%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV153+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:31:36 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV153+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 09:30:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(gt_type, type, (
% 0.19/0.42 gt: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_C_13_type, type, (
% 0.19/0.42 tptp_fun_C_13: $i)).
% 0.19/0.42 tff(pv12_type, type, (
% 0.19/0.42 pv12: $i)).
% 0.19/0.42 tff(leq_type, type, (
% 0.19/0.42 leq: ( $i * $i ) > $o)).
% 0.19/0.42 tff(pred_type, type, (
% 0.19/0.42 pred: $i > $i)).
% 0.19/0.42 tff(n0_type, type, (
% 0.19/0.42 n0: $i)).
% 0.19/0.42 tff(divide_type, type, (
% 0.19/0.42 divide: ( $i * $i ) > $i)).
% 0.19/0.42 tff(sum_type, type, (
% 0.19/0.42 sum: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(sqrt_type, type, (
% 0.19/0.42 sqrt: $i > $i)).
% 0.19/0.42 tff(times_type, type, (
% 0.19/0.42 times: ( $i * $i ) > $i)).
% 0.19/0.42 tff(minus_type, type, (
% 0.19/0.42 minus: ( $i * $i ) > $i)).
% 0.19/0.42 tff(a_select2_type, type, (
% 0.19/0.42 a_select2: ( $i * $i ) > $i)).
% 0.19/0.42 tff(pv10_type, type, (
% 0.19/0.42 pv10: $i)).
% 0.19/0.42 tff(x_type, type, (
% 0.19/0.42 x: $i)).
% 0.19/0.42 tff(a_select3_type, type, (
% 0.19/0.42 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_sum_index_type, type, (
% 0.19/0.42 tptp_sum_index: $i)).
% 0.19/0.42 tff(center_type, type, (
% 0.19/0.42 center: $i)).
% 0.19/0.42 tff(n4_type, type, (
% 0.19/0.42 n4: $i)).
% 0.19/0.42 tff(q_type, type, (
% 0.19/0.42 q: $i)).
% 0.19/0.42 tff(n1_type, type, (
% 0.19/0.42 n1: $i)).
% 0.19/0.42 tff(n135299_type, type, (
% 0.19/0.42 n135299: $i)).
% 0.19/0.42 tff(pv70_type, type, (
% 0.19/0.42 pv70: $i)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(4,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.42 tff(6,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[5])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(C!13, pred(pv12)) <=> gt(pv12, C!13))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (leq(C!13, pred(pv12)) <=> gt(pv12, C!13)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 ((C!13 = pv12) <=> (pv12 = C!13)),
% 0.19/0.42 inference(commutativity,[status(thm)],[])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 ((pv12 = C!13) <=> (C!13 = pv12)),
% 0.19/0.42 inference(symmetry,[status(thm)],[10])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 ((~(pv12 = C!13)) <=> (~(C!13 = pv12))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 ((~((a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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!13) | (~(leq(n0, C!13) & leq(C!13, pv12))))) <=> (~((a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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!13) | (~(leq(n0, C!13) & leq(C!13, pv12)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 ((~![C: $i] : ((a_select3(q, pv10, C) = 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] : ((a_select3(q, pv10, C) = 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)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 ((~((((((((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)) => (a_select3(q, pv10, C) = 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] : ((a_select3(q, pv10, C) = 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))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(16,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)) => (a_select3(q, pv10, C) = 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_0003')).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (~((~((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] : ((a_select3(q, pv10, C) = 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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (~![C: $i] : ((a_select3(q, pv10, C) = 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))))),
% 0.19/0.43 inference(or_elim,[status(thm)],[17])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (~![C: $i] : ((a_select3(q, pv10, C) = 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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (~![C: $i] : ((a_select3(q, pv10, C) = 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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (~![C: $i] : ((a_select3(q, pv10, C) = 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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.43 tff(22,plain,(
% 0.19/0.43 ~((a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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!13) | (~(leq(n0, C!13) & leq(C!13, pv12))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (~((a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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!13) | (~(leq(n0, C!13) & leq(C!13, pv12))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (~(pv12 = C!13)),
% 0.19/0.43 inference(or_elim,[status(thm)],[23])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (~(C!13 = pv12)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[24, 12])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (leq(n0, C!13) & leq(C!13, pv12)),
% 0.19/0.43 inference(or_elim,[status(thm)],[23])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (leq(C!13, pv12)),
% 0.19/0.43 inference(and_elim,[status(thm)],[26])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.43 tff(35,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.43 tff(38,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.19/0.43 inference(skolemize,[status(sab)],[37])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((C!13 = pv12) | gt(pv12, C!13) | (~leq(C!13, pv12)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (C!13 = pv12) | gt(pv12, C!13) | (~leq(C!13, pv12)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((C!13 = pv12) | gt(pv12, C!13) | (~leq(C!13, pv12)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (C!13 = pv12) | gt(pv12, C!13) | (~leq(C!13, pv12))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 ((C!13 = pv12) | gt(pv12, C!13)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[43, 40, 27])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (gt(pv12, C!13)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[44, 25])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (leq(n0, C!13)),
% 0.19/0.43 inference(and_elim,[status(thm)],[26])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (~(a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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)))))))),
% 0.19/0.43 inference(or_elim,[status(thm)],[23])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (^[A: $i] : refl(((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))))))) | (~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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12)))) <=> ![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, A) & leq(A, pred(pv12))) <=> (~((~leq(n0, A)) | (~leq(A, pred(pv12)))))), ((~(leq(n0, A) & leq(A, pred(pv12)))) <=> (~(~((~leq(n0, A)) | (~leq(A, pred(pv12)))))))), rewrite((~(~((~leq(n0, A)) | (~leq(A, pred(pv12)))))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv12))))), ((~(leq(n0, A) & leq(A, pred(pv12)))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv12)))))), (((~(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)))))))) <=> (((~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)))))))))), rewrite((((~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)))))))) <=> ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))), (((~(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)))))))) <=> ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![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)))))))) <=> ![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (![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)))))))) <=> ![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))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 ((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))),
% 0.19/0.44 inference(or_elim,[status(thm)],[17])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(and_elim,[status(thm)],[53])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.19/0.44 tff(56,plain,(
% 0.19/0.44 ![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))))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[55])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[57, 49])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (((~![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))) | ((a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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))))))) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv12))))) <=> ((~![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))) | (a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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))))))) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv12))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 ((~![A: $i] : ((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))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))) | ((a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, 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))))))) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv12))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 ((~![A: $i] : ((a_select3(q, pv10, A) = divide(sqrt(times(minus(a_select3(center, A, n0), a_select2(x, pv10)), minus(a_select3(center, A, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~leq(n0, A)) | (~leq(A, pred(pv12))))) | (a_select3(q, pv10, C!13) = divide(sqrt(times(minus(a_select3(center, C!13, n0), a_select2(x, pv10)), minus(a_select3(center, C!13, n0), a_select2(x, pv10)))), sum(n0, n4, sqrt(times(minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10)), minus(a_select3(center, tptp_sum_index, n0), a_select2(x, pv10))))))) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv12)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (~leq(C!13, pred(pv12))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[61, 58, 47, 46])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 ((~(leq(C!13, pred(pv12)) <=> gt(pv12, C!13))) | leq(C!13, pred(pv12)) | (~gt(pv12, C!13))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 ((~(leq(C!13, pred(pv12)) <=> gt(pv12, C!13))) | (~gt(pv12, C!13))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[64, 45, 9])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------