0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.b9Er3O6TCT 0.15/0.35 % Computer : n016.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 1200 0.15/0.35 % DateTime : Tue Jul 13 15:42:08 EDT 2021 0.15/0.35 % CPUTime : 0.15/0.35 % Running portfolio for 120 s 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.35 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.53/0.65 % Estimated wc time : 1286 0.53/0.65 % Estimated cpu time (7 cpus) : 183.71428571428572 0.54/0.69 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.54/0.71 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 69.32/10.55 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 103.83/15.59 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 105.48/15.85 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 144.05/21.50 % /export/starexec/sandbox/solver/bin/lams/b.lsimp.sh running for 17s 145.28/21.76 % /export/starexec/sandbox/solver/bin/lams/b.split.sh running for 31s 173.90/26.55 % /export/starexec/sandbox/solver/bin/lams/s4.sh running for 15s 179.55/27.59 % /export/starexec/sandbox/solver/bin/lams/b.rw.sh running for 26s 181.35/27.95 % /export/starexec/sandbox/solver/bin/lams/c_ic.sh running for 42s 195.17/30.20 % /export/starexec/sandbox/solver/bin/lams/s1.f.sh running for 15s 220.43/34.42 % Solved by lams/b.sh. 220.43/34.42 % Running : timeout 14 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.b9Er3O6TCT/e_input06bee7 --cpu-limit=12 --auto -s -p. 220.43/34.42 % done 83 iterations in 18.759s 220.43/34.42 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 220.43/34.42 % SZS output start Refutation 220.43/34.42 tff(thm_2Equotient_2EFUN__REL__EQ__REL, conjecture, 220.43/34.42 (![A_27a:d,A_27b:d,A_27c:d,A_27d:d,V0R1_2E0:u,V1abs1_2E0:u,V2rep1_2E0:u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27c), 220.43/34.42 V1abs1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun( 220.43/34.42 A_27c,A_27a), 220.43/34.42 V2rep1_2E0)))) => 220.43/34.42 (![V3R2_2E0:u,V4abs2_2E0:u,V5rep2_2E0:u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3(s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 A_27d), 220.43/34.42 V4abs2_2E0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27d, 220.43/34.42 A_27b), 220.43/34.42 V5rep2_2E0)))) => 220.43/34.42 (![V6f_2E0:u,V7g_2E0:u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V6f_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V7g_2E0)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0))), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V6f_2E0)))) & 220.43/34.42 (s(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a), 220.43/34.42 V2rep1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b,A_27d), 220.43/34.42 V4abs2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V6f_2E0))) = 220.43/34.42 s(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a), 220.43/34.42 V2rep1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b,A_27d), 220.43/34.42 V4abs2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V7g_2E0)))) & 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0))), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V7g_2E0)))))))))))). 220.43/34.42 tff(zf_stmt_0, negated_conjecture, 220.43/34.42 (~ 220.43/34.42 (![A_27a:d,A_27b:d,A_27c:d,A_27d:d,V0R1_2E0:u,V1abs1_2E0:u,V2rep1_2E0:u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 A_27c), 220.43/34.42 V1abs1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun( 220.43/34.42 A_27c, 220.43/34.42 A_27a), 220.43/34.42 V2rep1_2E0)))) => 220.43/34.42 (![V3R2_2E0:u,V4abs2_2E0:u,V5rep2_2E0:u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b,A_27d), 220.43/34.42 V4abs2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27d,A_27b), 220.43/34.42 V5rep2_2E0)))) => 220.43/34.42 (![V6f_2E0:u,V7g_2E0:u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V6f_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V7g_2E0)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0))), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V6f_2E0)))) & 220.43/34.42 (s(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c, 220.43/34.42 A_27a), 220.43/34.42 V2rep1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 A_27d), 220.43/34.42 V4abs2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 A_27b), 220.43/34.42 V6f_2E0))) = 220.43/34.42 s(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c, 220.43/34.42 A_27a), 220.43/34.42 V2rep1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 A_27d), 220.43/34.42 V4abs2_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 A_27b), 220.43/34.42 V7g_2E0)))) & 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s(tyop_2Emin_2Efun(A_27a, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V0R1_2E0), 220.43/34.42 s(tyop_2Emin_2Efun(A_27b, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27b, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 V3R2_2E0))), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 V7g_2E0))))))))))))). 220.43/34.42 tff('0', plain, 220.43/34.42 ~ (!!((^[Y0 : d]: 220.43/34.42 (!!((^[Y1 : d]: 220.43/34.42 (!!((^[Y2 : d]: 220.43/34.42 (!!((^[Y3 : d]: 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (!!((^[Y5 : u]: 220.43/34.42 (!!((^[Y6 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y2), 220.43/34.42 Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y2, Y0), 220.43/34.42 Y6)))) => 220.43/34.42 (!!((^[Y7 : u]: 220.43/34.42 (!!((^[Y8 : u]: 220.43/34.42 (!!(( 220.43/34.42 ^[Y9 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y7), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, Y3), 220.43/34.42 Y8), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y3, Y1), 220.43/34.42 Y9)))) => 220.43/34.42 (!!(( 220.43/34.42 ^[Y10 : u]: 220.43/34.42 (!!(( 220.43/34.42 ^[Y11 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y7), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 Y10), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 Y11)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y7))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 Y10))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y2, Y3), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y2, Y0), 220.43/34.42 Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, Y3), 220.43/34.42 Y8), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 Y10))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y2, Y3), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y2, Y0), 220.43/34.42 Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, Y3), 220.43/34.42 Y8), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 Y11))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y7))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 Y11)))))))))))))))))))))))))))))))))))))))))))), 220.43/34.42 inference('cnf', [status(esa)], [zf_stmt_0])). 