TSTP Solution File: GRP020-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP020-1 : 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 : n007.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 01:16:36 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP020-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 23:02:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --no-flatten-goal
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% 0.19/0.38 % SZS status Unsatisfiable
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% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 Take the following subset of the input axioms:
% 0.19/0.39 fof(left_inverse, axiom, ![X]: product(inverse(X), X, identity)).
% 0.19/0.39 fof(prove_inverse_X_times_X_is_id, negated_conjecture, multiply(inverse(a), a)!=identity).
% 0.19/0.39 fof(total_function1, axiom, ![Y, X2]: product(X2, Y, multiply(X2, Y))).
% 0.19/0.39 fof(total_function2, axiom, ![Z, W, X2, Y2]: (~product(X2, Y2, Z) | (~product(X2, Y2, W) | Z=W))).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (total_function2): fresh(X, X, Y, Z) = Z.
% 0.19/0.39 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true.
% 0.19/0.39 Axiom 3 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.19/0.39 Axiom 4 (total_function2): fresh2(X, X, Y, Z, W, V) = W.
% 0.19/0.39 Axiom 5 (total_function2): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.19/0.39
% 0.19/0.39 Goal 1 (prove_inverse_X_times_X_is_id): multiply(inverse(a), a) = identity.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(a), a)
% 0.19/0.39 = { by axiom 4 (total_function2) R->L }
% 0.19/0.39 fresh2(true, true, inverse(a), a, multiply(inverse(a), a), identity)
% 0.19/0.39 = { by axiom 2 (left_inverse) R->L }
% 0.19/0.39 fresh2(product(inverse(a), a, identity), true, inverse(a), a, multiply(inverse(a), a), identity)
% 0.19/0.39 = { by axiom 5 (total_function2) }
% 0.19/0.39 fresh(product(inverse(a), a, multiply(inverse(a), a)), true, multiply(inverse(a), a), identity)
% 0.19/0.39 = { by axiom 3 (total_function1) }
% 0.19/0.39 fresh(true, true, multiply(inverse(a), a), identity)
% 0.19/0.39 = { by axiom 1 (total_function2) }
% 0.19/0.39 identity
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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