TSTP Solution File: GRP010-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP010-1 : 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 : n021.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 01:16:32 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% 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
% 0.12/0.13 % Problem : GRP010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.14 % 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 : n021.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 01:58:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
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% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Take the following subset of the input axioms:
% 0.21/0.41 fof(a_multiply_b_is_identity, hypothesis, product(a, b, identity)).
% 0.21/0.41 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))))).
% 0.21/0.41 fof(left_identity, axiom, ![X2]: product(identity, X2, X2)).
% 0.21/0.41 fof(left_inverse, axiom, ![X2]: product(inverse(X2), X2, identity)).
% 0.21/0.41 fof(prove_b_multiply_a_is_identity, negated_conjecture, ~product(b, a, identity)).
% 0.21/0.41 fof(right_identity, axiom, ![X2]: product(X2, identity, X2)).
% 0.21/0.41 fof(total_function1, axiom, ![X2, Y2]: product(X2, Y2, multiply(X2, Y2))).
% 0.21/0.41 fof(total_function2, axiom, ![X2, Y2, Z2, W2]: (~product(X2, Y2, Z2) | (~product(X2, Y2, W2) | Z2=W2))).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (right_identity): product(X, identity, X) = true.
% 0.21/0.41 Axiom 2 (a_multiply_b_is_identity): product(a, b, identity) = true.
% 0.21/0.41 Axiom 3 (left_identity): product(identity, X, X) = true.
% 0.21/0.41 Axiom 4 (total_function2): fresh(X, X, Y, Z) = Z.
% 0.21/0.41 Axiom 5 (left_inverse): product(inverse(X), X, identity) = true.
% 0.21/0.41 Axiom 6 (associativity2): fresh6(X, X, Y, Z, W) = true.
% 0.21/0.41 Axiom 7 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.21/0.41 Axiom 8 (total_function2): fresh2(X, X, Y, Z, W, V) = W.
% 0.21/0.41 Axiom 9 (associativity2): fresh3(X, X, Y, Z, W, V, U) = product(W, V, U).
% 0.21/0.41 Axiom 10 (associativity2): fresh5(X, X, Y, Z, W, V, U, T) = fresh6(product(Y, Z, W), true, W, V, T).
% 0.21/0.41 Axiom 11 (total_function2): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.21/0.41 Axiom 12 (associativity2): fresh5(product(X, Y, Z), true, W, X, V, Y, Z, U) = fresh3(product(W, Z, U), true, W, X, V, Y, U).
% 0.21/0.41
% 0.21/0.41 Goal 1 (prove_b_multiply_a_is_identity): product(b, a, identity) = true.
% 0.21/0.41 Proof:
% 0.21/0.41 product(b, a, identity)
% 0.21/0.41 = { by axiom 4 (total_function2) R->L }
% 0.21/0.41 product(fresh(true, true, multiply(identity, b), b), a, identity)
% 0.21/0.41 = { by axiom 7 (total_function1) R->L }
% 0.21/0.41 product(fresh(product(identity, b, multiply(identity, b)), true, multiply(identity, b), b), a, identity)
% 0.21/0.41 = { by axiom 11 (total_function2) R->L }
% 0.21/0.41 product(fresh2(product(identity, b, b), true, identity, b, multiply(identity, b), b), a, identity)
% 0.21/0.41 = { by axiom 3 (left_identity) }
% 0.21/0.41 product(fresh2(true, true, identity, b, multiply(identity, b), b), a, identity)
% 0.21/0.41 = { by axiom 8 (total_function2) }
% 0.21/0.41 product(multiply(identity, b), a, identity)
% 0.21/0.41 = { by axiom 4 (total_function2) R->L }
% 0.21/0.41 product(multiply(fresh(true, true, multiply(inverse(a), a), identity), b), a, identity)
% 0.21/0.41 = { by axiom 7 (total_function1) R->L }
% 0.21/0.41 product(multiply(fresh(product(inverse(a), a, multiply(inverse(a), a)), true, multiply(inverse(a), a), identity), b), a, identity)
% 0.21/0.41 = { by axiom 11 (total_function2) R->L }
% 0.21/0.41 product(multiply(fresh2(product(inverse(a), a, identity), true, inverse(a), a, multiply(inverse(a), a), identity), b), a, identity)
% 0.21/0.41 = { by axiom 5 (left_inverse) }
% 0.21/0.41 product(multiply(fresh2(true, true, inverse(a), a, multiply(inverse(a), a), identity), b), a, identity)
% 0.21/0.41 = { by axiom 8 (total_function2) }
% 0.21/0.41 product(multiply(multiply(inverse(a), a), b), a, identity)
% 0.21/0.41 = { by axiom 4 (total_function2) R->L }
% 0.21/0.41 product(fresh(true, true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 6 (associativity2) R->L }
% 0.21/0.41 product(fresh(fresh6(true, true, multiply(inverse(a), a), b, inverse(a)), true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 7 (total_function1) R->L }
% 0.21/0.41 product(fresh(fresh6(product(inverse(a), a, multiply(inverse(a), a)), true, multiply(inverse(a), a), b, inverse(a)), true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 10 (associativity2) R->L }
% 0.21/0.41 product(fresh(fresh5(true, true, inverse(a), a, multiply(inverse(a), a), b, identity, inverse(a)), true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 2 (a_multiply_b_is_identity) R->L }
% 0.21/0.41 product(fresh(fresh5(product(a, b, identity), true, inverse(a), a, multiply(inverse(a), a), b, identity, inverse(a)), true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 12 (associativity2) }
% 0.21/0.41 product(fresh(fresh3(product(inverse(a), identity, inverse(a)), true, inverse(a), a, multiply(inverse(a), a), b, inverse(a)), true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 1 (right_identity) }
% 0.21/0.41 product(fresh(fresh3(true, true, inverse(a), a, multiply(inverse(a), a), b, inverse(a)), true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 9 (associativity2) }
% 0.21/0.41 product(fresh(product(multiply(inverse(a), a), b, inverse(a)), true, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 11 (total_function2) R->L }
% 0.21/0.41 product(fresh2(product(multiply(inverse(a), a), b, multiply(multiply(inverse(a), a), b)), true, multiply(inverse(a), a), b, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 7 (total_function1) }
% 0.21/0.41 product(fresh2(true, true, multiply(inverse(a), a), b, inverse(a), multiply(multiply(inverse(a), a), b)), a, identity)
% 0.21/0.41 = { by axiom 8 (total_function2) }
% 0.21/0.41 product(inverse(a), a, identity)
% 0.21/0.41 = { by axiom 5 (left_inverse) }
% 0.21/0.41 true
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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