220.43/34.42 tff('1', plain, 220.43/34.42 ~ (!!((^[Y0 : d]: 220.43/34.42 (!!((^[Y1 : d]: 220.43/34.42 (!!((^[Y2 : d]: 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (!!((^[Y5 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', Y1), Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, '#sk2'), Y5)))) => 220.43/34.42 (!!((^[Y6 : u]: 220.43/34.42 (!!((^[Y7 : u]: 220.43/34.42 (!!((^[Y8 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y2), 220.43/34.42 Y7), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y2, Y0), 220.43/34.42 Y8)))) => 220.43/34.42 (!!(( 220.43/34.42 ^[Y9 : u]: 220.43/34.42 (!!(( 220.43/34.42 ^[Y10 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), Y9), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), Y10)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y6))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), Y9))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, Y2), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 '#sk2'), 220.43/34.42 Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y2), 220.43/34.42 Y7), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), Y9))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, Y2), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 '#sk2'), 220.43/34.42 Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y2), 220.43/34.42 Y7), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), Y10))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y6))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 Y0), Y10))))))))))))))))))))))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['0'])). 220.43/34.42 tff('2', plain, 220.43/34.42 ~ (!!((^[Y0 : d]: 220.43/34.42 (!!((^[Y1 : d]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 Y0), Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun(Y0, 220.43/34.42 '#sk2'), Y4)))) => 220.43/34.42 (!!((^[Y5 : u]: 220.43/34.42 (!!((^[Y6 : u]: 220.43/34.42 (!!((^[Y7 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 Y1), Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y1, 220.43/34.42 '#sk3'), 220.43/34.42 Y7)))) => 220.43/34.42 (!!(( 220.43/34.42 ^[Y8 : u]: 220.43/34.42 (!!(( 220.43/34.42 ^[Y9 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y8), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y9)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y5))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y8))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 '#sk2'), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 Y1), Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y8))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, Y1), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 '#sk2'), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 Y1), Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y9))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y5))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y9)))))))))))))))))))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['1'])). 220.43/34.42 tff('3', plain, 220.43/34.42 ~ (!!((^[Y0 : d]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), Y1), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk4'), 220.43/34.42 Y2), 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), 220.43/34.42 Y3)))) => 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (!!((^[Y5 : u]: 220.43/34.42 (!!((^[Y6 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 Y0), Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 Y0, 220.43/34.42 '#sk3'), 220.43/34.42 Y6)))) => 220.43/34.42 (!!((^[Y7 : u]: 220.43/34.42 (!!(( 220.43/34.42 ^[Y8 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y7), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y8)))) <=> 220.43/34.42 ( 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y7))))& 220.43/34.42 ( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 Y0), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk2'), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 Y0), Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y7))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 Y0), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk2'), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 Y0), Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y8))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y4))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y8))))))))))))))))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['2'])). 220.43/34.42 tff('4', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), Y0), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk4'), Y1), 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), Y2)))) => 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (!!((^[Y5 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', '#sk5'), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk5', '#sk3'), 220.43/34.42 Y5)))) => 220.43/34.42 (!!((^[Y6 : u]: 220.43/34.42 (!!((^[Y7 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y6), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y7)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y6))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk2'), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 '#sk5'), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y6))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk2'), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 '#sk5'), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y7))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y3))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y7)))))))))))))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['3'])). 220.43/34.42 tff('5', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk4'), Y0), 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), Y1)))) => 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 '#sk5'), Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk5', 220.43/34.42 '#sk3'), Y4)))) => 220.43/34.42 (!!((^[Y5 : u]: 220.43/34.42 (!!((^[Y6 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y5), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y6)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y5))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk2'), 220.43/34.42 Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 '#sk5'), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y5))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', 220.43/34.42 '#sk2'), 220.43/34.42 Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 '#sk5'), 220.43/34.42 Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y6))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y2))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 Y6))))))))))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['4'])). 