TSTP Solution File: FLD039-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : FLD039-3 : 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 : n014.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 22:36:58 EDT 2023
% Result : Unsatisfiable 0.20s 0.57s
% 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 : FLD039-3 : 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
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 23:04:31 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
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% 0.20/0.57 % SZS status Unsatisfiable
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% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Take the following subset of the input axioms:
% 0.20/0.57 fof(associativity_addition_1, axiom, ![X, V, W, Y, U, Z]: (sum(X, V, W) | (~sum(X, Y, U) | (~sum(Y, Z, V) | ~sum(U, Z, W))))).
% 0.20/0.57 fof(different_identities, axiom, ~sum(additive_identity, additive_identity, multiplicative_identity)).
% 0.20/0.57 fof(existence_of_identity_addition, axiom, ![X2]: (sum(additive_identity, X2, X2) | ~defined(X2))).
% 0.20/0.57 fof(sum_3, negated_conjecture, sum(additive_identity, multiplicative_identity, additive_identity)).
% 0.20/0.57 fof(well_definedness_of_additive_identity, axiom, defined(additive_identity)).
% 0.20/0.57 fof(well_definedness_of_multiplicative_identity, axiom, defined(multiplicative_identity)).
% 0.20/0.57
% 0.20/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.57 fresh(y, y, x1...xn) = u
% 0.20/0.57 C => fresh(s, t, x1...xn) = v
% 0.20/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.57 variables of u and v.
% 0.20/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.57 input problem has no model of domain size 1).
% 0.20/0.57
% 0.20/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.57
% 0.20/0.57 Axiom 1 (well_definedness_of_multiplicative_identity): defined(multiplicative_identity) = true.
% 0.20/0.57 Axiom 2 (well_definedness_of_additive_identity): defined(additive_identity) = true.
% 0.20/0.57 Axiom 3 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 0.20/0.57 Axiom 4 (sum_3): sum(additive_identity, multiplicative_identity, additive_identity) = true.
% 0.20/0.57 Axiom 5 (existence_of_identity_addition): fresh14(defined(X), true, X) = sum(additive_identity, X, X).
% 0.20/0.57 Axiom 6 (associativity_addition_1): fresh44(X, X, Y, Z, W) = true.
% 0.20/0.57 Axiom 7 (associativity_addition_1): fresh22(X, X, Y, Z, W, V, U) = sum(Y, Z, W).
% 0.20/0.57 Axiom 8 (associativity_addition_1): fresh43(X, X, Y, Z, W, V, U, T) = fresh44(sum(Y, V, U), true, Y, Z, W).
% 0.20/0.57 Axiom 9 (associativity_addition_1): fresh43(sum(X, Y, Z), true, W, V, Z, U, X, Y) = fresh22(sum(U, Y, V), true, W, V, Z, U, X).
% 0.20/0.57
% 0.20/0.57 Goal 1 (different_identities): sum(additive_identity, additive_identity, multiplicative_identity) = true.
% 0.20/0.57 Proof:
% 0.20/0.57 sum(additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 7 (associativity_addition_1) R->L }
% 0.20/0.57 fresh22(true, true, additive_identity, additive_identity, multiplicative_identity, additive_identity, additive_identity)
% 0.20/0.57 = { by axiom 4 (sum_3) R->L }
% 0.20/0.57 fresh22(sum(additive_identity, multiplicative_identity, additive_identity), true, additive_identity, additive_identity, multiplicative_identity, additive_identity, additive_identity)
% 0.20/0.57 = { by axiom 9 (associativity_addition_1) R->L }
% 0.20/0.57 fresh43(sum(additive_identity, multiplicative_identity, multiplicative_identity), true, additive_identity, additive_identity, multiplicative_identity, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 5 (existence_of_identity_addition) R->L }
% 0.20/0.57 fresh43(fresh14(defined(multiplicative_identity), true, multiplicative_identity), true, additive_identity, additive_identity, multiplicative_identity, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 1 (well_definedness_of_multiplicative_identity) }
% 0.20/0.57 fresh43(fresh14(true, true, multiplicative_identity), true, additive_identity, additive_identity, multiplicative_identity, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 3 (existence_of_identity_addition) }
% 0.20/0.57 fresh43(true, true, additive_identity, additive_identity, multiplicative_identity, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 8 (associativity_addition_1) }
% 0.20/0.57 fresh44(sum(additive_identity, additive_identity, additive_identity), true, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 5 (existence_of_identity_addition) R->L }
% 0.20/0.57 fresh44(fresh14(defined(additive_identity), true, additive_identity), true, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 2 (well_definedness_of_additive_identity) }
% 0.20/0.57 fresh44(fresh14(true, true, additive_identity), true, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 3 (existence_of_identity_addition) }
% 0.20/0.57 fresh44(true, true, additive_identity, additive_identity, multiplicative_identity)
% 0.20/0.57 = { by axiom 6 (associativity_addition_1) }
% 0.20/0.57 true
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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