TSTP Solution File: GRP036-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP036-3 : 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 : n010.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 01:16:43 EDT 2023
% Result : Unsatisfiable 0.21s 0.43s
% 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
% 0.00/0.13 % Problem : GRP036-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 22:13:04 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.43 Command-line arguments: --no-flatten-goal
% 0.21/0.43
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.44
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Take the following subset of the input axioms:
% 0.21/0.44 fof(another_identity_in_subgroup, hypothesis, subgroup_member(another_identity)).
% 0.21/0.44 fof(another_left_identity, hypothesis, ![A2]: (~subgroup_member(A2) | product(another_identity, A2, A2))).
% 0.21/0.44 fof(closure_of_product_and_inverse, axiom, ![B, C, A2_2]: (~subgroup_member(A2_2) | (~subgroup_member(B) | (~product(A2_2, inverse(B), C) | subgroup_member(C))))).
% 0.21/0.44 fof(prove_identity_equals_another_identity, negated_conjecture, identity!=another_identity).
% 0.21/0.44 fof(right_identity, axiom, ![X]: product(X, identity, X)).
% 0.21/0.44 fof(right_inverse, axiom, ![X2]: product(X2, inverse(X2), identity)).
% 0.21/0.44 fof(total_function2, axiom, ![Y, Z, W, X2]: (~product(X2, Y, Z) | (~product(X2, Y, W) | Z=W))).
% 0.21/0.44
% 0.21/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.44 fresh(y, y, x1...xn) = u
% 0.21/0.44 C => fresh(s, t, x1...xn) = v
% 0.21/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.44 variables of u and v.
% 0.21/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.44 input problem has no model of domain size 1).
% 0.21/0.44
% 0.21/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.44
% 0.21/0.44 Axiom 1 (another_identity_in_subgroup): subgroup_member(another_identity) = true.
% 0.21/0.44 Axiom 2 (another_left_identity): fresh10(X, X, Y) = true.
% 0.21/0.44 Axiom 3 (closure_of_product_and_inverse): fresh3(X, X, Y) = true.
% 0.21/0.44 Axiom 4 (right_identity): product(X, identity, X) = true.
% 0.21/0.44 Axiom 5 (total_function2): fresh(X, X, Y, Z) = Z.
% 0.21/0.44 Axiom 6 (another_left_identity): fresh10(subgroup_member(X), true, X) = product(another_identity, X, X).
% 0.21/0.44 Axiom 7 (right_inverse): product(X, inverse(X), identity) = true.
% 0.21/0.44 Axiom 8 (closure_of_product_and_inverse): fresh12(X, X, Y, Z, W) = subgroup_member(W).
% 0.21/0.44 Axiom 9 (closure_of_product_and_inverse): fresh11(X, X, Y, Z, W) = fresh12(subgroup_member(Y), true, Y, Z, W).
% 0.21/0.44 Axiom 10 (total_function2): fresh2(X, X, Y, Z, W, V) = W.
% 0.21/0.44 Axiom 11 (closure_of_product_and_inverse): fresh11(subgroup_member(X), true, Y, X, Z) = fresh3(product(Y, inverse(X), Z), true, Z).
% 0.21/0.44 Axiom 12 (total_function2): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 0.21/0.44
% 0.21/0.44 Goal 1 (prove_identity_equals_another_identity): identity = another_identity.
% 0.21/0.44 Proof:
% 0.21/0.44 identity
% 0.21/0.44 = { by axiom 10 (total_function2) R->L }
% 0.21/0.44 fresh2(true, true, another_identity, identity, identity, another_identity)
% 0.21/0.44 = { by axiom 4 (right_identity) R->L }
% 0.21/0.44 fresh2(product(another_identity, identity, another_identity), true, another_identity, identity, identity, another_identity)
% 0.21/0.44 = { by axiom 12 (total_function2) }
% 0.21/0.44 fresh(product(another_identity, identity, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 6 (another_left_identity) R->L }
% 0.21/0.44 fresh(fresh10(subgroup_member(identity), true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 8 (closure_of_product_and_inverse) R->L }
% 0.21/0.44 fresh(fresh10(fresh12(true, true, another_identity, another_identity, identity), true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.21/0.44 fresh(fresh10(fresh12(subgroup_member(another_identity), true, another_identity, another_identity, identity), true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 9 (closure_of_product_and_inverse) R->L }
% 0.21/0.44 fresh(fresh10(fresh11(true, true, another_identity, another_identity, identity), true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 1 (another_identity_in_subgroup) R->L }
% 0.21/0.44 fresh(fresh10(fresh11(subgroup_member(another_identity), true, another_identity, another_identity, identity), true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 11 (closure_of_product_and_inverse) }
% 0.21/0.44 fresh(fresh10(fresh3(product(another_identity, inverse(another_identity), identity), true, identity), true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 7 (right_inverse) }
% 0.21/0.44 fresh(fresh10(fresh3(true, true, identity), true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 3 (closure_of_product_and_inverse) }
% 0.21/0.44 fresh(fresh10(true, true, identity), true, identity, another_identity)
% 0.21/0.44 = { by axiom 2 (another_left_identity) }
% 0.21/0.44 fresh(true, true, identity, another_identity)
% 0.21/0.44 = { by axiom 5 (total_function2) }
% 0.21/0.44 another_identity
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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