%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV161+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:37 AM UTC 2025
% Result : Theorem 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV161+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 09:30:41 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 tff(n1_type, type, (
% 0.22/0.44 n1: $i)).
% 0.22/0.44 tff(sum_type, type, (
% 0.22/0.44 sum: ( $i * $i * $i ) > $i)).
% 0.22/0.44 tff(a_select3_type, type, (
% 0.22/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_sum_index_type, type, (
% 0.22/0.44 tptp_sum_index: $i)).
% 0.22/0.44 tff(tptp_fun_B_13_type, type, (
% 0.22/0.44 tptp_fun_B_13: $i)).
% 0.22/0.44 tff(q_type, type, (
% 0.22/0.44 q: $i)).
% 0.22/0.44 tff(n4_type, type, (
% 0.22/0.44 n4: $i)).
% 0.22/0.44 tff(n0_type, type, (
% 0.22/0.44 n0: $i)).
% 0.22/0.44 tff(pv10_type, type, (
% 0.22/0.44 pv10: $i)).
% 0.22/0.44 tff(leq_type, type, (
% 0.22/0.44 leq: ( $i * $i ) > $o)).
% 0.22/0.44 tff(pred_type, type, (
% 0.22/0.44 pred: $i > $i)).
% 0.22/0.44 tff(n135299_type, type, (
% 0.22/0.44 n135299: $i)).
% 0.22/0.44 tff(gt_type, type, (
% 0.22/0.44 gt: ( $i * $i ) > $o)).
% 0.22/0.44 tff(1,plain,
% 0.22/0.44 ((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) <=> (sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1)),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(2,plain,
% 0.22/0.44 ((~(((((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & 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, pv10)) => (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))) <=> (~((~((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & 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, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(3,axiom,(~(((((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & 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, pv10)) => (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cl5_nebula_norm_0011')).
% 0.22/0.44 tff(4,plain,
% 0.22/0.44 (~((~((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & 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, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.44 tff(5,plain,
% 0.22/0.44 ((sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1) & 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))),
% 0.22/0.44 inference(or_elim,[status(thm)],[4])).
% 0.22/0.44 tff(6,plain,
% 0.22/0.44 (sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1),
% 0.22/0.44 inference(and_elim,[status(thm)],[5])).
% 0.22/0.44 tff(7,plain,
% 0.22/0.44 (sum(n0, n4, a_select3(q, pv10, tptp_sum_index)) = n1),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.44 tff(8,plain,
% 0.22/0.44 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(9,plain,
% 0.22/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[8])).
% 0.22/0.44 tff(10,plain,
% 0.22/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(11,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.22/0.44 tff(12,plain,
% 0.22/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.44 tff(13,plain,(
% 0.22/0.44 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.22/0.44 inference(skolemize,[status(sab)],[12])).
% 0.22/0.44 tff(14,plain,
% 0.22/0.44 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.22/0.44 tff(15,plain,
% 0.22/0.44 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(B!13, pred(pv10)) <=> gt(pv10, B!13))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 (leq(B!13, pred(pv10)) <=> gt(pv10, B!13)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 ((~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))) <=> (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(or_elim,[status(thm)],[4])).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.44 tff(20,plain,
% 0.22/0.44 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 (~![B: $i] : ((~(leq(n0, B) & leq(B, pv10))) | (sum(n0, n4, a_select3(q, B, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.22/0.44 tff(22,plain,(
% 0.22/0.44 ~((~(leq(n0, B!13) & leq(B!13, pv10))) | (sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(skolemize,[status(sab)],[21])).
% 0.22/0.44 tff(23,plain,
% 0.22/0.44 (~(sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = n1)),
% 0.22/0.44 inference(or_elim,[status(thm)],[22])).
% 0.22/0.44 tff(24,plain,
% 0.22/0.44 (leq(n0, B!13) & leq(B!13, pv10)),
% 0.22/0.44 inference(or_elim,[status(thm)],[22])).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (leq(n0, B!13)),
% 0.22/0.44 inference(and_elim,[status(thm)],[24])).
