TSTP Solution File: SWV154+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV154+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 15:10:10 EDT 2022
% Result : Theorem 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWV154+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Sep 4 01:39:33 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.17/0.39 % SZS status Theorem
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 tff(divide_type, type, (
% 0.17/0.39 divide: ( $i * $i ) > $i)).
% 0.17/0.39 tff(sum_type, type, (
% 0.17/0.39 sum: ( $i * $i * $i ) > $i)).
% 0.17/0.39 tff(sqrt_type, type, (
% 0.17/0.39 sqrt: $i > $i)).
% 0.17/0.39 tff(times_type, type, (
% 0.17/0.39 times: ( $i * $i ) > $i)).
% 0.17/0.39 tff(minus_type, type, (
% 0.17/0.39 minus: ( $i * $i ) > $i)).
% 0.17/0.39 tff(a_select2_type, type, (
% 0.17/0.39 a_select2: ( $i * $i ) > $i)).
% 0.17/0.39 tff(pv10_type, type, (
% 0.17/0.39 pv10: $i)).
% 0.17/0.39 tff(x_type, type, (
% 0.17/0.39 x: $i)).
% 0.17/0.39 tff(a_select3_type, type, (
% 0.17/0.39 a_select3: ( $i * $i * $i ) > $i)).
% 0.17/0.39 tff(succ_type, type, (
% 0.17/0.39 succ: $i > $i)).
% 0.17/0.39 tff(tptp_minus_1_type, type, (
% 0.17/0.39 tptp_minus_1: $i)).
% 0.17/0.39 tff(tptp_sum_index_type, type, (
% 0.17/0.39 tptp_sum_index: $i)).
% 0.17/0.39 tff(center_type, type, (
% 0.17/0.39 center: $i)).
% 0.17/0.39 tff(tptp_fun_C_13_type, type, (
% 0.17/0.39 tptp_fun_C_13: $i)).
% 0.17/0.39 tff(pv12_type, type, (
% 0.17/0.39 pv12: $i)).
% 0.17/0.39 tff(leq_type, type, (
% 0.17/0.39 leq: ( $i * $i ) > $o)).
% 0.17/0.39 tff(n0_type, type, (
% 0.17/0.39 n0: $i)).
% 0.17/0.39 tff(n4_type, type, (
% 0.17/0.39 n4: $i)).
% 0.17/0.39 tff(pv70_type, type, (
% 0.17/0.39 pv70: $i)).
% 0.17/0.39 tff(n1_type, type, (
% 0.17/0.39 n1: $i)).
% 0.17/0.39 tff(q_type, type, (
% 0.17/0.39 q: $i)).
% 0.17/0.39 tff(pred_type, type, (
% 0.17/0.39 pred: $i > $i)).
% 0.17/0.39 tff(n135299_type, type, (
% 0.17/0.39 n135299: $i)).
% 0.17/0.39 tff(1,plain,
% 0.17/0.39 ((~((~(pv12 = C!13)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pv12))))) <=> (~((~(pv12 = C!13)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pv12)))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(2,plain,
% 0.17/0.39 ((~![C: $i] : ((~(pv12 = C)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C) & leq(C, pv12))))) <=> (~![C: $i] : ((~(pv12 = C)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C) & leq(C, pv12)))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(3,plain,
% 0.17/0.40 ((~![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12))))) <=> (~![C: $i] : ((~(pv12 = C)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C) & leq(C, pv12)))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(4,plain,
% 0.17/0.40 ((~![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12))))) <=> (~![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12)))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(5,plain,
% 0.17/0.40 ((~((((((((pv70 = sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)))))) & leq(n0, pv10)) & leq(n0, pv12)) & leq(pv10, n135299)) & leq(pv12, n4)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv12))) => (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))))) & ![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, pv12)) => ((pv12 = C) => (divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))))))) <=> (~((~((pv70 = sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, n135299) & leq(pv12, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv12)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)))))))) & ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))) | ![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12))))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(6,axiom,(~((((((((pv70 = sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)))))) & leq(n0, pv10)) & leq(n0, pv12)) & leq(pv10, n135299)) & leq(pv12, n4)) & ![A: $i] : ((leq(n0, A) & leq(A, pred(pv12))) => (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))))) & ![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, pv12)) => ((pv12 = C) => (divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cl5_nebula_norm_0004')).
