TSTP Solution File: SWV221+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV221+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 15:10:26 EDT 2022
% Result : Theorem 0.06s 0.30s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.06 % Problem : SWV221+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.25 % Computer : n023.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Sun Sep 4 02:06:48 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.06/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26 Usage: tptp [options] [-file:]file
% 0.06/0.26 -h, -? prints this message.
% 0.06/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.26 -m, -model generate model.
% 0.06/0.26 -p, -proof generate proof.
% 0.06/0.26 -c, -core generate unsat core of named formulas.
% 0.06/0.26 -st, -statistics display statistics.
% 0.06/0.26 -t:timeout set timeout (in second).
% 0.06/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26 -<param>:<value> configuration parameter and value.
% 0.06/0.26 -o:<output-file> file to place output in.
% 0.06/0.30 % SZS status Theorem
% 0.06/0.30 % SZS output start Proof
% 0.06/0.30 tff(leq_type, type, (
% 0.06/0.30 leq: ( $i * $i ) > $o)).
% 0.06/0.30 tff(succ_type, type, (
% 0.06/0.30 succ: $i > $i)).
% 0.06/0.30 tff(tptp_minus_1_type, type, (
% 0.06/0.30 tptp_minus_1: $i)).
% 0.06/0.30 tff(a_select3_type, type, (
% 0.06/0.30 a_select3: ( $i * $i * $i ) > $i)).
% 0.06/0.30 tff(tptp_fun_M_13_type, type, (
% 0.06/0.30 tptp_fun_M_13: $i)).
% 0.06/0.30 tff(id_ds1_filter_type, type, (
% 0.06/0.30 id_ds1_filter: $i)).
% 0.06/0.30 tff(pred_type, type, (
% 0.06/0.30 pred: $i > $i)).
% 0.06/0.30 tff(pv57_type, type, (
% 0.06/0.30 pv57: $i)).
% 0.06/0.30 tff(tptp_fun_N_14_type, type, (
% 0.06/0.30 tptp_fun_N_14: $i)).
% 0.06/0.30 tff(n5_type, type, (
% 0.06/0.30 n5: $i)).
% 0.06/0.30 tff(n0_type, type, (
% 0.06/0.30 n0: $i)).
% 0.06/0.30 tff(gt_type, type, (
% 0.06/0.30 gt: ( $i * $i ) > $o)).
% 0.06/0.30 tff(pv58_type, type, (
% 0.06/0.30 pv58: $i)).
% 0.06/0.30 tff(pminus_ds1_filter_type, type, (
% 0.06/0.30 pminus_ds1_filter: $i)).
% 0.06/0.30 tff(r_ds1_filter_type, type, (
% 0.06/0.30 r_ds1_filter: $i)).
% 0.06/0.30 tff(n2_type, type, (
% 0.06/0.30 n2: $i)).
% 0.06/0.30 tff(q_ds1_filter_type, type, (
% 0.06/0.30 q_ds1_filter: $i)).
% 0.06/0.30 tff(n998_type, type, (
% 0.06/0.30 n998: $i)).
% 0.06/0.30 tff(pv5_type, type, (
% 0.06/0.30 pv5: $i)).
% 0.06/0.30 tff(1,plain,
% 0.06/0.30 (((leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57))) & (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))) <=> (leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57)) & (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))))),
% 0.06/0.30 inference(rewrite,[status(thm)],[])).
% 0.06/0.30 tff(2,plain,
% 0.06/0.30 ((~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))) <=> (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.06/0.30 inference(rewrite,[status(thm)],[])).
% 0.06/0.30 tff(3,plain,
% 0.06/0.30 ((~(~(leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57))))) <=> (leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57)))),
% 0.06/0.30 inference(rewrite,[status(thm)],[])).
% 0.06/0.30 tff(4,plain,
% 0.06/0.30 (((~(~(leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57))))) & (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))) <=> ((leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57))) & (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))))),
% 0.06/0.30 inference(monotonicity,[status(thm)],[3, 2])).
