%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV157+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:31:37 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV157+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:30:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(gt_type, type, (
% 0.20/0.43 gt: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_C_13_type, type, (
% 0.20/0.43 tptp_fun_C_13: $i)).
% 0.20/0.43 tff(pv47_type, type, (
% 0.20/0.43 pv47: $i)).
% 0.20/0.43 tff(leq_type, type, (
% 0.20/0.43 leq: ( $i * $i ) > $o)).
% 0.20/0.43 tff(pred_type, type, (
% 0.20/0.43 pred: $i > $i)).
% 0.20/0.43 tff(n0_type, type, (
% 0.20/0.43 n0: $i)).
% 0.20/0.43 tff(divide_type, type, (
% 0.20/0.43 divide: ( $i * $i ) > $i)).
% 0.20/0.43 tff(sum_type, type, (
% 0.20/0.43 sum: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(times_type, type, (
% 0.20/0.43 times: ( $i * $i ) > $i)).
% 0.20/0.43 tff(a_select2_type, type, (
% 0.20/0.43 a_select2: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_sum_index_type, type, (
% 0.20/0.43 tptp_sum_index: $i)).
% 0.20/0.43 tff(sigma_type, type, (
% 0.20/0.43 sigma: $i)).
% 0.20/0.43 tff(sqrt_type, type, (
% 0.20/0.43 sqrt: $i > $i)).
% 0.20/0.43 tff(tptp_pi_type, type, (
% 0.20/0.43 tptp_pi: $i)).
% 0.20/0.43 tff(n2_type, type, (
% 0.20/0.43 n2: $i)).
% 0.20/0.43 tff(rho_type, type, (
% 0.20/0.43 rho: $i)).
% 0.20/0.43 tff(exp_type, type, (
% 0.20/0.43 exp: $i > $i)).
% 0.20/0.43 tff(tptp_minus_2_type, type, (
% 0.20/0.43 tptp_minus_2: $i)).
% 0.20/0.43 tff(minus_type, type, (
% 0.20/0.43 minus: ( $i * $i ) > $i)).
% 0.20/0.43 tff(mu_type, type, (
% 0.20/0.43 mu: $i)).
% 0.20/0.43 tff(pv10_type, type, (
% 0.20/0.43 pv10: $i)).
% 0.20/0.43 tff(x_type, type, (
% 0.20/0.43 x: $i)).
% 0.20/0.43 tff(n4_type, type, (
% 0.20/0.43 n4: $i)).
% 0.20/0.43 tff(a_select3_type, type, (
% 0.20/0.43 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(q_type, type, (
% 0.20/0.43 q: $i)).
% 0.20/0.43 tff(n1_type, type, (
% 0.20/0.43 n1: $i)).
% 0.20/0.43 tff(n135299_type, type, (
% 0.20/0.43 n135299: $i)).
% 0.20/0.43 tff(pv84_type, type, (
% 0.20/0.43 pv84: $i)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(4,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.43 tff(6,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(C!13, pred(pv47)) <=> gt(pv47, C!13))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (leq(C!13, pred(pv47)) <=> gt(pv47, C!13)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 ((C!13 = pv47) <=> (pv47 = C!13)),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 ((pv47 = C!13) <=> (C!13 = pv47)),
% 0.20/0.43 inference(symmetry,[status(thm)],[10])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 ((~(pv47 = C!13)) <=> (~(C!13 = pv47))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[11])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 ((~((a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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)))))) | (pv47 = C!13) | (~(leq(n0, C!13) & leq(C!13, pv47))))) <=> (~((a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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)))))) | (pv47 = C!13) | (~(leq(n0, C!13) & leq(C!13, pv47)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 ((~![C: $i] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47))))) <=> (~![C: $i] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ((~((((((((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, pv47)) => ((~(pv47 = C)) => (a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))))))) <=> (~((~((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] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(16,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, pv47)) => ((~(pv47 = C)) => (a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_norm_0007')).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (~((~((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] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (~![C: $i] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47))))),
% 0.20/0.44 inference(or_elim,[status(thm)],[17])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (~![C: $i] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (~![C: $i] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (~![C: $i] : ((a_select3(q, pv10, C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C)), minus(a_select2(x, pv10), a_select2(mu, C))), tptp_minus_2), times(a_select2(sigma, C), a_select2(sigma, C)))), a_select2(rho, C)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C))), 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)))))) | (pv47 = C) | (~(leq(n0, C) & leq(C, pv47))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.20/0.44 tff(22,plain,(
% 0.20/0.44 ~((a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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)))))) | (pv47 = C!13) | (~(leq(n0, C!13) & leq(C!13, pv47))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[21])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (~((a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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)))))) | (pv47 = C!13) | (~(leq(n0, C!13) & leq(C!13, pv47))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (~(pv47 = C!13)),
% 0.20/0.44 inference(or_elim,[status(thm)],[23])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (~(C!13 = pv47)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 12])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (leq(n0, C!13) & leq(C!13, pv47)),