% 0.22/0.44 tff(26,plain,
% 0.22/0.44 (^[A: $i] : refl(((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10)))) <=> ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 (![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10)))) <=> ![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.44 tff(28,plain,
% 0.22/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, A) & leq(A, pred(pv10))) <=> (~((~leq(n0, A)) | (~leq(A, pred(pv10)))))), ((~(leq(n0, A) & leq(A, pred(pv10)))) <=> (~(~((~leq(n0, A)) | (~leq(A, pred(pv10)))))))), rewrite((~(~((~leq(n0, A)) | (~leq(A, pred(pv10)))))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10))))), ((~(leq(n0, A) & leq(A, pred(pv10)))) <=> ((~leq(n0, A)) | (~leq(A, pred(pv10)))))), (((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> (((~leq(n0, A)) | (~leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)))), rewrite((((~leq(n0, A)) | (~leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))), (((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(29,plain,
% 0.22/0.44 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> ![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.44 tff(30,plain,
% 0.22/0.44 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1)) <=> ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(and_elim,[status(thm)],[5])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.44 tff(33,plain,(
% 0.22/0.44 ![A: $i] : ((~(leq(n0, A) & leq(A, pred(pv10)))) | (sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1))),
% 0.22/0.44 inference(skolemize,[status(sab)],[32])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 (![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.22/0.45 tff(35,plain,
% 0.22/0.45 (![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.22/0.45 tff(36,plain,
% 0.22/0.45 (((~![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))) | ((sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = n1) | (~leq(n0, B!13)) | (~leq(B!13, pred(pv10))))) <=> ((~![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))) | (sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = n1) | (~leq(n0, B!13)) | (~leq(B!13, pred(pv10))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(37,plain,
% 0.22/0.45 ((~![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))) | ((sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = n1) | (~leq(n0, B!13)) | (~leq(B!13, pred(pv10))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(38,plain,
% 0.22/0.45 ((~![A: $i] : ((sum(n0, n4, a_select3(q, A, tptp_sum_index)) = n1) | (~leq(n0, A)) | (~leq(A, pred(pv10))))) | (sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = n1) | (~leq(n0, B!13)) | (~leq(B!13, pred(pv10)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.45 tff(39,plain,
% 0.22/0.45 (~leq(B!13, pred(pv10))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[38, 35, 25, 23])).
% 0.22/0.45 tff(40,plain,
% 0.22/0.45 ((~(leq(B!13, pred(pv10)) <=> gt(pv10, B!13))) | leq(B!13, pred(pv10)) | (~gt(pv10, B!13))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(41,plain,
% 0.22/0.45 ((~(leq(B!13, pred(pv10)) <=> gt(pv10, B!13))) | (~gt(pv10, B!13))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.22/0.45 tff(42,plain,
% 0.22/0.45 (~gt(pv10, B!13)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[41, 16])).
% 0.22/0.45 tff(43,plain,
% 0.22/0.45 (leq(B!13, pv10)),
% 0.22/0.45 inference(and_elim,[status(thm)],[24])).
% 0.22/0.45 tff(44,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(45,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.45 tff(46,plain,
% 0.22/0.45 (^[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)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(47,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.45 tff(48,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(49,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(50,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.22/0.45 tff(51,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.22/0.45 tff(54,plain,(
% 0.22/0.46 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.22/0.46 inference(skolemize,[status(sab)],[53])).
% 0.22/0.46 tff(55,plain,
% 0.22/0.46 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.22/0.46 tff(56,plain,
% 0.22/0.46 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.22/0.46 tff(57,plain,
% 0.22/0.46 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(58,plain,
% 0.22/0.46 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (B!13 = pv10) | gt(pv10, B!13) | (~leq(B!13, pv10))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 ((B!13 = pv10) | gt(pv10, B!13)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[59, 56, 43])).
% 0.22/0.46 tff(61,plain,
% 0.22/0.46 (B!13 = pv10),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[60, 42])).
% 0.22/0.46 tff(62,plain,
% 0.22/0.46 (a_select3(q, B!13, tptp_sum_index) = a_select3(q, pv10, tptp_sum_index)),
% 0.22/0.46 inference(monotonicity,[status(thm)],[61])).
% 0.22/0.46 tff(63,plain,
% 0.22/0.46 (sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = sum(n0, n4, a_select3(q, pv10, tptp_sum_index))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[62])).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 (sum(n0, n4, a_select3(q, B!13, tptp_sum_index)) = n1),
% 0.22/0.46 inference(transitivity,[status(thm)],[63, 7])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[23, 64])).
% 0.22/0.46 % SZS output end Proof
% 0.22/0.46 % E exiting
%------------------------------------------------------------------------------