220.43/34.42 tff('6', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk4'), '#sk7'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), Y0)))) => 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', '#sk5'), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk5', '#sk3'), 220.43/34.42 Y3)))) => 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (!!((^[Y5 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 Y4), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 Y5)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y1))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 Y4))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', '#sk2'), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', '#sk5'), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 Y4))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk4', '#sk2'), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', '#sk5'), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 Y5))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y1))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 Y5)))))))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['5'])). 220.43/34.42 tff('7', plain, 220.43/34.42 ~ (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk4'), '#sk7'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8')))) => 220.43/34.42 (!!((^[Y0 : u]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), Y0), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), Y1), 220.43/34.42 s(tyop_2Emin_2Efun('#sk5', '#sk3'), Y2)))) => 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y4)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), Y3))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk2'), '#sk8'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 '#sk5'), Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y3))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk2'), '#sk8'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 '#sk5'), Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y4))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), Y4))))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['6'])). 220.43/34.42 tff('8', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), Y0), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), Y1), 220.43/34.42 s(tyop_2Emin_2Efun('#sk5', '#sk3'), Y2)))) => 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (!!((^[Y4 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y3), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y4)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y3))))& 220.43/34.42 (s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk2'), '#sk8'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 '#sk5'), Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y3))) = 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', 220.43/34.42 '#sk2'), '#sk8'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 '#sk5'), Y1), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y4))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 '#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 Y0))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), Y4)))))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_imply', [status(thm)], ['7'])). 220.43/34.42 tff('9', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), Y0), 220.43/34.42 s(tyop_2Emin_2Efun('#sk5', '#sk3'), Y1)))) => 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 Y2), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 Y3)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk9'))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 Y2))))& 220.43/34.42 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', '#sk2'), 220.43/34.42 '#sk8'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', '#sk5'), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 Y2))) = 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk4', '#sk2'), 220.43/34.42 '#sk8'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', '#sk5'), 220.43/34.42 Y0), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 Y3))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 '#sk9'))), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 Y3))))))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['8'])). 220.43/34.42 tff('10', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk5', '#sk3'), Y0)))) => 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y2)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1))))& 220.43/34.42 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), 220.43/34.42 '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), 220.43/34.42 '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1))) = 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), 220.43/34.42 '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), 220.43/34.42 '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y2))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y2)))))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['9'])). 220.43/34.42 tff('11', plain, 220.43/34.42 ~ (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk5', '#sk3'), '#sk11')))) => 220.43/34.42 (!!((^[Y0 : u]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0))))& 220.43/34.42 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0))) = 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1))))))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['10'])). 220.43/34.42 tff('12', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (!!((^[Y1 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0))))& 220.43/34.42 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0))) = 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y1)))))))))))), 220.43/34.42 inference('lazy_cnf_imply', [status(thm)], ['11'])). 220.43/34.42 tff('13', plain, 220.43/34.42 ~ (!!((^[Y0 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0)))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.42 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), 220.43/34.42 '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), Y0))))))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['12'])). 