TSTP Solution File: FLD017-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD017-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n010.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 : Wed Aug 30 22:36:50 EDT 2023
% Result : Unsatisfiable 4.93s 1.06s
% Output : Proof 4.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD017-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 00:27:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.93/1.06 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 4.93/1.06
% 4.93/1.06 % SZS status Unsatisfiable
% 4.93/1.06
% 4.93/1.06 % SZS output start Proof
% 4.93/1.06 Take the following subset of the input axioms:
% 4.93/1.06 fof(associativity_addition_2, axiom, ![X, V, W, Y, U, Z]: (sum(U, Z, W) | (~sum(X, Y, U) | (~sum(Y, Z, V) | ~sum(X, V, W))))).
% 4.93/1.06 fof(c_is_defined, hypothesis, defined(c)).
% 4.93/1.06 fof(existence_of_identity_addition, axiom, ![X2]: (sum(additive_identity, X2, X2) | ~defined(X2))).
% 4.93/1.06 fof(not_sum_7, negated_conjecture, ~sum(x, b, c)).
% 4.93/1.06 fof(sum_5, negated_conjecture, sum(additive_identity, a, x)).
% 4.93/1.06 fof(sum_6, negated_conjecture, sum(a, b, c)).
% 4.93/1.06
% 4.93/1.06 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.93/1.06 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.93/1.06 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.93/1.06 fresh(y, y, x1...xn) = u
% 4.93/1.06 C => fresh(s, t, x1...xn) = v
% 4.93/1.06 where fresh is a fresh function symbol and x1..xn are the free
% 4.93/1.06 variables of u and v.
% 4.93/1.06 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.93/1.06 input problem has no model of domain size 1).
% 4.93/1.06
% 4.93/1.06 The encoding turns the above axioms into the following unit equations and goals:
% 4.93/1.06
% 4.93/1.06 Axiom 1 (c_is_defined): defined(c) = true.
% 4.93/1.06 Axiom 2 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 4.93/1.06 Axiom 3 (sum_6): sum(a, b, c) = true.
% 4.93/1.06 Axiom 4 (sum_5): sum(additive_identity, a, x) = true.
% 4.93/1.06 Axiom 5 (existence_of_identity_addition): fresh14(defined(X), true, X) = sum(additive_identity, X, X).
% 4.93/1.06 Axiom 6 (associativity_addition_2): fresh42(X, X, Y, Z, W) = true.
% 4.93/1.06 Axiom 7 (associativity_addition_2): fresh21(X, X, Y, Z, W, V, U) = sum(Y, Z, W).
% 4.93/1.06 Axiom 8 (associativity_addition_2): fresh41(X, X, Y, Z, W, V, U, T) = fresh42(sum(V, U, Y), true, Y, Z, W).
% 4.93/1.06 Axiom 9 (associativity_addition_2): fresh41(sum(X, Y, Z), true, W, Y, V, U, X, Z) = fresh21(sum(U, Z, V), true, W, Y, V, U, X).
% 4.93/1.06
% 4.93/1.06 Goal 1 (not_sum_7): sum(x, b, c) = true.
% 4.93/1.06 Proof:
% 4.93/1.06 sum(x, b, c)
% 4.93/1.06 = { by axiom 7 (associativity_addition_2) R->L }
% 4.93/1.06 fresh21(true, true, x, b, c, additive_identity, a)
% 4.93/1.06 = { by axiom 2 (existence_of_identity_addition) R->L }
% 4.93/1.06 fresh21(fresh14(true, true, c), true, x, b, c, additive_identity, a)
% 4.93/1.06 = { by axiom 1 (c_is_defined) R->L }
% 4.93/1.06 fresh21(fresh14(defined(c), true, c), true, x, b, c, additive_identity, a)
% 4.93/1.06 = { by axiom 5 (existence_of_identity_addition) }
% 4.93/1.06 fresh21(sum(additive_identity, c, c), true, x, b, c, additive_identity, a)
% 4.93/1.06 = { by axiom 9 (associativity_addition_2) R->L }
% 4.93/1.06 fresh41(sum(a, b, c), true, x, b, c, additive_identity, a, c)
% 4.93/1.06 = { by axiom 3 (sum_6) }
% 4.93/1.06 fresh41(true, true, x, b, c, additive_identity, a, c)
% 4.93/1.06 = { by axiom 8 (associativity_addition_2) }
% 4.93/1.06 fresh42(sum(additive_identity, a, x), true, x, b, c)
% 4.93/1.06 = { by axiom 4 (sum_5) }
% 4.93/1.06 fresh42(true, true, x, b, c)
% 4.93/1.06 = { by axiom 6 (associativity_addition_2) }
% 4.93/1.06 true
% 4.93/1.06 % SZS output end Proof
% 4.93/1.06
% 4.93/1.06 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------