TSTP Solution File: NUM925+5 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n001.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 : Mon Jun 24 13:10:27 EDT 2024
% Result : Theorem 3.90s 0.90s
% Output : Proof 3.90s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.13 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.13/0.34 % Computer : n001.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 : Sat Jun 22 23:54:39 EDT 2024
% 0.13/0.35 % CPUTime :
% 3.90/0.90 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.90/0.90
% 3.90/0.90 % SZS status Theorem
% 3.90/0.90
% 3.90/0.90 % SZS output start Proof
% 3.90/0.90 Take the following subset of the input axioms:
% 3.90/0.90 fof(arity_Int_Oint___Int_Onumber__ring, axiom, number_ring(int)).
% 3.90/0.90 fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors, axiom, ring_11004092258visors(int)).
% 3.90/0.90 fof(conj_0, conjecture, power_power(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), number_number_of(nat, bit0(bit1(pls))))!=zero_zero(int)).
% 3.90/0.90 fof(fact_0_n1pos, axiom, ord_less(int, zero_zero(int), plus_plus(int, one_one(int), semiring_1_of_nat(int, n)))).
% 3.90/0.90 fof(fact_19_zero__is__num__zero, axiom, zero_zero(int)=number_number_of(int, pls)).
% 3.90/0.90 fof(fact_32_rel__simps_I2_J, axiom, ~ord_less(int, pls, pls)).
% 3.90/0.90 fof(fact_57_bin__less__0__simps_I1_J, axiom, ~ord_less(int, pls, zero_zero(int))).
% 3.90/0.90 fof(fact_5_zero__eq__power2, axiom, ![X_a]: (ring_11004092258visors(X_a) => ![A_2]: (power_power(X_a, A_2, number_number_of(nat, bit0(bit1(pls))))=zero_zero(X_a) <=> ti(X_a, A_2)=zero_zero(X_a)))).
% 3.90/0.90 fof(fact_73_Pls__def, axiom, pls=zero_zero(int)).
% 3.90/0.90 fof(fact_76_add__Pls, axiom, ![K]: plus_plus(int, pls, K)=K).
% 3.90/0.90 fof(fact_84_add__numeral__0, axiom, ![X_a2]: (number_ring(X_a2) => ![A_1]: plus_plus(X_a2, number_number_of(X_a2, pls), A_1)=ti(X_a2, A_1))).
% 3.90/0.90
% 3.90/0.90 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.90/0.90 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.90/0.90 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.90/0.90 fresh(y, y, x1...xn) = u
% 3.90/0.90 C => fresh(s, t, x1...xn) = v
% 3.90/0.90 where fresh is a fresh function symbol and x1..xn are the free
% 3.90/0.90 variables of u and v.
% 3.90/0.90 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.90/0.90 input problem has no model of domain size 1).
% 3.90/0.90
% 3.90/0.90 The encoding turns the above axioms into the following unit equations and goals:
% 3.90/0.90
% 3.90/0.90 Axiom 1 (fact_73_Pls__def): pls = zero_zero(int).
% 3.90/0.90 Axiom 2 (arity_Int_Oint___Int_Onumber__ring): number_ring(int) = true2.
% 3.90/0.90 Axiom 3 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors): ring_11004092258visors(int) = true2.
% 3.90/0.90 Axiom 4 (fact_19_zero__is__num__zero): zero_zero(int) = number_number_of(int, pls).
% 3.90/0.90 Axiom 5 (fact_76_add__Pls): plus_plus(int, pls, X) = X.
% 3.90/0.90 Axiom 6 (fact_5_zero__eq__power2_1): fresh69(X, X, Y, Z) = ti(Y, Z).
% 3.90/0.90 Axiom 7 (fact_5_zero__eq__power2_1): fresh68(X, X, Y, Z) = zero_zero(Y).
% 3.90/0.90 Axiom 8 (fact_84_add__numeral__0): fresh48(X, X, Y, Z) = ti(Y, Z).
% 3.90/0.90 Axiom 9 (fact_84_add__numeral__0): fresh48(number_ring(X), true2, X, Y) = plus_plus(X, number_number_of(X, pls), Y).