% 0.17/0.40 tff(7,plain,
% 0.17/0.40 (~((~((pv70 = sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)))))) & leq(n0, pv10) & leq(n0, pv12) & leq(pv10, n135299) & leq(pv12, n4) & ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv12)))) | (a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)))))))) & ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))) | ![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.17/0.40 tff(8,plain,
% 0.17/0.40 (~![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12))))),
% 0.17/0.40 inference(or_elim,[status(thm)],[7])).
% 0.17/0.40 tff(9,plain,
% 0.17/0.40 (~![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.17/0.40 tff(10,plain,
% 0.17/0.40 (~![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.17/0.40 tff(11,plain,
% 0.17/0.40 (~![C: $i] : ((divide(sqrt(times(minus(a_select3(center, pv12, n0), a_select2(x, pv10)), minus(a_select3(center, pv12, n0), a_select2(x, pv10)))), pv70) = divide(sqrt(times(minus(a_select3(center, C, n0), a_select2(x, pv10)), minus(a_select3(center, C, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~(pv12 = C)) | (~(leq(n0, C) & leq(C, pv12))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.17/0.40 tff(12,plain,
% 0.17/0.40 (~![C: $i] : ((~(pv12 = C)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C) & leq(C, pv12))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.17/0.40 tff(13,plain,
% 0.17/0.40 (~![C: $i] : ((~(pv12 = C)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C) & leq(C, pv12))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.17/0.41 tff(14,plain,
% 0.17/0.41 (~![C: $i] : ((~(pv12 = C)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C) & leq(C, pv12))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.17/0.41 tff(15,plain,
% 0.17/0.41 (~![C: $i] : ((~(pv12 = C)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C) & leq(C, pv12))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.17/0.41 tff(16,plain,(
% 0.17/0.41 ~((~(pv12 = C!13)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pv12))))),
% 0.17/0.41 inference(skolemize,[status(sab)],[15])).
% 0.17/0.41 tff(17,plain,
% 0.17/0.41 (~((~(pv12 = C!13)) | (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))) | (~(leq(succ(tptp_minus_1), C!13) & leq(C!13, pv12))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[16, 1])).
% 0.17/0.41 tff(18,plain,
% 0.17/0.41 (pv12 = C!13),
% 0.17/0.41 inference(or_elim,[status(thm)],[17])).
% 0.17/0.41 tff(19,plain,
% 0.17/0.41 (a_select3(center, pv12, succ(tptp_minus_1)) = a_select3(center, C!13, succ(tptp_minus_1))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.17/0.41 tff(20,plain,
% 0.17/0.41 (minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)) = minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[19])).
% 0.17/0.41 tff(21,plain,
% 0.17/0.41 (times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10))) = times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[20, 20])).
% 0.17/0.41 tff(22,plain,
% 0.17/0.41 (sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))) = sqrt(times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10))))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[21])).
% 0.17/0.41 tff(23,plain,
% 0.17/0.41 (divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10))))))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[22])).
% 0.17/0.41 tff(24,plain,
% 0.17/0.41 (~(divide(sqrt(times(minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, pv12, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))) = divide(sqrt(times(minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, C!13, succ(tptp_minus_1)), a_select2(x, pv10)))), sum(succ(tptp_minus_1), succ(succ(succ(succ(succ(tptp_minus_1))))), sqrt(times(minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, succ(tptp_minus_1)), a_select2(x, pv10)))))))),
% 0.17/0.41 inference(or_elim,[status(thm)],[17])).
% 0.17/0.41 tff(25,plain,
% 0.17/0.41 ($false),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.17/0.41 % SZS output end Proof
%------------------------------------------------------------------------------