% 0.20/0.44 inference(or_elim,[status(thm)],[23])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (leq(C!13, pv47)),
% 0.20/0.44 inference(and_elim,[status(thm)],[26])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & (~(X = Y))) <=> (~((~leq(X, Y)) | (X = Y)))), ((~(leq(X, Y) & (~(X = Y)))) <=> (~(~((~leq(X, Y)) | (X = Y)))))), rewrite((~(~((~leq(X, Y)) | (X = Y)))) <=> ((~leq(X, Y)) | (X = Y))), ((~(leq(X, Y) & (~(X = Y)))) <=> ((~leq(X, Y)) | (X = Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> (((~leq(X, Y)) | (X = Y)) | gt(Y, X)))), rewrite((((~leq(X, Y)) | (X = Y)) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.45 tff(35,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.45 tff(38,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.20/0.45 inference(skolemize,[status(sab)],[37])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((C!13 = pv47) | gt(pv47, C!13) | (~leq(C!13, pv47)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (C!13 = pv47) | gt(pv47, C!13) | (~leq(C!13, pv47)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((C!13 = pv47) | gt(pv47, C!13) | (~leq(C!13, pv47)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (C!13 = pv47) | gt(pv47, C!13) | (~leq(C!13, pv47))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 ((C!13 = pv47) | gt(pv47, C!13)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[43, 40, 27])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (gt(pv47, C!13)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[44, 25])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (leq(n0, C!13)),
% 0.20/0.45 inference(and_elim,[status(thm)],[26])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (~(a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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))))))),
% 0.20/0.45 inference(or_elim,[status(thm)],[23])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (^[A: $i] : refl(((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)))))) | (~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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47)))) <=> ![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, A) & leq(A, pred(pv47))) <=> (~((~leq(n0, A)) | (~leq(A, pred(pv47)))))), ((~(leq(n0, A) & leq(A, pred(pv47)))) <=> (~(~((~leq(n0, A)) | (~leq(A, pred(pv47)))))))), rewrite((~(~((~leq(n0, A)) | (~leq(A, pred(pv47)))))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv47))))), ((~(leq(n0, A) & leq(A, pred(pv47)))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv47)))))), (((~(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))))))) <=> (((~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))))))))), rewrite((((~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))))))) <=> ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))), (((~(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))))))) <=> ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (![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))))))) <=> ![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (![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))))))) <=> ![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)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 ((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))),
% 0.20/0.46 inference(or_elim,[status(thm)],[17])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(and_elim,[status(thm)],[53])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (![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)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.20/0.46 tff(56,plain,(
% 0.20/0.46 ![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)))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[55])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[57, 49])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (((~![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))) | ((a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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, C!13)) | (~leq(C!13, pred(pv47))))) <=> ((~![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))) | (a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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, C!13)) | (~leq(C!13, pred(pv47))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 ((~![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))) | ((a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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, C!13)) | (~leq(C!13, pred(pv47))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 ((~![A: $i] : ((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)))))) | (~leq(n0, A)) | (~leq(A, pred(pv47))))) | (a_select3(q, pv10, C!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, C!13)), minus(a_select2(x, pv10), a_select2(mu, C!13))), tptp_minus_2), times(a_select2(sigma, C!13), a_select2(sigma, C!13)))), a_select2(rho, C!13)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, C!13))), 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, C!13)) | (~leq(C!13, pred(pv47)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (~leq(C!13, pred(pv47))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[61, 58, 47, 46])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 ((~(leq(C!13, pred(pv47)) <=> gt(pv47, C!13))) | leq(C!13, pred(pv47)) | (~gt(pv47, C!13))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 ((~(leq(C!13, pred(pv47)) <=> gt(pv47, C!13))) | (~gt(pv47, C!13))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[64, 45, 9])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------