TSTP Solution File: NUM924+6 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% 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 : 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 : Thu Aug 31 11:58:56 EDT 2023
% Result : Theorem 29.88s 4.23s
% Output : Proof 29.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM924+6 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 11:03:28 EDT 2023
% 0.13/0.33 % CPUTime :
% 29.88/4.23 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 29.88/4.23
% 29.88/4.23 % SZS status Theorem
% 29.88/4.23
% 29.88/4.24 % SZS output start Proof
% 29.88/4.24 Take the following subset of the input axioms:
% 29.88/4.24 fof(conj_0, conjecture, ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), zero_zero(int))).
% 29.88/4.24 fof(fact_120_Pls__def, axiom, pls=zero_zero(int)).
% 29.88/4.24 fof(fact_22_number__of__is__id, axiom, ![K]: number_number_of(int, K)=ti(int, K)).
% 29.88/4.24 fof(fact_23_zmult__commute, axiom, ![W, Z]: times_times(int, Z, W)=times_times(int, W, Z)).
% 29.88/4.24 fof(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096, axiom, ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int)))).
% 29.88/4.24 fof(fact_3_t, axiom, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int))=times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t)).
% 29.88/4.24 fof(fact_62_mult__Pls, axiom, ![W2]: times_times(int, pls, W2)=pls).
% 29.88/4.24 fof(fact_96_zadd__commute, axiom, ![Z2, W2]: plus_plus(int, Z2, W2)=plus_plus(int, W2, Z2)).
% 29.88/4.24 fof(tsy_c_Int_OBit0_res, hypothesis, ![B_1_1]: ti(int, bit0(B_1_1))=bit0(B_1_1)).
% 29.88/4.24
% 29.88/4.24 Now clausify the problem and encode Horn clauses using encoding 3 of
% 29.88/4.24 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 29.88/4.24 We repeatedly replace C & s=t => u=v by the two clauses:
% 29.88/4.24 fresh(y, y, x1...xn) = u
% 29.88/4.24 C => fresh(s, t, x1...xn) = v
% 29.88/4.24 where fresh is a fresh function symbol and x1..xn are the free
% 29.88/4.24 variables of u and v.
% 29.88/4.24 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 29.88/4.24 input problem has no model of domain size 1).
% 29.88/4.24
% 29.88/4.24 The encoding turns the above axioms into the following unit equations and goals:
% 29.88/4.24
% 29.88/4.24 Axiom 1 (fact_120_Pls__def): pls = zero_zero(int).
% 29.88/4.24 Axiom 2 (fact_22_number__of__is__id): number_number_of(int, X) = ti(int, X).
% 29.88/4.24 Axiom 3 (fact_23_zmult__commute): times_times(int, X, Y) = times_times(int, Y, X).
% 29.88/4.24 Axiom 4 (fact_62_mult__Pls): times_times(int, pls, X) = pls.
% 29.88/4.24 Axiom 5 (fact_96_zadd__commute): plus_plus(int, X, Y) = plus_plus(int, Y, X).
% 29.88/4.24 Axiom 6 (tsy_c_Int_OBit0_res): ti(int, bit0(X)) = bit0(X).
% 29.88/4.24 Axiom 7 (fact_3_t): plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)) = times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t).
% 29.88/4.24 Axiom 8 (fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096): ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int))) = true2.
% 29.88/4.24
% 29.88/4.24 Lemma 9: number_number_of(int, bit0(X)) = bit0(X).
% 29.88/4.24 Proof:
% 29.88/4.24 number_number_of(int, bit0(X))
% 29.88/4.24 = { by axiom 2 (fact_22_number__of__is__id) }
% 29.88/4.24 ti(int, bit0(X))
% 29.88/4.24 = { by axiom 6 (tsy_c_Int_OBit0_res) }
% 29.88/4.24 bit0(X)
% 29.88/4.24
% 29.88/4.24 Goal 1 (conj_0): ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), zero_zero(int)) = true2.