% 0.06/0.30 tff(5,plain,
% 0.06/0.30 (((~(~(leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57))))) & (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))) <=> (leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57)) & (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))))),
% 0.06/0.30 inference(transitivity,[status(thm)],[4, 1])).
% 0.06/0.30 tff(6,plain,
% 0.06/0.30 ((~![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))) | (~(leq(succ(tptp_minus_1), N) & leq(N, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))) <=> (~![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))) | (~(leq(succ(tptp_minus_1), N) & leq(N, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))))),
% 0.06/0.31 inference(rewrite,[status(thm)],[])).
% 0.06/0.31 tff(7,plain,
% 0.06/0.31 ((~![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M))))))) <=> (~![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))) | (~(leq(succ(tptp_minus_1), N) & leq(N, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))))),
% 0.06/0.31 inference(rewrite,[status(thm)],[])).
% 0.06/0.31 tff(8,plain,
% 0.06/0.31 ((~![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M))))))) <=> (~![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))))))),
% 0.06/0.31 inference(rewrite,[status(thm)],[])).
% 0.06/0.31 tff(9,plain,
% 0.06/0.31 ((~((((((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, n998)) & leq(pv57, n5)) & leq(pv58, n5)) & gt(pv58, pv57)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n5)) & leq(B, n5)) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, n2)) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n5)) & leq(F, n5)) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, n5)) & leq(H, n5)) => (((G = pv57) & gt(pv58, H)) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, n5)) & leq(J, n5)) => (gt(pv57, I) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) & ![K: $i] : ((leq(n0, K) & leq(K, pred(pv57))) => ![L: $i] : ((leq(n0, L) & leq(L, n5)) => (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))) => ![M: $i] : ((leq(n0, M) & leq(M, pred(pv57))) => ![N: $i] : ((leq(n0, N) & leq(N, n5)) => (((~((pv57 = N) & (N = M))) & (~(pv57 = M))) => (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))) <=> (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, n998) & leq(pv57, n5) & leq(pv58, n5) & gt(pv58, pv57) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n5) & leq(B, n5))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n5) & leq(F, n5))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~(leq(n0, G) & leq(n0, H) & leq(G, n5) & leq(H, n5))) | (~((G = pv57) & gt(pv58, H)))) & ![I: $i, J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~(leq(n0, I) & leq(n0, J) & leq(I, n5) & leq(J, n5))) | (~gt(pv57, I))) & ![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))))) | ![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M))))))))),
% 0.06/0.31 inference(rewrite,[status(thm)],[])).
% 0.06/0.31 tff(10,axiom,(~((((((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, n998)) & leq(pv57, n5)) & leq(pv58, n5)) & gt(pv58, pv57)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n5)) & leq(B, n5)) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, n2)) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n5)) & leq(F, n5)) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, n5)) & leq(H, n5)) => (((G = pv57) & gt(pv58, H)) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, n5)) & leq(J, n5)) => (gt(pv57, I) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) & ![K: $i] : ((leq(n0, K) & leq(K, pred(pv57))) => ![L: $i] : ((leq(n0, L) & leq(L, n5)) => (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))) => ![M: $i] : ((leq(n0, M) & leq(M, pred(pv57))) => ![N: $i] : ((leq(n0, N) & leq(N, n5)) => (((~((pv57 = N) & (N = M))) & (~(pv57 = M))) => (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0401')).
% 0.10/0.31 tff(11,plain,
% 0.10/0.31 (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, n998) & leq(pv57, n5) & leq(pv58, n5) & gt(pv58, pv57) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n5) & leq(B, n5))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n5) & leq(F, n5))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~(leq(n0, G) & leq(n0, H) & leq(G, n5) & leq(H, n5))) | (~((G = pv57) & gt(pv58, H)))) & ![I: $i, J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~(leq(n0, I) & leq(n0, J) & leq(I, n5) & leq(J, n5))) | (~gt(pv57, I))) & ![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))))) | ![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.10/0.31 tff(12,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M))))))),
% 0.10/0.31 inference(or_elim,[status(thm)],[11])).
