TSTP Solution File: GRP033-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP033-3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n032.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 0.14s 0.34s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP033-3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.05/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 20:11:16 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.34 Command-line arguments: --no-flatten-goal
% 0.14/0.34
% 0.14/0.34 % SZS status Unsatisfiable
% 0.14/0.34
% 0.14/0.34 % SZS output start Proof
% 0.14/0.34 Take the following subset of the input axioms:
% 0.14/0.34 fof(a_is_in_subgroup, hypothesis, subgroup_member(a)).
% 0.14/0.34 fof(closure_of_product_and_inverse, axiom, ![B, C, A2]: (~subgroup_member(A2) | (~subgroup_member(B) | (~product(A2, inverse(B), C) | subgroup_member(C))))).
% 0.14/0.34 fof(left_identity, axiom, ![X]: product(identity, X, X)).
% 0.14/0.34 fof(prove_subgr2, negated_conjecture, ![A]: (~product(j(A), A, j(A)) | (~product(A, j(A), j(A)) | ~subgroup_member(A)))).
% 0.14/0.34 fof(right_identity, axiom, ![X2]: product(X2, identity, X2)).
% 0.14/0.34 fof(right_inverse, axiom, ![X2]: product(X2, inverse(X2), identity)).
% 0.14/0.34
% 0.14/0.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.34 fresh(y, y, x1...xn) = u
% 0.14/0.34 C => fresh(s, t, x1...xn) = v
% 0.14/0.34 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.34 variables of u and v.
% 0.14/0.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.34 input problem has no model of domain size 1).
% 0.14/0.34
% 0.14/0.34 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.34
% 0.14/0.34 Axiom 1 (a_is_in_subgroup): subgroup_member(a) = true2.
% 0.14/0.34 Axiom 2 (closure_of_product_and_inverse): fresh18(X, X, Y) = true2.
% 0.14/0.34 Axiom 3 (right_identity): product(X, identity, X) = true2.
% 0.14/0.34 Axiom 4 (left_identity): product(identity, X, X) = true2.
% 0.14/0.34 Axiom 5 (right_inverse): product(X, inverse(X), identity) = true2.
% 0.14/0.34 Axiom 6 (closure_of_product_and_inverse): fresh22(X, X, Y, Z, W) = subgroup_member(W).
% 0.14/0.34 Axiom 7 (closure_of_product_and_inverse): fresh21(X, X, Y, Z, W) = fresh22(subgroup_member(Y), true2, Y, Z, W).
% 0.14/0.35 Axiom 8 (closure_of_product_and_inverse): fresh21(subgroup_member(X), true2, Y, X, Z) = fresh18(product(Y, inverse(X), Z), true2, Z).
% 0.14/0.35
% 0.14/0.35 Goal 1 (prove_subgr2): tuple(product(X, j(X), j(X)), product(j(X), X, j(X)), subgroup_member(X)) = tuple(true2, true2, true2).
% 0.14/0.35 The goal is true when:
% 0.14/0.35 X = identity
% 0.14/0.35
% 0.14/0.35 Proof:
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), subgroup_member(identity))
% 0.14/0.35 = { by axiom 6 (closure_of_product_and_inverse) R->L }
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), fresh22(true2, true2, a, a, identity))
% 0.14/0.35 = { by axiom 1 (a_is_in_subgroup) R->L }
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), fresh22(subgroup_member(a), true2, a, a, identity))
% 0.14/0.35 = { by axiom 7 (closure_of_product_and_inverse) R->L }
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), fresh21(true2, true2, a, a, identity))
% 0.14/0.35 = { by axiom 1 (a_is_in_subgroup) R->L }
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), fresh21(subgroup_member(a), true2, a, a, identity))
% 0.14/0.35 = { by axiom 8 (closure_of_product_and_inverse) }
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), fresh18(product(a, inverse(a), identity), true2, identity))
% 0.14/0.35 = { by axiom 5 (right_inverse) }
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), fresh18(true2, true2, identity))
% 0.14/0.35 = { by axiom 2 (closure_of_product_and_inverse) }
% 0.14/0.35 tuple(product(identity, j(identity), j(identity)), product(j(identity), identity, j(identity)), true2)
% 0.14/0.35 = { by axiom 4 (left_identity) }
% 0.14/0.35 tuple(true2, product(j(identity), identity, j(identity)), true2)
% 0.14/0.35 = { by axiom 3 (right_identity) }
% 0.14/0.35 tuple(true2, true2, true2)
% 0.14/0.35 % SZS output end Proof
% 0.14/0.35
% 0.14/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
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