TSTP Solution File: SWV159+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 Sep 29 15:10:11 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.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 Sep 4 01:36:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(succ_type, type, (
% 0.21/0.44 succ: $i > $i)).
% 0.21/0.44 tff(tptp_minus_1_type, type, (
% 0.21/0.44 tptp_minus_1: $i)).
% 0.21/0.44 tff(sum_type, type, (
% 0.21/0.44 sum: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(a_select3_type, type, (
% 0.21/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_sum_index_type, type, (
% 0.21/0.44 tptp_sum_index: $i)).
% 0.21/0.44 tff(tptp_fun_C_13_type, type, (
% 0.21/0.44 tptp_fun_C_13: $i)).
% 0.21/0.44 tff(q_type, type, (
% 0.21/0.44 q: $i)).
% 0.21/0.44 tff(leq_type, type, (
% 0.21/0.44 leq: ( $i * $i ) > $o)).
% 0.21/0.44 tff(pred_type, type, (
% 0.21/0.44 pred: $i > $i)).
% 0.21/0.44 tff(pv10_type, type, (
% 0.21/0.44 pv10: $i)).
% 0.21/0.44 tff(n0_type, type, (
% 0.21/0.44 n0: $i)).
% 0.21/0.44 tff(n1_type, type, (
% 0.21/0.44 n1: $i)).
% 0.21/0.44 tff(n4_type, type, (
% 0.21/0.44 n4: $i)).
% 0.21/0.44 tff(divide_type, type, (
% 0.21/0.44 divide: ( $i * $i ) > $i)).
% 0.21/0.44 tff(times_type, type, (
% 0.21/0.44 times: ( $i * $i ) > $i)).
% 0.21/0.44 tff(a_select2_type, type, (
% 0.21/0.44 a_select2: ( $i * $i ) > $i)).
% 0.21/0.44 tff(sigma_type, type, (
% 0.21/0.44 sigma: $i)).
% 0.21/0.44 tff(sqrt_type, type, (
% 0.21/0.44 sqrt: $i > $i)).
% 0.21/0.44 tff(tptp_pi_type, type, (
% 0.21/0.44 tptp_pi: $i)).
% 0.21/0.44 tff(n2_type, type, (
% 0.21/0.44 n2: $i)).
% 0.21/0.44 tff(rho_type, type, (
% 0.21/0.44 rho: $i)).
% 0.21/0.44 tff(exp_type, type, (
% 0.21/0.44 exp: $i > $i)).
% 0.21/0.44 tff(tptp_minus_2_type, type, (
% 0.21/0.44 tptp_minus_2: $i)).
% 0.21/0.44 tff(minus_type, type, (
% 0.21/0.44 minus: ( $i * $i ) > $i)).
% 0.21/0.44 tff(mu_type, type, (
% 0.21/0.44 mu: $i)).
% 0.21/0.44 tff(x_type, type, (
% 0.21/0.44 x: $i)).
% 0.21/0.44 tff(pv47_type, type, (
% 0.21/0.44 pv47: $i)).
% 0.21/0.44 tff(n135299_type, type, (
% 0.21/0.44 n135299: $i)).
% 0.21/0.44 tff(pv84_type, type, (
% 0.21/0.44 pv84: $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 ((~((pv10 = C!13) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1))))) <=> (~((pv10 = C!13) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 ((~![C: $i] : ((pv10 = C) | (~(leq(succ(tptp_minus_1), C) & leq(C, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C, tptp_sum_index)) = succ(succ(tptp_minus_1))))) <=> (~![C: $i] : ((pv10 = C) | (~(leq(succ(tptp_minus_1), C) & leq(C, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C, tptp_sum_index)) = succ(succ(tptp_minus_1)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 ((~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))) <=> (~![C: $i] : ((pv10 = C) | (~(leq(succ(tptp_minus_1), C) & leq(C, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C, tptp_sum_index)) = succ(succ(tptp_minus_1)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 ((~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))) <=> (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 ((~((((((((pv84 = sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))) & leq(n0, pv10)) & leq(n0, pv47)) & leq(pv10, n135299)) & leq(pv47, n4)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv47))) => (a_select3(q, pv10, A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, A)), minus(a_select2(x, pv10), a_select2(mu, A))), tptp_minus_2), times(a_select2(sigma, A), a_select2(sigma, A)))), a_select2(rho, A)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, A))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))))) & ![B: $i] : ((leq(n0, B) & leq(B, pred(pv10))) => (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))) => ![C: $i] : ((leq(n0, C) & leq(C, pred(pv10))) => ((~(pv10 = C)) => (sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1))))) <=> (~((~((pv84 = sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))) & leq(n0, pv10) & leq(n0, pv47) & leq(pv10, n135299) & leq(pv47, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv47)))) | (a_select3(q, pv10, A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, A)), minus(a_select2(x, pv10), a_select2(mu, A))), tptp_minus_2), times(a_select2(sigma, A), a_select2(sigma, A)))), a_select2(rho, A)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, A))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))))) & ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))) | ![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(6,axiom,(~((((((((pv84 = sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))) & leq(n0, pv10)) & leq(n0, pv47)) & leq(pv10, n135299)) & leq(pv47, n4)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv47))) => (a_select3(q, pv10, A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, A)), minus(a_select2(x, pv10), a_select2(mu, A))), tptp_minus_2), times(a_select2(sigma, A), a_select2(sigma, A)))), a_select2(rho, A)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, A))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index)))))))) & ![B: $i] : ((leq(n0, B) & leq(B, pred(pv10))) => (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))) => ![C: $i] : ((leq(n0, C) & leq(C, pred(pv10))) => ((~(pv10 = C)) => (sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_norm_0009')).