TSTP Solution File: GRP044-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP044-2 : TPTP v8.1.2. Released v1.0.0.
% 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 : n013.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 : Thu Aug 31 01:16:46 EDT 2023
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP044-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % 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 : n013.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 : Tue Aug 29 00:07:46 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.44 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Take the following subset of the input axioms:
% 0.21/0.44 fof(a_equals_b, hypothesis, equalish(a, b)).
% 0.21/0.44 fof(associativity2, axiom, ![X, Y, Z, W, U, V]: (~product(X, Y, U) | (~product(Y, Z, V) | (~product(X, V, W) | product(U, Z, W))))).
% 0.21/0.44 fof(left_identity, axiom, ![X2]: product(identity, X2, X2)).
% 0.21/0.44 fof(product_substitution3, axiom, ![X2, Y2, Z2, W2]: (~equalish(X2, Y2) | (~product(W2, Z2, X2) | product(W2, Z2, Y2)))).
% 0.21/0.44 fof(product_with_a, hypothesis, product(a, c, result)).
% 0.21/0.44 fof(prove_product_with_b, negated_conjecture, ~product(b, c, result)).
% 0.21/0.44
% 0.21/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.44 fresh(y, y, x1...xn) = u
% 0.21/0.44 C => fresh(s, t, x1...xn) = v
% 0.21/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.44 variables of u and v.
% 0.21/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.44 input problem has no model of domain size 1).
% 0.21/0.44
% 0.21/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.44
% 0.21/0.44 Axiom 1 (a_equals_b): equalish(a, b) = true.
% 0.21/0.44 Axiom 2 (left_identity): product(identity, X, X) = true.
% 0.21/0.44 Axiom 3 (product_with_a): product(a, c, result) = true.
% 0.21/0.44 Axiom 4 (associativity2): fresh8(X, X, Y, Z, W) = true.
% 0.21/0.44 Axiom 5 (product_substitution3): fresh3(X, X, Y, Z, W) = true.
% 0.21/0.44 Axiom 6 (product_substitution3): fresh4(X, X, Y, Z, W, V) = product(W, V, Z).
% 0.21/0.44 Axiom 7 (associativity2): fresh5(X, X, Y, Z, W, V, U) = product(W, V, U).
% 0.21/0.44 Axiom 8 (product_substitution3): fresh4(equalish(X, Y), true, X, Y, Z, W) = fresh3(product(Z, W, X), true, Y, Z, W).
% 0.21/0.44 Axiom 9 (associativity2): fresh7(X, X, Y, Z, W, V, U, T) = fresh8(product(Y, Z, W), true, W, V, T).
% 0.21/0.44 Axiom 10 (associativity2): fresh7(product(X, Y, Z), true, W, X, V, Y, Z, U) = fresh5(product(W, Z, U), true, W, X, V, Y, U).
% 0.21/0.44
% 0.21/0.44 Goal 1 (prove_product_with_b): product(b, c, result) = true.
% 0.21/0.44 Proof:
% 0.21/0.44 product(b, c, result)
% 0.21/0.44 = { by axiom 7 (associativity2) R->L }
% 0.21/0.44 fresh5(true, true, identity, a, b, c, result)
% 0.21/0.44 = { by axiom 2 (left_identity) R->L }
% 0.21/0.44 fresh5(product(identity, result, result), true, identity, a, b, c, result)
% 0.21/0.44 = { by axiom 10 (associativity2) R->L }
% 0.21/0.44 fresh7(product(a, c, result), true, identity, a, b, c, result, result)
% 0.21/0.44 = { by axiom 3 (product_with_a) }
% 0.21/0.44 fresh7(true, true, identity, a, b, c, result, result)
% 0.21/0.44 = { by axiom 9 (associativity2) }
% 0.21/0.44 fresh8(product(identity, a, b), true, b, c, result)
% 0.21/0.44 = { by axiom 6 (product_substitution3) R->L }
% 0.21/0.44 fresh8(fresh4(true, true, a, b, identity, a), true, b, c, result)
% 0.21/0.44 = { by axiom 1 (a_equals_b) R->L }
% 0.21/0.44 fresh8(fresh4(equalish(a, b), true, a, b, identity, a), true, b, c, result)
% 0.21/0.44 = { by axiom 8 (product_substitution3) }
% 0.21/0.44 fresh8(fresh3(product(identity, a, a), true, b, identity, a), true, b, c, result)
% 0.21/0.44 = { by axiom 2 (left_identity) }
% 0.21/0.44 fresh8(fresh3(true, true, b, identity, a), true, b, c, result)
% 0.21/0.44 = { by axiom 5 (product_substitution3) }
% 0.21/0.44 fresh8(true, true, b, c, result)
% 0.21/0.44 = { by axiom 4 (associativity2) }
% 0.21/0.44 true
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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