%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV221+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:31:45 AM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV221+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:36:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(a_select3_type, type, (
% 0.20/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_M_13_type, type, (
% 0.20/0.44 tptp_fun_M_13: $i)).
% 0.20/0.44 tff(id_ds1_filter_type, type, (
% 0.20/0.44 id_ds1_filter: $i)).
% 0.20/0.44 tff(leq_type, type, (
% 0.20/0.44 leq: ( $i * $i ) > $o)).
% 0.20/0.44 tff(n5_type, type, (
% 0.20/0.44 n5: $i)).
% 0.20/0.44 tff(n0_type, type, (
% 0.20/0.44 n0: $i)).
% 0.20/0.44 tff(pred_type, type, (
% 0.20/0.44 pred: $i > $i)).
% 0.20/0.44 tff(pv57_type, type, (
% 0.20/0.44 pv57: $i)).
% 0.20/0.44 tff(tptp_fun_N_14_type, type, (
% 0.20/0.44 tptp_fun_N_14: $i)).
% 0.20/0.44 tff(gt_type, type, (
% 0.20/0.44 gt: ( $i * $i ) > $o)).
% 0.20/0.44 tff(pv58_type, type, (
% 0.20/0.44 pv58: $i)).
% 0.20/0.44 tff(pminus_ds1_filter_type, type, (
% 0.20/0.44 pminus_ds1_filter: $i)).
% 0.20/0.44 tff(r_ds1_filter_type, type, (
% 0.20/0.44 r_ds1_filter: $i)).
% 0.20/0.44 tff(n2_type, type, (
% 0.20/0.44 n2: $i)).
% 0.20/0.44 tff(q_ds1_filter_type, type, (
% 0.20/0.44 q_ds1_filter: $i)).
% 0.20/0.44 tff(n998_type, type, (
% 0.20/0.44 n998: $i)).
% 0.20/0.44 tff(pv5_type, type, (
% 0.20/0.44 pv5: $i)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 (((leq(n0, 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)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13))))))) <=> (leq(n0, 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)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 ((~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))))) <=> (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (((leq(n0, 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)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13))))))) <=> ((leq(n0, 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)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (((leq(n0, 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)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13))))))) <=> (leq(n0, 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)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 ((~![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)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 ((~((((((((((((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))) & ![H: $i] : ((~gt(pv58, H)) | (~leq(n0, H)) | (~leq(H, n5)) | (a_select3(id_ds1_filter, pv57, H) = a_select3(id_ds1_filter, H, pv57)) | (~leq(n0, pv57)) | (~leq(pv57, n5))) & ![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))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(7,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/sandbox/benchmark/theBenchmark.p','quaternion_ds1_symm_0401')).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (~((~(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))) & ![H: $i] : ((~gt(pv58, H)) | (~leq(n0, H)) | (~leq(H, n5)) | (a_select3(id_ds1_filter, pv57, H) = a_select3(id_ds1_filter, H, pv57)) | (~leq(n0, pv57)) | (~leq(pv57, n5))) & ![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)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (~![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))))))),
% 0.20/0.44 inference(or_elim,[status(thm)],[8])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (~![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))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 (~![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))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (~![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))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (leq(n0, 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)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (leq(M!13, pred(pv57))),
% 0.20/0.44 inference(and_elim,[status(thm)],[13])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (leq(n0, M!13)),
% 0.20/0.44 inference(and_elim,[status(thm)],[13])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (^[K: $i] : refl(((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))) <=> ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))) <=> ![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (^[K: $i] : rewrite(((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))) <=> ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))) <=> ![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))) <=> ![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, K) & leq(K, pred(pv57))) <=> (~((~leq(n0, K)) | (~leq(K, pred(pv57)))))), ((~(leq(n0, K) & leq(K, pred(pv57)))) <=> (~(~((~leq(n0, K)) | (~leq(K, pred(pv57)))))))), rewrite((~(~((~leq(n0, K)) | (~leq(K, pred(pv57)))))) <=> ((~leq(n0, K)) | (~leq(K, pred(pv57))))), ((~(leq(n0, K) & leq(K, pred(pv57)))) <=> ((~leq(n0, K)) | (~leq(K, pred(pv57)))))), quant_intro(proof_bind(^[L: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, L) & leq(L, n5)) <=> (~((~leq(n0, L)) | (~leq(L, n5))))), ((~(leq(n0, L) & leq(L, n5))) <=> (~(~((~leq(n0, L)) | (~leq(L, n5))))))), rewrite((~(~((~leq(n0, L)) | (~leq(L, n5))))) <=> ((~leq(n0, L)) | (~leq(L, n5)))), ((~(leq(n0, L) & leq(L, n5))) <=> ((~leq(n0, L)) | (~leq(L, n5))))), (((~(leq(n0, L) & leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))) <=> (((~leq(n0, L)) | (~leq(L, n5))) | (a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K))))), rewrite((((~leq(n0, L)) | (~leq(L, n5))) | (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(n0, L)) | (~leq(L, n5)))), (((~(leq(n0, L) & leq(L, n5))) | (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(n0, L)) | (~leq(L, n5)))))), (![L: $i] : ((~(leq(n0, L) & leq(L, n5))) | (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(n0, L)) | (~leq(L, n5))))), (((~(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(n0, K)) | (~leq(K, pred(pv57)))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))))), rewrite((((~leq(n0, K)) | (~leq(K, pred(pv57)))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5)))) <=> ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))), (((~(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(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (![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] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (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))) & ![H: $i] : ((~gt(pv58, H)) | (~leq(n0, H)) | (~leq(H, n5)) | (a_select3(id_ds1_filter, pv57, H) = a_select3(id_ds1_filter, H, pv57)) | (~leq(n0, pv57)) | (~leq(pv57, n5))) & ![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))))),
% 0.20/0.45 inference(or_elim,[status(thm)],[8])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(and_elim,[status(thm)],[24])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.20/0.45 tff(27,plain,(
% 0.20/0.45 ![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))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[26])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | ((~leq(n0, M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13))))) <=> ((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | (~leq(n0, M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (((~leq(n0, 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(n0, L)) | (~leq(L, n5)))) <=> ((~leq(n0, M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | ((~leq(n0, 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(n0, L)) | (~leq(L, n5))))) <=> ((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | ((~leq(n0, M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | ((~leq(n0, 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(n0, L)) | (~leq(L, n5))))) <=> ((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | (~leq(n0, M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 ((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | ((~leq(n0, 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(n0, L)) | (~leq(L, n5))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 ((~![K: $i] : ((~leq(n0, K)) | (~leq(K, pred(pv57))) | ![L: $i] : ((a_select3(id_ds1_filter, K, L) = a_select3(id_ds1_filter, L, K)) | (~leq(n0, L)) | (~leq(L, n5))))) | (~leq(n0, M!13)) | (~leq(M!13, pred(pv57))) | ![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[35, 29, 15, 14])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (~((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~(leq(n0, N!14) & leq(N!14, n5))) | (~((~((pv57 = N!14) & (N!14 = M!13))) & (~(pv57 = M!13)))))),
% 0.20/0.46 inference(and_elim,[status(thm)],[13])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (leq(n0, N!14) & leq(N!14, n5)),
% 0.20/0.46 inference(or_elim,[status(thm)],[37])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (leq(N!14, n5)),
% 0.20/0.46 inference(and_elim,[status(thm)],[38])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (leq(n0, N!14)),
% 0.20/0.46 inference(and_elim,[status(thm)],[38])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (~(a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13))),
% 0.20/0.46 inference(or_elim,[status(thm)],[37])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | ((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(n0, N!14)) | (~leq(N!14, n5)))) <=> ((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(n0, N!14)) | (~leq(N!14, n5)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (((~leq(n0, N!14)) | (~leq(N!14, n5)) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13))) <=> ((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(n0, N!14)) | (~leq(N!14, n5)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | ((~leq(n0, N!14)) | (~leq(N!14, n5)) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)))) <=> ((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | ((a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(n0, N!14)) | (~leq(N!14, n5))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | ((~leq(n0, N!14)) | (~leq(N!14, n5)) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)))) <=> ((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(n0, N!14)) | (~leq(N!14, n5)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | ((~leq(n0, N!14)) | (~leq(N!14, n5)) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ((~![L: $i] : ((~leq(n0, L)) | (~leq(L, n5)) | (a_select3(id_ds1_filter, M!13, L) = a_select3(id_ds1_filter, L, M!13)))) | (a_select3(id_ds1_filter, M!13, N!14) = a_select3(id_ds1_filter, N!14, M!13)) | (~leq(n0, N!14)) | (~leq(N!14, n5))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[47, 41, 40, 39, 36])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------