TSTP Solution File: RNG038-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG038-2 : 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 : n021.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 13:58:58 EDT 2023
% Result : Unsatisfiable 0.19s 0.47s
% 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
% 0.00/0.12 % Problem : RNG038-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % 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 : n021.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 : Sun Aug 27 02:53:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Command-line arguments: --no-flatten-goal
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% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 Take the following subset of the input axioms:
% 0.19/0.47 fof(a_not_additive_identity, negated_conjecture, ~equalish(a, additive_identity)).
% 0.19/0.47 fof(addition_is_well_defined, axiom, ![X, Y, U, V]: (~sum(X, Y, U) | (~sum(X, Y, V) | equalish(U, V)))).
% 0.19/0.47 fof(additive_identity2, axiom, ![X2]: sum(X2, additive_identity, X2)).
% 0.19/0.47 fof(multiplication_is_well_defined, axiom, ![V2, X2, Y2, U2]: (~product(X2, Y2, U2) | (~product(X2, Y2, V2) | equalish(U2, V2)))).
% 0.19/0.47 fof(multiplicative_identity1, axiom, ![X2]: product(additive_identity, X2, additive_identity)).
% 0.19/0.47 fof(prove_b_is_additive_identity, negated_conjecture, ~equalish(b, additive_identity)).
% 0.19/0.47 fof(some_property, hypothesis, ![X2, Y2]: (~equalish(X2, additive_identity) | product(X2, h(X2, Y2), Y2))).
% 0.19/0.47
% 0.19/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.47 fresh(y, y, x1...xn) = u
% 0.19/0.47 C => fresh(s, t, x1...xn) = v
% 0.19/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.47 variables of u and v.
% 0.19/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.47 input problem has no model of domain size 1).
% 0.19/0.47
% 0.19/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.47
% 0.19/0.47 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 0.19/0.47 Axiom 2 (multiplicative_identity1): product(additive_identity, X, additive_identity) = true.
% 0.19/0.47 Axiom 3 (addition_is_well_defined): fresh23(X, X, Y, Z) = true.
% 0.19/0.47 Axiom 4 (multiplication_is_well_defined): fresh15(X, X, Y, Z) = true.
% 0.19/0.47 Axiom 5 (some_property): fresh7(X, X, Y, Z) = true.
% 0.19/0.47 Axiom 6 (addition_is_well_defined): fresh25(X, X, Y, Z, W, V) = equalish(W, V).
% 0.19/0.47 Axiom 7 (multiplication_is_well_defined): fresh16(X, X, Y, Z, W, V) = equalish(W, V).
% 0.19/0.47 Axiom 8 (some_property): fresh7(equalish(X, additive_identity), true, X, Y) = product(X, h(X, Y), Y).
% 0.19/0.47 Axiom 9 (addition_is_well_defined): fresh25(sum(X, Y, Z), true, X, Y, W, Z) = fresh23(sum(X, Y, W), true, W, Z).
% 0.19/0.47 Axiom 10 (multiplication_is_well_defined): fresh16(product(X, Y, Z), true, X, Y, W, Z) = fresh15(product(X, Y, W), true, W, Z).
% 0.19/0.47
% 0.19/0.47 Lemma 11: equalish(X, additive_identity) = true.
% 0.19/0.47 Proof:
% 0.19/0.47 equalish(X, additive_identity)
% 0.19/0.47 = { by axiom 7 (multiplication_is_well_defined) R->L }
% 0.19/0.47 fresh16(true, true, additive_identity, h(additive_identity, X), X, additive_identity)
% 0.19/0.47 = { by axiom 2 (multiplicative_identity1) R->L }
% 0.19/0.47 fresh16(product(additive_identity, h(additive_identity, X), additive_identity), true, additive_identity, h(additive_identity, X), X, additive_identity)
% 0.19/0.47 = { by axiom 10 (multiplication_is_well_defined) }
% 0.19/0.47 fresh15(product(additive_identity, h(additive_identity, X), X), true, X, additive_identity)
% 0.19/0.47 = { by axiom 8 (some_property) R->L }
% 0.19/0.47 fresh15(fresh7(equalish(additive_identity, additive_identity), true, additive_identity, X), true, X, additive_identity)
% 0.19/0.47 = { by axiom 6 (addition_is_well_defined) R->L }
% 0.19/0.47 fresh15(fresh7(fresh25(true, true, additive_identity, additive_identity, additive_identity, additive_identity), true, additive_identity, X), true, X, additive_identity)
% 0.19/0.47 = { by axiom 1 (additive_identity2) R->L }
% 0.19/0.47 fresh15(fresh7(fresh25(sum(additive_identity, additive_identity, additive_identity), true, additive_identity, additive_identity, additive_identity, additive_identity), true, additive_identity, X), true, X, additive_identity)
% 0.19/0.47 = { by axiom 9 (addition_is_well_defined) }
% 0.19/0.47 fresh15(fresh7(fresh23(sum(additive_identity, additive_identity, additive_identity), true, additive_identity, additive_identity), true, additive_identity, X), true, X, additive_identity)
% 0.19/0.47 = { by axiom 1 (additive_identity2) }
% 0.19/0.47 fresh15(fresh7(fresh23(true, true, additive_identity, additive_identity), true, additive_identity, X), true, X, additive_identity)
% 0.19/0.47 = { by axiom 3 (addition_is_well_defined) }
% 0.19/0.47 fresh15(fresh7(true, true, additive_identity, X), true, X, additive_identity)
% 0.19/0.47 = { by axiom 5 (some_property) }
% 0.19/0.47 fresh15(true, true, X, additive_identity)
% 0.19/0.47 = { by axiom 4 (multiplication_is_well_defined) }
% 0.19/0.47 true
% 0.19/0.47
% 0.19/0.47 Goal 1 (prove_b_is_additive_identity): equalish(b, additive_identity) = true.
% 0.19/0.47 Proof:
% 0.19/0.47 equalish(b, additive_identity)
% 0.19/0.47 = { by lemma 11 }
% 0.19/0.47 true
% 0.19/0.47
% 0.19/0.47 Goal 2 (a_not_additive_identity): equalish(a, additive_identity) = true.
% 0.19/0.47 Proof:
% 0.19/0.47 equalish(a, additive_identity)
% 0.19/0.47 = { by lemma 11 }
% 0.19/0.47 true
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47
% 0.19/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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