictory).
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