% 0.10/0.31 tff(13,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.10/0.31 tff(14,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.10/0.31 tff(15,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(n0, M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~(leq(n0, N) & leq(N, n5))) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.10/0.31 tff(16,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))) | (~(leq(succ(tptp_minus_1), N) & leq(N, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.10/0.31 tff(17,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))) | (~(leq(succ(tptp_minus_1), N) & leq(N, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.10/0.31 tff(18,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))) | (~(leq(succ(tptp_minus_1), N) & leq(N, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[17, 6])).
% 0.10/0.31 tff(19,plain,
% 0.10/0.31 (~![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, pred(pv57)))) | ![N: $i] : ((a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)) | (~((~((pv57 = N) & (N = M))) & (~(pv57 = M)))) | (~(leq(succ(tptp_minus_1), N) & leq(N, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[18, 6])).
% 0.10/0.31 tff(20,plain,
% 0.10/0.31 (leq(succ(tptp_minus_1), M!13) & leq(M!13, pred(pv57)) & (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[19, 5])).
% 0.10/0.31 tff(21,plain,
% 0.10/0.31 (leq(M!13, pred(pv57))),
% 0.10/0.31 inference(and_elim,[status(thm)],[20])).
% 0.10/0.31 tff(22,plain,
% 0.10/0.31 (leq(succ(tptp_minus_1), M!13)),
% 0.10/0.31 inference(and_elim,[status(thm)],[20])).
% 0.10/0.31 tff(23,plain,
% 0.10/0.31 (^[K: $i] : refl(((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.10/0.31 inference(bind,[status(th)],[])).
% 0.10/0.31 tff(24,plain,
% 0.10/0.31 (![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(quant_intro,[status(thm)],[23])).
% 0.10/0.31 tff(25,plain,
% 0.10/0.31 (^[K: $i] : rewrite(((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))),
% 0.10/0.31 inference(bind,[status(th)],[])).
% 0.10/0.31 tff(26,plain,
% 0.10/0.31 (![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(quant_intro,[status(thm)],[25])).
% 0.10/0.31 tff(27,plain,
% 0.10/0.31 (![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(transitivity,[status(thm)],[26, 24])).
% 0.10/0.31 tff(28,plain,
% 0.10/0.31 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), K) & leq(K, pred(pv57))) <=> (~((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57)))))), ((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) <=> (~(~((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57)))))) <=> ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))))), ((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) <=> ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57)))))), quant_intro(proof_bind(^[L: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> (~((~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))), ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> (~(~((~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))) <=> ((~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))), ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))), (((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))) <=> (((~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))), rewrite((((~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))) <=> ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))), (((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))) <=> ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))), (![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))) <=> ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))), (((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))) <=> (((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57)))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))))), rewrite((((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57)))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))), (((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))) <=> ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))))),
% 0.10/0.31 inference(bind,[status(th)],[])).
% 0.10/0.31 tff(29,plain,
% 0.10/0.31 (![K: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))) <=> ![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(quant_intro,[status(thm)],[28])).
% 0.10/0.31 tff(30,plain,
% 0.10/0.31 (^[K: $i] : rewrite(((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))) <=> ((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))))),
% 0.10/0.31 inference(bind,[status(th)],[])).
% 0.10/0.31 tff(31,plain,
% 0.10/0.31 (![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))) <=> ![K: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))),
% 0.10/0.31 inference(quant_intro,[status(thm)],[30])).
% 0.10/0.31 tff(32,plain,
% 0.10/0.31 (![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)))) <=> ![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))),
% 0.10/0.31 inference(rewrite,[status(thm)],[])).
% 0.10/0.31 tff(33,plain,
% 0.10/0.31 (leq(n0, pv5) & leq(n0, pv57) & leq(pv5, n998) & leq(pv57, n5) & leq(pv58, n5) & gt(pv58, pv57) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n5) & leq(B, n5))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n5) & leq(F, n5))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~(leq(n0, G) & leq(n0, H) & leq(G, n5) & leq(H, n5))) | (~((G = pv57) & gt(pv58, H)))) & ![I: $i, J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~(leq(n0, I) & leq(n0, J) & leq(I, n5) & leq(J, n5))) | (~gt(pv57, I))) & ![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))),
% 0.10/0.31 inference(or_elim,[status(thm)],[11])).
