TSTP Solution File: FLD017-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : FLD017-1 : 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 : n026.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 11.10s 1.81s
% Output : Proof 11.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD017-1 : 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
% 0.13/0.34 % Computer : n026.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 : Mon Aug 28 00:06:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 11.10/1.81 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 11.10/1.81
% 11.10/1.81 % SZS status Unsatisfiable
% 11.10/1.81
% 11.10/1.82 % SZS output start Proof
% 11.10/1.82 Take the following subset of the input axioms:
% 11.10/1.82 fof(a_equals_x_5, negated_conjecture, equalish(a, x)).
% 11.10/1.82 fof(add_equals_c_6, negated_conjecture, equalish(add(a, b), c)).
% 11.10/1.82 fof(add_not_equal_to_c_7, negated_conjecture, ~equalish(add(x, b), c)).
% 11.10/1.82 fof(b_is_defined, hypothesis, defined(b)).
% 11.10/1.82 fof(compatibility_of_equality_and_addition, axiom, ![X, Y, Z]: (equalish(add(X, Z), add(Y, Z)) | (~defined(Z) | ~equalish(X, Y)))).
% 11.10/1.82 fof(symmetry_of_equality, axiom, ![X2, Y2]: (equalish(X2, Y2) | ~equalish(Y2, X2))).
% 11.10/1.82 fof(transitivity_of_equality, axiom, ![X2, Y2, Z2]: (equalish(X2, Z2) | (~equalish(X2, Y2) | ~equalish(Y2, Z2)))).
% 11.10/1.82
% 11.10/1.82 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.10/1.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.10/1.82 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.10/1.82 fresh(y, y, x1...xn) = u
% 11.10/1.82 C => fresh(s, t, x1...xn) = v
% 11.10/1.82 where fresh is a fresh function symbol and x1..xn are the free
% 11.10/1.82 variables of u and v.
% 11.10/1.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.10/1.82 input problem has no model of domain size 1).
% 11.10/1.82
% 11.10/1.82 The encoding turns the above axioms into the following unit equations and goals:
% 11.10/1.82
% 11.10/1.82 Axiom 1 (b_is_defined): defined(b) = true.
% 11.10/1.82 Axiom 2 (a_equals_x_5): equalish(a, x) = true.
% 11.10/1.82 Axiom 3 (add_equals_c_6): equalish(add(a, b), c) = true.
% 11.10/1.82 Axiom 4 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 11.10/1.82 Axiom 5 (transitivity_of_equality): fresh8(X, X, Y, Z) = true.
% 11.10/1.82 Axiom 6 (compatibility_of_equality_and_addition): fresh24(X, X, Y, Z, W) = equalish(add(Y, Z), add(W, Z)).
% 11.10/1.82 Axiom 7 (compatibility_of_equality_and_addition): fresh23(X, X, Y, Z, W) = true.
% 11.10/1.82 Axiom 8 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 11.10/1.82 Axiom 9 (transitivity_of_equality): fresh9(X, X, Y, Z, W) = equalish(Y, Z).
% 11.10/1.82 Axiom 10 (compatibility_of_equality_and_addition): fresh24(defined(X), true, Y, X, Z) = fresh23(equalish(Y, Z), true, Y, X, Z).
% 11.10/1.82 Axiom 11 (transitivity_of_equality): fresh9(equalish(X, Y), true, Z, Y, X) = fresh8(equalish(Z, X), true, Z, Y).
% 11.10/1.82
% 11.10/1.82 Goal 1 (add_not_equal_to_c_7): equalish(add(x, b), c) = true.
% 11.10/1.82 Proof:
% 11.10/1.82 equalish(add(x, b), c)
% 11.10/1.82 = { by axiom 9 (transitivity_of_equality) R->L }
% 11.10/1.82 fresh9(true, true, add(x, b), c, add(a, b))
% 11.10/1.82 = { by axiom 3 (add_equals_c_6) R->L }
% 11.10/1.82 fresh9(equalish(add(a, b), c), true, add(x, b), c, add(a, b))
% 11.10/1.82 = { by axiom 11 (transitivity_of_equality) }
% 11.10/1.82 fresh8(equalish(add(x, b), add(a, b)), true, add(x, b), c)
% 11.10/1.82 = { by axiom 8 (symmetry_of_equality) R->L }
% 11.10/1.82 fresh8(fresh10(equalish(add(a, b), add(x, b)), true, add(x, b), add(a, b)), true, add(x, b), c)
% 11.10/1.82 = { by axiom 6 (compatibility_of_equality_and_addition) R->L }
% 11.10/1.82 fresh8(fresh10(fresh24(true, true, a, b, x), true, add(x, b), add(a, b)), true, add(x, b), c)
% 11.10/1.82 = { by axiom 1 (b_is_defined) R->L }
% 11.10/1.82 fresh8(fresh10(fresh24(defined(b), true, a, b, x), true, add(x, b), add(a, b)), true, add(x, b), c)
% 11.10/1.82 = { by axiom 10 (compatibility_of_equality_and_addition) }
% 11.10/1.82 fresh8(fresh10(fresh23(equalish(a, x), true, a, b, x), true, add(x, b), add(a, b)), true, add(x, b), c)
% 11.10/1.82 = { by axiom 2 (a_equals_x_5) }
% 11.10/1.82 fresh8(fresh10(fresh23(true, true, a, b, x), true, add(x, b), add(a, b)), true, add(x, b), c)
% 11.10/1.82 = { by axiom 7 (compatibility_of_equality_and_addition) }
% 11.10/1.82 fresh8(fresh10(true, true, add(x, b), add(a, b)), true, add(x, b), c)
% 11.10/1.82 = { by axiom 4 (symmetry_of_equality) }
% 11.10/1.82 fresh8(true, true, add(x, b), c)
% 11.10/1.82 = { by axiom 5 (transitivity_of_equality) }
% 11.10/1.82 true
% 11.10/1.82 % SZS output end Proof
% 11.10/1.82
% 11.10/1.82 RESULT: Unsatisfiable (the axioms are contradictory).
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