TSTP Solution File: FLD006-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : FLD006-3 : 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 : n017.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 22:36:46 EDT 2023
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% 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 : FLD006-3 : 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
% 0.13/0.34 % Computer : n017.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 : Sun Aug 27 23:39:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.45 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.20/0.45 % SZS status Unsatisfiable
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% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Take the following subset of the input axioms:
% 0.20/0.45 fof(commutativity_addition, axiom, ![X, Y, Z]: (sum(Y, X, Z) | ~sum(X, Y, Z))).
% 0.20/0.45 fof(existence_of_inverse_addition, axiom, ![X2]: (sum(additive_inverse(X2), X2, additive_identity) | ~defined(X2))).
% 0.20/0.45 fof(not_sum_1, negated_conjecture, ~sum(additive_identity, additive_inverse(additive_identity), additive_identity)).
% 0.20/0.45 fof(well_definedness_of_additive_identity, axiom, defined(additive_identity)).
% 0.20/0.45
% 0.20/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.46 fresh(y, y, x1...xn) = u
% 0.20/0.46 C => fresh(s, t, x1...xn) = v
% 0.20/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.46 variables of u and v.
% 0.20/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.46 input problem has no model of domain size 1).
% 0.20/0.46
% 0.20/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.46
% 0.20/0.46 Axiom 1 (well_definedness_of_additive_identity): defined(additive_identity) = true.
% 0.20/0.46 Axiom 2 (existence_of_inverse_addition): fresh12(X, X, Y) = true.
% 0.20/0.46 Axiom 3 (existence_of_inverse_addition): fresh12(defined(X), true, X) = sum(additive_inverse(X), X, additive_identity).
% 0.20/0.46 Axiom 4 (commutativity_addition): fresh18(X, X, Y, Z, W) = true.
% 0.20/0.46 Axiom 5 (commutativity_addition): fresh18(sum(X, Y, Z), true, Y, X, Z) = sum(Y, X, Z).
% 0.20/0.46
% 0.20/0.46 Goal 1 (not_sum_1): sum(additive_identity, additive_inverse(additive_identity), additive_identity) = true.
% 0.20/0.46 Proof:
% 0.20/0.46 sum(additive_identity, additive_inverse(additive_identity), additive_identity)
% 0.20/0.46 = { by axiom 5 (commutativity_addition) R->L }
% 0.20/0.46 fresh18(sum(additive_inverse(additive_identity), additive_identity, additive_identity), true, additive_identity, additive_inverse(additive_identity), additive_identity)
% 0.20/0.46 = { by axiom 3 (existence_of_inverse_addition) R->L }
% 0.20/0.46 fresh18(fresh12(defined(additive_identity), true, additive_identity), true, additive_identity, additive_inverse(additive_identity), additive_identity)
% 0.20/0.46 = { by axiom 1 (well_definedness_of_additive_identity) }
% 0.20/0.46 fresh18(fresh12(true, true, additive_identity), true, additive_identity, additive_inverse(additive_identity), additive_identity)
% 0.20/0.46 = { by axiom 2 (existence_of_inverse_addition) }
% 0.20/0.46 fresh18(true, true, additive_identity, additive_inverse(additive_identity), additive_identity)
% 0.20/0.46 = { by axiom 4 (commutativity_addition) }
% 0.20/0.46 true
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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