% 0.10/0.31 tff(34,plain,
% 0.10/0.31 (![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))),
% 0.10/0.31 inference(and_elim,[status(thm)],[33])).
% 0.10/0.31 tff(35,plain,
% 0.10/0.31 (![K: $i] : ((~(leq(n0, K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.10/0.31 tff(36,plain,
% 0.10/0.31 (![K: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.10/0.31 tff(37,plain,(
% 0.10/0.31 ![K: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(K, pred(pv57)))) | ![L: $i] : ((~(leq(succ(tptp_minus_1), L) & leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))),
% 0.10/0.31 inference(skolemize,[status(sab)],[36])).
% 0.10/0.31 tff(38,plain,
% 0.10/0.31 (![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[37, 29])).
% 0.10/0.31 tff(39,plain,
% 0.10/0.31 (![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[38, 27])).
% 0.10/0.31 tff(40,plain,
% 0.10/0.31 (((~![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))) | ((~leq(succ(tptp_minus_1), M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))) <=> ((~![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))) | (~leq(succ(tptp_minus_1), M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(rewrite,[status(thm)],[])).
% 0.10/0.31 tff(41,plain,
% 0.10/0.31 ((~![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))) | ((~leq(succ(tptp_minus_1), M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(quant_inst,[status(thm)],[])).
% 0.10/0.31 tff(42,plain,
% 0.10/0.31 ((~![K: $i] : ((~leq(succ(tptp_minus_1), K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))) | (~leq(succ(tptp_minus_1), M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.10/0.31 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.10/0.31 tff(43,plain,
% 0.10/0.31 (![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.10/0.31 inference(unit_resolution,[status(thm)],[42, 39, 22, 21])).
% 0.10/0.31 tff(44,plain,
% 0.10/0.31 (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))) | (~(leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))))),
% 0.10/0.31 inference(and_elim,[status(thm)],[20])).
% 0.10/0.31 tff(45,plain,
% 0.10/0.31 (leq(succ(tptp_minus_1), N!14) & leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.10/0.31 inference(or_elim,[status(thm)],[44])).
% 0.10/0.31 tff(46,plain,
% 0.10/0.31 (leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.10/0.31 inference(and_elim,[status(thm)],[45])).
% 0.10/0.31 tff(47,plain,
% 0.10/0.31 (leq(succ(tptp_minus_1), N!14)),
% 0.10/0.32 inference(and_elim,[status(thm)],[45])).
% 0.10/0.32 tff(48,plain,
% 0.10/0.32 (~(a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13))),
% 0.10/0.32 inference(or_elim,[status(thm)],[44])).
% 0.10/0.32 tff(49,plain,
% 0.10/0.32 (((~![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | ((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(succ(tptp_minus_1), N!14)) | (~leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) <=> ((~![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(succ(tptp_minus_1), N!14)) | (~leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.10/0.32 inference(rewrite,[status(thm)],[])).
% 0.10/0.32 tff(50,plain,
% 0.10/0.32 ((~![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | ((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(succ(tptp_minus_1), N!14)) | (~leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.10/0.32 inference(quant_inst,[status(thm)],[])).
% 0.10/0.32 tff(51,plain,
% 0.10/0.32 ((~![L: $i] : ((a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)) | (~leq(succ(tptp_minus_1), L)) | (~leq(L, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(succ(tptp_minus_1), N!14)) | (~leq(N!14, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.10/0.32 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.10/0.32 tff(52,plain,
% 0.10/0.32 ($false),
% 0.10/0.32 inference(unit_resolution,[status(thm)],[51, 48, 47, 46, 43])).
% 0.10/0.32 % SZS output end Proof
%------------------------------------------------------------------------------