% 29.88/4.24 Proof:
% 29.88/4.24 ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), zero_zero(int))
% 29.88/4.24 = { by axiom 1 (fact_120_Pls__def) R->L }
% 29.88/4.24 ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), pls)
% 29.88/4.24 = { by axiom 4 (fact_62_mult__Pls) R->L }
% 29.88/4.24 ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), times_times(int, pls, plus_plus(int, one_one(int), times_times(int, m, bit0(bit0(bit1(pls)))))))
% 29.88/4.24 = { by axiom 3 (fact_23_zmult__commute) R->L }
% 29.88/4.24 ord_less(int, plus_plus(int, power_power(int, s, number_number_of(nat, bit0(bit1(pls)))), one_one(int)), times_times(int, plus_plus(int, one_one(int), times_times(int, m, bit0(bit0(bit1(pls))))), pls))
% 29.88/4.24 = { by axiom 7 (fact_3_t) }
% 29.88/4.24 ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, one_one(int), times_times(int, m, bit0(bit0(bit1(pls))))), pls))
% 29.88/4.24 = { by lemma 9 }
% 29.88/4.24 ord_less(int, times_times(int, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int)), t), times_times(int, plus_plus(int, one_one(int), times_times(int, m, bit0(bit0(bit1(pls))))), pls))
% 29.88/4.24 = { by axiom 3 (fact_23_zmult__commute) }
% 29.88/4.24 ord_less(int, times_times(int, t, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int))), times_times(int, plus_plus(int, one_one(int), times_times(int, m, bit0(bit0(bit1(pls))))), pls))
% 29.88/4.24 = { by axiom 5 (fact_96_zadd__commute) }
% 29.88/4.24 ord_less(int, times_times(int, t, plus_plus(int, one_one(int), times_times(int, bit0(bit0(bit1(pls))), m))), times_times(int, plus_plus(int, one_one(int), times_times(int, m, bit0(bit0(bit1(pls))))), pls))
% 29.88/4.24 = { by axiom 3 (fact_23_zmult__commute) R->L }
% 29.88/4.25 ord_less(int, times_times(int, t, plus_plus(int, one_one(int), times_times(int, bit0(bit0(bit1(pls))), m))), times_times(int, plus_plus(int, one_one(int), times_times(int, bit0(bit0(bit1(pls))), m)), pls))
% 29.88/4.25 = { by axiom 5 (fact_96_zadd__commute) R->L }
% 29.88/4.25 ord_less(int, times_times(int, t, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int))), times_times(int, plus_plus(int, one_one(int), times_times(int, bit0(bit0(bit1(pls))), m)), pls))
% 29.88/4.25 = { by axiom 5 (fact_96_zadd__commute) R->L }
% 29.88/4.25 ord_less(int, times_times(int, t, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int))), times_times(int, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int)), pls))
% 29.88/4.25 = { by axiom 3 (fact_23_zmult__commute) R->L }
% 29.88/4.25 ord_less(int, times_times(int, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int)), pls))
% 29.88/4.25 = { by axiom 1 (fact_120_Pls__def) }
% 29.88/4.25 ord_less(int, times_times(int, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int)), zero_zero(int)))
% 29.88/4.25 = { by lemma 9 R->L }
% 29.88/4.25 ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, bit0(bit0(bit1(pls))), m), one_one(int)), zero_zero(int)))
% 29.88/4.25 = { by lemma 9 R->L }
% 29.88/4.25 ord_less(int, times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), t), times_times(int, plus_plus(int, times_times(int, number_number_of(int, bit0(bit0(bit1(pls)))), m), one_one(int)), zero_zero(int)))
% 29.88/4.25 = { by axiom 8 (fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) }
% 29.88/4.25 true2
% 29.88/4.25 % SZS output end Proof
% 29.88/4.25
% 29.88/4.25 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------