TSTP Solution File: GRP034-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP034-3 : 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 : n003.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 01:16:42 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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
% 0.07/0.12 % Problem : GRP034-3 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 00:03:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
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% 0.20/0.40 % SZS status Unsatisfiable
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% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Take the following subset of the input axioms:
% 0.20/0.41 fof(a_is_in_subgroup, hypothesis, subgroup_member(a)).
% 0.20/0.41 fof(closure_of_product_and_inverse, axiom, ![B, C, A2]: (~subgroup_member(A2) | (~subgroup_member(B) | (~product(A2, inverse(B), C) | subgroup_member(C))))).
% 0.20/0.41 fof(left_identity, axiom, ![X]: product(identity, X, X)).
% 0.20/0.41 fof(prove_a_inverse_is_in_subgroup, negated_conjecture, ~subgroup_member(inverse(a))).
% 0.20/0.41 fof(right_inverse, axiom, ![X2]: product(X2, inverse(X2), identity)).
% 0.20/0.41
% 0.20/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.41 fresh(y, y, x1...xn) = u
% 0.20/0.41 C => fresh(s, t, x1...xn) = v
% 0.20/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.41 variables of u and v.
% 0.20/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.41 input problem has no model of domain size 1).
% 0.20/0.41
% 0.20/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.41
% 0.20/0.41 Axiom 1 (a_is_in_subgroup): subgroup_member(a) = true.
% 0.20/0.41 Axiom 2 (closure_of_product_and_inverse): fresh3(X, X, Y) = true.
% 0.20/0.41 Axiom 3 (left_identity): product(identity, X, X) = true.
% 0.20/0.41 Axiom 4 (right_inverse): product(X, inverse(X), identity) = true.
% 0.20/0.41 Axiom 5 (closure_of_product_and_inverse): fresh7(X, X, Y, Z, W) = subgroup_member(W).
% 0.20/0.41 Axiom 6 (closure_of_product_and_inverse): fresh6(X, X, Y, Z, W) = fresh7(subgroup_member(Y), true, Y, Z, W).
% 0.20/0.41 Axiom 7 (closure_of_product_and_inverse): fresh6(subgroup_member(X), true, Y, X, Z) = fresh3(product(Y, inverse(X), Z), true, Z).
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_a_inverse_is_in_subgroup): subgroup_member(inverse(a)) = true.
% 0.20/0.41 Proof:
% 0.20/0.41 subgroup_member(inverse(a))
% 0.20/0.41 = { by axiom 5 (closure_of_product_and_inverse) R->L }
% 0.20/0.41 fresh7(true, true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 2 (closure_of_product_and_inverse) R->L }
% 0.20/0.41 fresh7(fresh3(true, true, identity), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 4 (right_inverse) R->L }
% 0.20/0.41 fresh7(fresh3(product(a, inverse(a), identity), true, identity), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 7 (closure_of_product_and_inverse) R->L }
% 0.20/0.41 fresh7(fresh6(subgroup_member(a), true, a, a, identity), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 1 (a_is_in_subgroup) }
% 0.20/0.41 fresh7(fresh6(true, true, a, a, identity), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 6 (closure_of_product_and_inverse) }
% 0.20/0.41 fresh7(fresh7(subgroup_member(a), true, a, a, identity), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 1 (a_is_in_subgroup) }
% 0.20/0.41 fresh7(fresh7(true, true, a, a, identity), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 5 (closure_of_product_and_inverse) }
% 0.20/0.41 fresh7(subgroup_member(identity), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 6 (closure_of_product_and_inverse) R->L }
% 0.20/0.41 fresh6(true, true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 1 (a_is_in_subgroup) R->L }
% 0.20/0.41 fresh6(subgroup_member(a), true, identity, a, inverse(a))
% 0.20/0.41 = { by axiom 7 (closure_of_product_and_inverse) }
% 0.20/0.41 fresh3(product(identity, inverse(a), inverse(a)), true, inverse(a))
% 0.20/0.41 = { by axiom 3 (left_identity) }
% 0.20/0.41 fresh3(true, true, inverse(a))
% 0.20/0.41 = { by axiom 2 (closure_of_product_and_inverse) }
% 0.20/0.41 true
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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