TSTP Solution File: GRP046-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP046-2 : 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 : n027.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 0.20s 0.49s
% 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 : GRP046-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 02:37:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Take the following subset of the input axioms:
% 0.20/0.50 fof(a_equals_b, hypothesis, equalish(a, b)).
% 0.20/0.50 fof(associativity1, axiom, ![X, Y, Z, W, U, V]: (~product(X, Y, U) | (~product(Y, Z, V) | (~product(U, Z, W) | product(X, V, W))))).
% 0.20/0.50 fof(left_identity, axiom, ![X2]: product(identity, X2, X2)).
% 0.20/0.50 fof(product_substitution3, axiom, ![X2, Y2, Z2, W2]: (~equalish(X2, Y2) | (~product(W2, Z2, X2) | product(W2, Z2, Y2)))).
% 0.20/0.50 fof(prove_multiply_substitution1, negated_conjecture, ~equalish(multiply(a, c), multiply(b, c))).
% 0.20/0.50 fof(total_function1, axiom, ![X2, Y2]: product(X2, Y2, multiply(X2, Y2))).
% 0.20/0.50 fof(total_function2, axiom, ![X2, Y2, Z2, W2]: (~product(X2, Y2, Z2) | (~product(X2, Y2, W2) | equalish(Z2, W2)))).
% 0.20/0.50
% 0.20/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.50 fresh(y, y, x1...xn) = u
% 0.20/0.50 C => fresh(s, t, x1...xn) = v
% 0.20/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.50 variables of u and v.
% 0.20/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.50 input problem has no model of domain size 1).
% 0.20/0.50
% 0.20/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.50
% 0.20/0.50 Axiom 1 (a_equals_b): equalish(a, b) = true.
% 0.20/0.50 Axiom 2 (left_identity): product(identity, X, X) = true.
% 0.20/0.50 Axiom 3 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.20/0.50 Axiom 4 (total_function2): fresh(X, X, Y, Z) = true.
% 0.20/0.50 Axiom 5 (associativity1): fresh10(X, X, Y, Z, W) = true.
% 0.20/0.50 Axiom 6 (product_substitution3): fresh3(X, X, Y, Z, W) = true.
% 0.20/0.50 Axiom 7 (product_substitution3): fresh4(X, X, Y, Z, W, V) = product(W, V, Z).
% 0.20/0.50 Axiom 8 (total_function2): fresh2(X, X, Y, Z, W, V) = equalish(W, V).
% 0.20/0.50 Axiom 9 (associativity1): fresh6(X, X, Y, Z, W, V, U) = product(Y, V, U).
% 0.20/0.50 Axiom 10 (product_substitution3): fresh4(equalish(X, Y), true, X, Y, Z, W) = fresh3(product(Z, W, X), true, Y, Z, W).
% 0.20/0.50 Axiom 11 (associativity1): fresh9(X, X, Y, Z, W, V, U, T) = fresh10(product(Y, Z, W), true, Y, U, T).
% 0.20/0.50 Axiom 12 (total_function2): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.20/0.50 Axiom 13 (associativity1): fresh9(product(X, Y, Z), true, W, V, X, Y, U, Z) = fresh6(product(V, Y, U), true, W, V, X, U, Z).
% 0.20/0.50
% 0.20/0.50 Lemma 14: fresh(product(identity, X, Y), true, Y, X) = equalish(Y, X).
% 0.20/0.50 Proof:
% 0.20/0.50 fresh(product(identity, X, Y), true, Y, X)
% 0.20/0.50 = { by axiom 12 (total_function2) R->L }
% 0.20/0.50 fresh2(product(identity, X, X), true, identity, X, Y, X)
% 0.20/0.50 = { by axiom 2 (left_identity) }
% 0.20/0.50 fresh2(true, true, identity, X, Y, X)
% 0.20/0.50 = { by axiom 8 (total_function2) }
% 0.20/0.50 equalish(Y, X)
% 0.20/0.50
% 0.20/0.50 Lemma 15: fresh4(equalish(X, Y), true, X, Y, identity, X) = true.
% 0.20/0.50 Proof:
% 0.20/0.50 fresh4(equalish(X, Y), true, X, Y, identity, X)
% 0.20/0.50 = { by axiom 10 (product_substitution3) }
% 0.20/0.50 fresh3(product(identity, X, X), true, Y, identity, X)
% 0.20/0.50 = { by axiom 2 (left_identity) }
% 0.20/0.50 fresh3(true, true, Y, identity, X)
% 0.20/0.50 = { by axiom 6 (product_substitution3) }
% 0.20/0.50 true
% 0.20/0.50
% 0.20/0.50 Goal 1 (prove_multiply_substitution1): equalish(multiply(a, c), multiply(b, c)) = true.
% 0.20/0.50 Proof:
% 0.20/0.50 equalish(multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 fresh(product(identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 9 (associativity1) R->L }
% 0.20/0.50 fresh(fresh6(true, true, identity, b, a, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 3 (total_function1) R->L }
% 0.20/0.50 fresh(fresh6(product(b, c, multiply(b, c)), true, identity, b, a, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 13 (associativity1) R->L }
% 0.20/0.50 fresh(fresh9(product(a, c, multiply(a, c)), true, identity, b, a, c, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 3 (total_function1) }
% 0.20/0.50 fresh(fresh9(true, true, identity, b, a, c, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 11 (associativity1) }
% 0.20/0.50 fresh(fresh10(product(identity, b, a), true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 7 (product_substitution3) R->L }
% 0.20/0.50 fresh(fresh10(fresh4(true, true, b, a, identity, b), true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 4 (total_function2) R->L }
% 0.20/0.50 fresh(fresh10(fresh4(fresh(true, true, b, a), true, b, a, identity, b), true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by lemma 15 R->L }
% 0.20/0.50 fresh(fresh10(fresh4(fresh(fresh4(equalish(a, b), true, a, b, identity, a), true, b, a), true, b, a, identity, b), true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 1 (a_equals_b) }
% 0.20/0.50 fresh(fresh10(fresh4(fresh(fresh4(true, true, a, b, identity, a), true, b, a), true, b, a, identity, b), true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 7 (product_substitution3) }
% 0.20/0.50 fresh(fresh10(fresh4(fresh(product(identity, a, b), true, b, a), true, b, a, identity, b), true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by lemma 14 }
% 0.20/0.50 fresh(fresh10(fresh4(equalish(b, a), true, b, a, identity, b), true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by lemma 15 }
% 0.20/0.50 fresh(fresh10(true, true, identity, multiply(b, c), multiply(a, c)), true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 5 (associativity1) }
% 0.20/0.50 fresh(true, true, multiply(a, c), multiply(b, c))
% 0.20/0.50 = { by axiom 4 (total_function2) }
% 0.20/0.50 true
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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