220.43/34.42 tff('14', plain, 220.43/34.42 ~ (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) <=> 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.42 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))))), 220.43/34.42 inference('lazy_cnf_exists', [status(thm)], ['13'])). 220.43/34.42 tff('15', plain, 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) 220.43/34.42 != (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.42 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.42 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.42 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))& 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk2', 220.43/34.42 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.42 s( 220.43/34.42 tyop_2Emin_2Efun('#sk3', 220.43/34.42 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.42 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))), 220.43/34.42 inference('simplify nested equalities', [status(thm)], ['14'])). 220.43/34.42 tff(arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool, axiom, 220.43/34.42 (![A_27a:d,A_27b:d,X0_2E0:u,X1_2E0:u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 X0_2E0), 220.43/34.42 s(tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 X1_2E0)))) = 220.43/34.42 j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.42 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool), 220.43/34.42 app_2E2(s(tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 c_2Equotient_2Erespects_2E0), 220.43/34.42 s(tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 tyop_2Emin_2Efun( 220.43/34.42 A_27a,A_27b), 220.43/34.42 tyop_2Emin_2Ebool)), 220.43/34.42 X0_2E0))), 220.43/34.42 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.42 X1_2E0))))))). 220.43/34.42 tff('16', plain, 220.43/34.42 (!!((^[Y0 : d]: 220.43/34.42 (!!((^[Y1 : d]: 220.43/34.42 (!!((^[Y2 : u]: 220.43/34.42 (!!((^[Y3 : u]: 220.43/34.42 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.42 s(tyop_2Emin_2Ebool, 220.43/34.42 c_2Equotient_2Erespects_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool)), Y2), 220.43/34.43 s(tyop_2Emin_2Efun(Y0, Y1), Y3)))) = 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2Erespects_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool)), Y2))), 220.43/34.43 s(tyop_2Emin_2Efun(Y0, Y1), Y3))))))))))))))))), 220.43/34.43 inference('cnf', [status(esa)], 220.43/34.43 [arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool])). 220.43/34.43 tff('17', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2Erespects_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Ebool)), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), Y2)))) = 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Ebool), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2Erespects_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Ebool)), Y1))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), Y2)))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['16'])). 220.43/34.43 tff('18', plain, 220.43/34.43 ![X1 : d, X2 : d]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2Erespects_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y1)))) = 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2Erespects_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), Y0))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y1))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['17'])). 220.43/34.43 tff('19', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2Erespects_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), X3), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y0)))) = 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2Erespects_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), X3))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y0)))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['18'])). 220.43/34.43 tff('20', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2Erespects_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), tyop_2Emin_2Ebool)), 220.43/34.43 X3), s(tyop_2Emin_2Efun(X1, X2), X4)))) 220.43/34.43 = j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), c_2Equotient_2Erespects_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), X3))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), X4)))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['19'])). 220.43/34.43 tff(thm_2Equotient_2Erespects__def, axiom, 220.43/34.43 (![A_27a:d,A_27b:d]: 220.43/34.43 (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 c_2Equotient_2Erespects_2E0) = 220.43/34.43 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 c_2Ecombin_2EW_2E0)))). 220.43/34.43 tff('21', plain, 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 c_2Equotient_2Erespects_2E0) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), c_2Ecombin_2EW_2E0)))))))), 220.43/34.43 inference('cnf', [status(esa)], [thm_2Equotient_2Erespects__def])). 220.43/34.43 tff('22', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, Y0)), 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), c_2Equotient_2Erespects_2E0) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, Y0)), 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), c_2Ecombin_2EW_2E0))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['21'])). 220.43/34.43 tff('23', plain, 220.43/34.43 ![X1 : d, X2 : d]: 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), c_2Equotient_2Erespects_2E0) 220.43/34.43 = s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), c_2Ecombin_2EW_2E0), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['22'])). 220.43/34.43 tff(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b, axiom, 220.43/34.43 (![A_27a:d,A_27b:d,X0_2E0:u,X1_2E0:u]: 220.43/34.43 (s(A_27b, 220.43/34.43 c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a, 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 X0_2E0), 220.43/34.43 s(A_27a,X1_2E0))) = 220.43/34.43 s(A_27b, 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b)), 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 c_2Ecombin_2EW_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(A_27a, 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 X0_2E0))), 220.43/34.43 s(A_27a,X1_2E0)))))). 220.43/34.43 tff('24', plain, 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (s(Y1, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), Y2), 220.43/34.43 s(Y0, Y3))) = 220.43/34.43 s(Y1, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 c_2Ecombin_2EW_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), Y2))), 220.43/34.43 s(Y0, Y3)))))))))))))))), 220.43/34.43 inference('cnf', [status(esa)], 220.43/34.43 [arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b])). 