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (~((~((pv84 = sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))) & leq(n0, pv10) & leq(n0, pv47) & leq(pv10, n135299) & leq(pv47, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv47)))) | (a_select3(q, pv10, A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, A)), minus(a_select2(x, pv10), a_select2(mu, A))), tptp_minus_2), times(a_select2(sigma, A), a_select2(sigma, A)))), a_select2(rho, A)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, A))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))))) & ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))) | ![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.21/0.45 inference(or_elim,[status(thm)],[7])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (~![C: $i] : ((pv10 = C) | (~(leq(succ(tptp_minus_1), C) & leq(C, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (~![C: $i] : ((pv10 = C) | (~(leq(succ(tptp_minus_1), C) & leq(C, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (~![C: $i] : ((pv10 = C) | (~(leq(succ(tptp_minus_1), C) & leq(C, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (~![C: $i] : ((pv10 = C) | (~(leq(succ(tptp_minus_1), C) & leq(C, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.21/0.45 tff(16,plain,(
% 0.21/0.45 ~((pv10 = C!13) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[15])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (~((pv10 = C!13) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[16, 1])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (~(sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1)))),
% 0.21/0.45 inference(or_elim,[status(thm)],[17])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (leq(succ(tptp_minus_1), C!13) & leq(C!13, pred(pv10))),
% 0.21/0.45 inference(or_elim,[status(thm)],[17])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 (leq(C!13, pred(pv10))),
% 0.21/0.45 inference(and_elim,[status(thm)],[19])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 (leq(succ(tptp_minus_1), C!13)),
% 0.21/0.45 inference(and_elim,[status(thm)],[19])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (^[B: $i] : refl(((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))) <=> ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 (![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))) <=> ![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), B) & leq(B, pred(pv10))) <=> (~((~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))))), ((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) <=> (~(~((~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))))) <=> ((~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))), ((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) <=> ((~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))))), (((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> (((~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))))), rewrite((((~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))), (((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))) <=> ![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (^[B: $i] : rewrite(((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> ((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 ((pv84 = sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))) & leq(n0, pv10) & leq(n0, pv47) & leq(pv10, n135299) & leq(pv47, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv47)))) | (a_select3(q, pv10, A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, A)), minus(a_select2(x, pv10), a_select2(mu, A))), tptp_minus_2), times(a_select2(sigma, A), a_select2(sigma, A)))), a_select2(rho, A)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, A))), sum(n0, n4, divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index)), minus(a_select2(x, pv10), a_select2(mu, tptp_sum_index))), tptp_minus_2), times(a_select2(sigma, tptp_sum_index), a_select2(sigma, tptp_sum_index)))), a_select2(rho, tptp_sum_index)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, tptp_sum_index))))))) & ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(or_elim,[status(thm)],[7])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(and_elim,[status(thm)],[29])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.45 tff(33,plain,(
% 0.21/0.45 ![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, pred(pv10)))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[32])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[34, 23])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (((~![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))) | ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), C!13)) | (~leq(C!13, pred(pv10))))) <=> ((~![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), C!13)) | (~leq(C!13, pred(pv10))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 ((~![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))) | ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), C!13)) | (~leq(C!13, pred(pv10))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 ((~![B: $i] : ((sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, B, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(B, pred(pv10))))) | (sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), a_select3(q, C!13, tptp_sum_index)) = succ(succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), C!13)) | (~leq(C!13, pred(pv10)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[38, 35, 21, 20, 18])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------