TSTP Solution File: GRP006-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP006-1 : 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 : n006.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 01:16:31 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% 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
% 0.11/0.12 % Problem : GRP006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % 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 : n006.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:17:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --no-flatten-goal
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% 0.20/0.39 % SZS status Unsatisfiable
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% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(condition, axiom, ![X, Y, Z]: (~an_element(X) | (~an_element(Y) | (~product(X, inverse(Y), Z) | an_element(Z))))).
% 0.20/0.40 fof(element_of_set, hypothesis, an_element(the_element)).
% 0.20/0.40 fof(left_identity, axiom, ![X2]: product(identity, X2, X2)).
% 0.20/0.40 fof(prove_b_inverse_is_in_set, negated_conjecture, ~an_element(inverse(the_element))).
% 0.20/0.40 fof(right_inverse, axiom, ![X2]: product(X2, inverse(X2), identity)).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (element_of_set): an_element(the_element) = true.
% 0.20/0.40 Axiom 2 (condition): fresh(X, X, Y) = true.
% 0.20/0.40 Axiom 3 (left_identity): product(identity, X, X) = true.
% 0.20/0.40 Axiom 4 (right_inverse): product(X, inverse(X), identity) = true.
% 0.20/0.40 Axiom 5 (condition): fresh9(X, X, Y, Z, W) = an_element(W).
% 0.20/0.40 Axiom 6 (condition): fresh8(X, X, Y, Z, W) = fresh9(an_element(Y), true, Y, Z, W).
% 0.20/0.40 Axiom 7 (condition): fresh8(an_element(X), true, Y, X, Z) = fresh(product(Y, inverse(X), Z), true, Z).
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_b_inverse_is_in_set): an_element(inverse(the_element)) = true.
% 0.20/0.40 Proof:
% 0.20/0.40 an_element(inverse(the_element))
% 0.20/0.40 = { by axiom 5 (condition) R->L }
% 0.20/0.40 fresh9(true, true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 2 (condition) R->L }
% 0.20/0.40 fresh9(fresh(true, true, identity), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 4 (right_inverse) R->L }
% 0.20/0.40 fresh9(fresh(product(the_element, inverse(the_element), identity), true, identity), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 7 (condition) R->L }
% 0.20/0.40 fresh9(fresh8(an_element(the_element), true, the_element, the_element, identity), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 1 (element_of_set) }
% 0.20/0.40 fresh9(fresh8(true, true, the_element, the_element, identity), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 6 (condition) }
% 0.20/0.40 fresh9(fresh9(an_element(the_element), true, the_element, the_element, identity), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 1 (element_of_set) }
% 0.20/0.40 fresh9(fresh9(true, true, the_element, the_element, identity), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 5 (condition) }
% 0.20/0.40 fresh9(an_element(identity), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 6 (condition) R->L }
% 0.20/0.40 fresh8(true, true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 1 (element_of_set) R->L }
% 0.20/0.40 fresh8(an_element(the_element), true, identity, the_element, inverse(the_element))
% 0.20/0.40 = { by axiom 7 (condition) }
% 0.20/0.40 fresh(product(identity, inverse(the_element), inverse(the_element)), true, inverse(the_element))
% 0.20/0.40 = { by axiom 3 (left_identity) }
% 0.20/0.40 fresh(true, true, inverse(the_element))
% 0.20/0.40 = { by axiom 2 (condition) }
% 0.20/0.40 true
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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