220.43/34.43 tff('25', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (s(Y0, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), Y1), 220.43/34.43 s(X1, Y2))) = 220.43/34.43 s(Y0, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), 220.43/34.43 c_2Ecombin_2EW_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), Y1))), 220.43/34.43 s(X1, Y2))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['24'])). 220.43/34.43 tff('26', plain, 220.43/34.43 ![X1 : d, X2 : d]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (s(X2, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 Y0), s(X1, Y1))) = 220.43/34.43 s(X2, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Ecombin_2EW_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), Y0))), 220.43/34.43 s(X1, Y1)))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['25'])). 220.43/34.43 tff('27', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (s(X2, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), 220.43/34.43 s(X1, Y0))) = 220.43/34.43 s(X2, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), c_2Ecombin_2EW_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3))), 220.43/34.43 s(X1, Y0))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['26'])). 220.43/34.43 tff('28', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.43 s(X2, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), s(X1, X4))) 220.43/34.43 = s(X2, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), c_2Ecombin_2EW_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3))), 220.43/34.43 s(X1, X4))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['27'])). 220.43/34.43 tff('29', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2Erespects_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), tyop_2Emin_2Ebool)), 220.43/34.43 X3), s(tyop_2Emin_2Efun(X1, X2), X4)))) 220.43/34.43 = j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), X3), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), X4)))), 220.43/34.43 inference('demod', [status(thm)], ['20', '23', '28'])). 220.43/34.43 tff('30', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2Erespects_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), tyop_2Emin_2Ebool)), 220.43/34.43 X3), s(tyop_2Emin_2Efun(X1, X2), X4)))) 220.43/34.43 = j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), X3), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), X4)))), 220.43/34.43 inference('demod', [status(thm)], ['20', '23', '28'])). 220.43/34.43 tff('31', plain, 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) 220.43/34.43 != (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.43 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))& 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))), 220.43/34.43 inference('demod', [status(thm)], ['15', '29', '30'])). 220.43/34.43 tff('32', plain, 220.43/34.43 (~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) 220.43/34.43 | ~ (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.43 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))& 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))))), 220.43/34.43 inference('eq_elim', [status(thm)], ['31'])). 220.43/34.43 tff('33', plain, 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) 220.43/34.43 != (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.43 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))& 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))), 220.43/34.43 inference('demod', [status(thm)], ['15', '29', '30'])). 220.43/34.43 tff('34', plain, 220.43/34.43 ( j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) 220.43/34.43 | (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.43 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))& 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))))), 220.43/34.43 inference('eq_elim', [status(thm)], ['33'])). 220.43/34.43 tff('35', plain, 220.43/34.43 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) 220.43/34.43 = s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))) 220.43/34.43 | j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))), 220.43/34.43 inference('lazy_cnf_and', [status(thm)], ['34'])). 220.43/34.43 tff('36', plain, 220.43/34.43 ( j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) 220.43/34.43 | (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))))& 220.43/34.43 (s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'))) = 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk5'), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))& 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))))), 220.43/34.43 inference('eq_elim', [status(thm)], ['33'])). 220.43/34.43 tff('37', plain, 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk3', '#sk5'), '#sk10'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk5', '#sk3'), '#sk11')))), 220.43/34.43 inference('lazy_cnf_imply', [status(thm)], ['11'])). 220.43/34.43 tff('38', plain, 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk4'), '#sk7'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk4', '#sk2'), '#sk8')))), 220.43/34.43 inference('lazy_cnf_imply', [status(thm)], ['7'])). 220.43/34.43 tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d, axiom, 220.43/34.43 (![A_27a:d,A_27b:d,A_27c:d,A_27d:d,X0_2E0:u,X1_2E0:u,X2_2E0:u]: 220.43/34.43 (s(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = 220.43/34.43 s(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Efun(A_27c,A_27d)), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27c,A_27d))), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.43 A_27c,A_27a), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b,A_27d), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27c,A_27d)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))), 220.43/34.43 s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))), 220.43/34.43 s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))))). 220.43/34.43 tff('39', plain, 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : d]: 220.43/34.43 (!!((^[Y3 : d]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (!!((^[Y6 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y3), Y5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), Y6))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y3), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y3), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), 220.43/34.43 Y4))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y3), 220.43/34.43 Y5))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), Y6))))))))))))))))))))))))), 220.43/34.43 inference('cnf', [status(esa)], 220.43/34.43 [arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d])). 