TSTP Solution File: SWV164+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV164+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 15:10:12 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV164+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Sun Sep 4 01:02:39 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(gt_type, type, (
% 0.21/0.45 gt: ( $i * $i ) > $o)).
% 0.21/0.45 tff(succ_type, type, (
% 0.21/0.45 succ: $i > $i)).
% 0.21/0.45 tff(tptp_minus_1_type, type, (
% 0.21/0.45 tptp_minus_1: $i)).
% 0.21/0.45 tff(leq_type, type, (
% 0.21/0.45 leq: ( $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_B_13_type, type, (
% 0.21/0.45 tptp_fun_B_13: $i)).
% 0.21/0.45 tff(divide_type, type, (
% 0.21/0.45 divide: ( $i * $i ) > $i)).
% 0.21/0.45 tff(sum_type, type, (
% 0.21/0.45 sum: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(times_type, type, (
% 0.21/0.45 times: ( $i * $i ) > $i)).
% 0.21/0.45 tff(a_select2_type, type, (
% 0.21/0.45 a_select2: ( $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_sum_index_type, type, (
% 0.21/0.45 tptp_sum_index: $i)).
% 0.21/0.45 tff(sigma_type, type, (
% 0.21/0.45 sigma: $i)).
% 0.21/0.45 tff(sqrt_type, type, (
% 0.21/0.45 sqrt: $i > $i)).
% 0.21/0.45 tff(tptp_pi_type, type, (
% 0.21/0.45 tptp_pi: $i)).
% 0.21/0.45 tff(rho_type, type, (
% 0.21/0.45 rho: $i)).
% 0.21/0.45 tff(exp_type, type, (
% 0.21/0.45 exp: $i > $i)).
% 0.21/0.45 tff(tptp_minus_2_type, type, (
% 0.21/0.45 tptp_minus_2: $i)).
% 0.21/0.45 tff(minus_type, type, (
% 0.21/0.45 minus: ( $i * $i ) > $i)).
% 0.21/0.45 tff(mu_type, type, (
% 0.21/0.45 mu: $i)).
% 0.21/0.45 tff(pv10_type, type, (
% 0.21/0.45 pv10: $i)).
% 0.21/0.45 tff(x_type, type, (
% 0.21/0.45 x: $i)).
% 0.21/0.45 tff(a_select3_type, type, (
% 0.21/0.45 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(q_type, type, (
% 0.21/0.45 q: $i)).
% 0.21/0.45 tff(n2_type, type, (
% 0.21/0.45 n2: $i)).
% 0.21/0.45 tff(n4_type, type, (
% 0.21/0.45 n4: $i)).
% 0.21/0.45 tff(n0_type, type, (
% 0.21/0.45 n0: $i)).
% 0.21/0.45 tff(n1_type, type, (
% 0.21/0.45 n1: $i)).
% 0.21/0.45 tff(pred_type, type, (
% 0.21/0.45 pred: $i > $i)).
% 0.21/0.45 tff(n135299_type, type, (
% 0.21/0.45 n135299: $i)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(4,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.45 tff(6,plain,(
% 0.21/0.45 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.21/0.45 inference(skolemize,[status(sab)],[5])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 ((~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index)))))))) <=> (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 ((~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 ((~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 ((~(((leq(n0, pv10) & leq(pv10, n135299)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv10))) => (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))) => ![B: $i] : ((leq(n0, B) & leq(B, tptp_minus_1)) => (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(14,axiom,(~(((leq(n0, pv10) & leq(pv10, n135299)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv10))) => (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))) => ![B: $i] : ((leq(n0, B) & leq(B, tptp_minus_1)) => (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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/sandbox/benchmark/theBenchmark.p','cl5_nebula_norm_0014')).
% 0.21/0.46 tff(15,plain,
% 0.21/0.46 (~((~(leq(n0, pv10) & leq(pv10, n135299) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)))) | ![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.46 tff(16,plain,
% 0.21/0.46 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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)))))))),
% 0.21/0.46 inference(or_elim,[status(thm)],[15])).
% 0.21/0.46 tff(17,plain,
% 0.21/0.46 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (~![B: $i] : ((~(leq(n0, B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(n2, tptp_pi)), a_select2(sigma, B))), 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)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 (~![B: $i] : ((~(leq(succ(tptp_minus_1), B) & leq(B, tptp_minus_1))) | (a_select3(q, pv10, B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B)), minus(a_select2(x, pv10), a_select2(mu, B))), tptp_minus_2), times(a_select2(sigma, B), a_select2(sigma, B)))), a_select2(rho, B)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[22, 10])).
% 0.21/0.48 tff(24,plain,(
% 0.21/0.48 ~((~(leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1))) | (a_select3(q, pv10, B!13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x, pv10), a_select2(mu, B!13)), minus(a_select2(x, pv10), a_select2(mu, B!13))), tptp_minus_2), times(a_select2(sigma, B!13), a_select2(sigma, B!13)))), a_select2(rho, B!13)), times(sqrt(times(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, B!13))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), 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(succ(succ(succ(tptp_minus_1))), tptp_pi)), a_select2(sigma, tptp_sum_index)))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[23])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 (leq(succ(tptp_minus_1), B!13) & leq(B!13, tptp_minus_1)),
% 0.21/0.48 inference(or_elim,[status(thm)],[24])).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 (leq(B!13, tptp_minus_1)),
% 0.21/0.48 inference(and_elim,[status(thm)],[25])).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 (leq(succ(tptp_minus_1), B!13)),
% 0.21/0.48 inference(and_elim,[status(thm)],[25])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(30,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.48 tff(31,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(32,plain,
% 0.21/0.48 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.48 tff(34,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.21/0.48 tff(35,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.48 tff(37,plain,(
% 0.21/0.48 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.21/0.48 inference(skolemize,[status(sab)],[36])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 ((leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13))) <=> ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1)) | (~leq(succ(tptp_minus_1), B!13)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(45,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), B!13)) | leq(succ(tptp_minus_1), tptp_minus_1) | (~leq(B!13, tptp_minus_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.48 tff(46,plain,
% 0.21/0.48 (leq(succ(tptp_minus_1), tptp_minus_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[45, 39, 27, 26])).
% 0.21/0.48 tff(47,plain,
% 0.21/0.48 ((~(leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))) | (~leq(succ(tptp_minus_1), tptp_minus_1)) | gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(48,plain,
% 0.21/0.48 ((~(leq(succ(tptp_minus_1), tptp_minus_1) <=> gt(succ(tptp_minus_1), succ(tptp_minus_1)))) | gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.48 tff(49,plain,
% 0.21/0.48 (gt(succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[48, 9])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(53,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (![X: $i] : (~gt(X, X))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.49 tff(55,plain,(
% 0.21/0.49 ![X: $i] : (~gt(X, X))),
% 0.21/0.49 inference(skolemize,[status(sab)],[54])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (![X: $i] : (~gt(X, X))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 ((~![X: $i] : (~gt(X, X))) | (~gt(succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[57, 56, 49])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------