% 3.90/0.90 Axiom 10 (fact_0_n1pos): ord_less(int, zero_zero(int), plus_plus(int, one_one(int), semiring_1_of_nat(int, n))) = true2.
% 3.90/0.90 Axiom 11 (fact_5_zero__eq__power2_1): fresh69(ring_11004092258visors(X), true2, X, Y) = fresh68(power_power(X, Y, number_number_of(nat, bit0(bit1(pls)))), zero_zero(X), X, Y).
% 3.90/0.90 Axiom 12 (conj_0): power_power(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), number_number_of(nat, bit0(bit1(pls)))) = zero_zero(int).
% 3.90/0.90
% 3.90/0.91 Lemma 13: ord_less(int, pls, zero_zero(int)) = true2.
% 3.90/0.91 Proof:
% 3.90/0.91 ord_less(int, pls, zero_zero(int))
% 3.90/0.91 = { by axiom 7 (fact_5_zero__eq__power2_1) R->L }
% 3.90/0.91 ord_less(int, pls, fresh68(pls, pls, int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 1 (fact_73_Pls__def) }
% 3.90/0.91 ord_less(int, pls, fresh68(pls, zero_zero(int), int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 1 (fact_73_Pls__def) }
% 3.90/0.91 ord_less(int, pls, fresh68(zero_zero(int), zero_zero(int), int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 12 (conj_0) R->L }
% 3.90/0.91 ord_less(int, pls, fresh68(power_power(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)), number_number_of(nat, bit0(bit1(pls)))), zero_zero(int), int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 11 (fact_5_zero__eq__power2_1) R->L }
% 3.90/0.91 ord_less(int, pls, fresh69(ring_11004092258visors(int), true2, int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 3 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors) }
% 3.90/0.91 ord_less(int, pls, fresh69(true2, true2, int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 6 (fact_5_zero__eq__power2_1) }
% 3.90/0.91 ord_less(int, pls, ti(int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 8 (fact_84_add__numeral__0) R->L }
% 3.90/0.91 ord_less(int, pls, fresh48(true2, true2, int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 2 (arity_Int_Oint___Int_Onumber__ring) R->L }
% 3.90/0.91 ord_less(int, pls, fresh48(number_ring(int), true2, int, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 9 (fact_84_add__numeral__0) }
% 3.90/0.91 ord_less(int, pls, plus_plus(int, number_number_of(int, pls), plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 4 (fact_19_zero__is__num__zero) R->L }
% 3.90/0.91 ord_less(int, pls, plus_plus(int, zero_zero(int), plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 1 (fact_73_Pls__def) R->L }
% 3.90/0.91 ord_less(int, pls, plus_plus(int, pls, plus_plus(int, one_one(int), semiring_1_of_nat(int, n))))
% 3.90/0.91 = { by axiom 5 (fact_76_add__Pls) }
% 3.90/0.91 ord_less(int, pls, plus_plus(int, one_one(int), semiring_1_of_nat(int, n)))
% 3.90/0.91 = { by axiom 1 (fact_73_Pls__def) }
% 3.90/0.91 ord_less(int, zero_zero(int), plus_plus(int, one_one(int), semiring_1_of_nat(int, n)))
% 3.90/0.91 = { by axiom 10 (fact_0_n1pos) }
% 3.90/0.91 true2
% 3.90/0.91
% 3.90/0.91 Goal 1 (fact_57_bin__less__0__simps_I1_J): ord_less(int, pls, zero_zero(int)) = true2.
% 3.90/0.91 Proof:
% 3.90/0.91 ord_less(int, pls, zero_zero(int))
% 3.90/0.91 = { by lemma 13 }
% 3.90/0.91 true2
% 3.90/0.91
% 3.90/0.91 Goal 2 (fact_32_rel__simps_I2_J): ord_less(int, pls, pls) = true2.
% 3.90/0.91 Proof:
% 3.90/0.91 ord_less(int, pls, pls)
% 3.90/0.91 = { by axiom 1 (fact_73_Pls__def) }
% 3.90/0.91 ord_less(int, pls, zero_zero(int))
% 3.90/0.91 = { by lemma 13 }
% 3.90/0.91 true2
% 3.90/0.91 % SZS output end Proof
% 3.90/0.91
% 3.90/0.91 RESULT: Theorem (the conjecture is true).
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