%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV155+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV155+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:31:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(leq_type, type, (
% 0.19/0.40 leq: ( $i * $i ) > $o)).
% 0.19/0.40 tff(pred_type, type, (
% 0.19/0.40 pred: $i > $i)).
% 0.19/0.40 tff(pv10_type, type, (
% 0.19/0.40 pv10: $i)).
% 0.19/0.40 tff(tptp_fun_C_13_type, type, (
% 0.19/0.40 tptp_fun_C_13: $i)).
% 0.19/0.40 tff(n0_type, type, (
% 0.19/0.40 n0: $i)).
% 0.19/0.40 tff(n1_type, type, (
% 0.19/0.40 n1: $i)).
% 0.19/0.40 tff(sum_type, type, (
% 0.19/0.40 sum: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(a_select3_type, type, (
% 0.19/0.40 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_sum_index_type, type, (
% 0.19/0.40 tptp_sum_index: $i)).
% 0.19/0.40 tff(q_type, type, (
% 0.19/0.40 q: $i)).
% 0.19/0.40 tff(n4_type, type, (
% 0.19/0.40 n4: $i)).
% 0.19/0.40 tff(divide_type, type, (
% 0.19/0.40 divide: ( $i * $i ) > $i)).
% 0.19/0.40 tff(sqrt_type, type, (
% 0.19/0.40 sqrt: $i > $i)).
% 0.19/0.40 tff(times_type, type, (
% 0.19/0.40 times: ( $i * $i ) > $i)).
% 0.19/0.40 tff(minus_type, type, (
% 0.19/0.40 minus: ( $i * $i ) > $i)).
% 0.19/0.40 tff(a_select2_type, type, (
% 0.19/0.40 a_select2: ( $i * $i ) > $i)).
% 0.19/0.40 tff(x_type, type, (
% 0.19/0.40 x: $i)).
% 0.19/0.40 tff(center_type, type, (
% 0.19/0.40 center: $i)).
% 0.19/0.40 tff(pv12_type, type, (
% 0.19/0.40 pv12: $i)).
% 0.19/0.40 tff(n135299_type, type, (
% 0.19/0.40 n135299: $i)).
% 0.19/0.40 tff(pv70_type, type, (
% 0.19/0.40 pv70: $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((~((sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (pv10 = C!13) | (~(leq(n0, C!13) & leq(C!13, pred(pv10)))))) <=> (~((sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (pv10 = C!13) | (~(leq(n0, C!13) & leq(C!13, pred(pv10))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))) <=> (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 ((~((((((((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, pred(pv10))) => ((~(pv10 = C)) => (sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1))))) <=> (~((~((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] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,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, pred(pv10))) => ((~(pv10 = C)) => (sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_norm_0005')).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~((~((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] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.19/0.40 inference(or_elim,[status(thm)],[5])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![C: $i] : ((sum(n0, n4, a_select3(q, C, tptp_sum_index)) = n1) | (pv10 = C) | (~(leq(n0, C) & leq(C, pred(pv10)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.40 tff(10,plain,(
% 0.19/0.40 ~((sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (pv10 = C!13) | (~(leq(n0, C!13) & leq(C!13, pred(pv10)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[9])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (~((sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (pv10 = C!13) | (~(leq(n0, C!13) & leq(C!13, pred(pv10)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (leq(n0, C!13) & leq(C!13, pred(pv10))),
% 0.19/0.40 inference(or_elim,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (leq(C!13, pred(pv10))),
% 0.19/0.40 inference(and_elim,[status(thm)],[12])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (leq(n0, C!13)),
% 0.19/0.40 inference(and_elim,[status(thm)],[12])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (~(sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1)),
% 0.19/0.40 inference(or_elim,[status(thm)],[11])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (^[B: $i] : refl(((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10)))) <=> ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10)))) <=> ![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, B) & leq(B, pred(pv10))) <=> (~((~leq(n0, B)) | (~leq(B, pred(pv10)))))), ((~(leq(n0, B) & leq(B, pred(pv10)))) <=> (~(~((~leq(n0, B)) | (~leq(B, pred(pv10)))))))), rewrite((~(~((~leq(n0, B)) | (~leq(B, pred(pv10)))))) <=> ((~leq(n0, B)) | (~leq(B, pred(pv10))))), ((~(leq(n0, B) & leq(B, pred(pv10)))) <=> ((~leq(n0, B)) | (~leq(B, pred(pv10)))))), (((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> (((~leq(n0, B)) | (~leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))), rewrite((((~leq(n0, B)) | (~leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))), (((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> ![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)) <=> ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(21,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))),
% 0.19/0.42 inference(or_elim,[status(thm)],[5])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.19/0.42 inference(and_elim,[status(thm)],[21])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.19/0.42 tff(24,plain,(
% 0.19/0.42 ![B: $i] : ((~(leq(n0, B) & leq(B, pred(pv10)))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.19/0.42 inference(skolemize,[status(sab)],[23])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (((~![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))) | ((sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv10))))) <=> ((~![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))) | (sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv10))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 ((~![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))) | ((sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv10))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 ((~![B: $i] : ((sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1) | (~leq(n0, B)) | (~leq(B, pred(pv10))))) | (sum(n0, n4, a_select3(q, C!13, tptp_sum_index)) = n1) | (~leq(n0, C!13)) | (~leq(C!13, pred(pv10)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[29, 26, 15, 14, 13])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------