TSTP Solution File: FLD030-4 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD030-4 : 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 : n002.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 22:36:56 EDT 2023
% Result : Unsatisfiable 4.46s 0.85s
% Output : Proof 4.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : FLD030-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.08 % 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 : n002.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 : Mon Aug 28 00:19:19 EDT 2023
% 0.07/0.26 % CPUTime :
% 4.46/0.85 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 4.46/0.85
% 4.46/0.85 % SZS status Unsatisfiable
% 4.46/0.85
% 4.46/0.86 % SZS output start Proof
% 4.46/0.86 Take the following subset of the input axioms:
% 4.46/0.86 fof(associativity_multiplication_2, axiom, ![X, V, W, Y, U, Z]: (product(U, Z, W) | (~product(X, Y, U) | (~product(Y, Z, V) | ~product(X, V, W))))).
% 4.46/0.86 fof(c_is_defined, hypothesis, defined(c)).
% 4.46/0.86 fof(existence_of_identity_multiplication, axiom, ![X2]: (product(multiplicative_identity, X2, X2) | ~defined(X2))).
% 4.46/0.86 fof(not_product_7, negated_conjecture, ~product(d, b, c)).
% 4.46/0.86 fof(product_5, negated_conjecture, product(a, b, c)).
% 4.46/0.86 fof(product_6, negated_conjecture, product(multiplicative_identity, a, d)).
% 4.46/0.86
% 4.46/0.86 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.46/0.86 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.46/0.86 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.46/0.86 fresh(y, y, x1...xn) = u
% 4.46/0.86 C => fresh(s, t, x1...xn) = v
% 4.46/0.86 where fresh is a fresh function symbol and x1..xn are the free
% 4.46/0.86 variables of u and v.
% 4.46/0.86 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.46/0.86 input problem has no model of domain size 1).
% 4.46/0.86
% 4.46/0.86 The encoding turns the above axioms into the following unit equations and goals:
% 4.46/0.86
% 4.46/0.86 Axiom 1 (c_is_defined): defined(c) = true.
% 4.46/0.86 Axiom 2 (existence_of_identity_multiplication): fresh13(X, X, Y) = true.
% 4.46/0.86 Axiom 3 (product_5): product(a, b, c) = true.
% 4.46/0.86 Axiom 4 (product_6): product(multiplicative_identity, a, d) = true.
% 4.46/0.86 Axiom 5 (existence_of_identity_multiplication): fresh13(defined(X), true, X) = product(multiplicative_identity, X, X).
% 4.46/0.86 Axiom 6 (associativity_multiplication_2): fresh38(X, X, Y, Z, W) = true.
% 4.46/0.86 Axiom 7 (associativity_multiplication_2): fresh19(X, X, Y, Z, W, V, U) = product(Y, Z, W).
% 4.46/0.86 Axiom 8 (associativity_multiplication_2): fresh37(X, X, Y, Z, W, V, U, T) = fresh38(product(V, U, Y), true, Y, Z, W).
% 4.46/0.86 Axiom 9 (associativity_multiplication_2): fresh37(product(X, Y, Z), true, W, Y, V, U, X, Z) = fresh19(product(U, Z, V), true, W, Y, V, U, X).
% 4.46/0.86
% 4.46/0.86 Goal 1 (not_product_7): product(d, b, c) = true.
% 4.46/0.86 Proof:
% 4.46/0.86 product(d, b, c)
% 4.46/0.86 = { by axiom 7 (associativity_multiplication_2) R->L }
% 4.46/0.86 fresh19(true, true, d, b, c, multiplicative_identity, a)
% 4.46/0.86 = { by axiom 2 (existence_of_identity_multiplication) R->L }
% 4.46/0.86 fresh19(fresh13(true, true, c), true, d, b, c, multiplicative_identity, a)
% 4.46/0.86 = { by axiom 1 (c_is_defined) R->L }
% 4.46/0.86 fresh19(fresh13(defined(c), true, c), true, d, b, c, multiplicative_identity, a)
% 4.46/0.86 = { by axiom 5 (existence_of_identity_multiplication) }
% 4.46/0.86 fresh19(product(multiplicative_identity, c, c), true, d, b, c, multiplicative_identity, a)
% 4.46/0.86 = { by axiom 9 (associativity_multiplication_2) R->L }
% 4.46/0.86 fresh37(product(a, b, c), true, d, b, c, multiplicative_identity, a, c)
% 4.46/0.86 = { by axiom 3 (product_5) }
% 4.46/0.86 fresh37(true, true, d, b, c, multiplicative_identity, a, c)
% 4.46/0.86 = { by axiom 8 (associativity_multiplication_2) }
% 4.46/0.86 fresh38(product(multiplicative_identity, a, d), true, d, b, c)
% 4.46/0.86 = { by axiom 4 (product_6) }
% 4.46/0.86 fresh38(true, true, d, b, c)
% 4.46/0.86 = { by axiom 6 (associativity_multiplication_2) }
% 4.46/0.86 true
% 4.46/0.86 % SZS output end Proof
% 4.46/0.86
% 4.46/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
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