220.43/34.43 tff('40', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : d]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun(Y1, Y2), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y1, 220.43/34.43 X1), Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 Y2), Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 Y0), Y5))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y1, Y2), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y2)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y2))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, X1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y2)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, X1), 220.43/34.43 Y3))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), Y4))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 Y0), Y5)))))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['39'])). 220.43/34.43 tff('41', plain, 220.43/34.43 ![X1 : d, X2 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (s(tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun(Y0, X1), 220.43/34.43 Y2), 220.43/34.43 s(tyop_2Emin_2Efun(X2, Y1), 220.43/34.43 Y3), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 Y4))) = 220.43/34.43 s(tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, X1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, X1), Y2))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, Y1), 220.43/34.43 Y3))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 Y4))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['40'])). 220.43/34.43 tff('42', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (s(tyop_2Emin_2Efun(X3, Y0), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X2, Y0), Y2), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y3))) = 220.43/34.43 s(tyop_2Emin_2Efun(X3, Y0), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, Y0)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X2, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, Y0))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, X1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 X2), 220.43/34.43 tyop_2Emin_2Efun(X3, 220.43/34.43 Y0)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), 220.43/34.43 Y1))), 220.43/34.43 s(tyop_2Emin_2Efun(X2, Y0), Y2))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y3)))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['41'])). 220.43/34.43 tff('43', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y2))) = 220.43/34.43 s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, X1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), Y0))), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y1))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y2))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['42'])). 220.43/34.43 tff('44', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y1))) = 220.43/34.43 s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, X1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X5))), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y0))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y1)))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['43'])). 220.43/34.43 tff('45', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y0))) = 220.43/34.43 s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X1), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X5))), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X6))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), Y0))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['44'])). 220.43/34.43 tff('46', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u]: 220.43/34.43 s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(X3, X1), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X6), s(tyop_2Emin_2Efun(X1, X2), X7))) 220.43/34.43 = s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X1), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X2, X4), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X5))), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X6))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), X7))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['45'])). 220.43/34.43 tff(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b, axiom, 220.43/34.43 (![A_27a:d,A_27b:d,A_27c:d,A_27d:d,X0_2E0:u,X1_2E0:u]: 220.43/34.43 (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))) = 220.43/34.43 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d), 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.43 A_27c,A_27d), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b))), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.43 A_27d,A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27c,A_27d), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))), 220.43/34.43 s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0)))))). 220.43/34.43 tff('47', plain, 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : d]: 220.43/34.43 (!!((^[Y3 : d]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y2, Y3), 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 Y2), Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y3, 220.43/34.43 Y1), Y5))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y2, Y3), 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y3, 220.43/34.43 Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y3, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), Y4))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y3, 220.43/34.43 Y1), Y5)))))))))))))))))))))), 220.43/34.43 inference('cnf', [status(esa)], 220.43/34.43 [arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b])). 220.43/34.43 tff('48', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : d]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y1, Y2), 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y1), 220.43/34.43 Y3), 220.43/34.43 s(tyop_2Emin_2Efun(Y2, Y0), 220.43/34.43 Y4))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y1, Y2), 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y2, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y1, Y2), 220.43/34.43 tyop_2Emin_2Efun(X1, Y0))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, Y1), 220.43/34.43 Y3))), 220.43/34.43 s(tyop_2Emin_2Efun(Y2, Y0), 220.43/34.43 Y4))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['47'])). 220.43/34.43 tff('49', plain, 220.43/34.43 ![X1 : d, X2 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), Y2), 220.43/34.43 s(tyop_2Emin_2Efun(Y1, X2), Y3))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun(X1, X2))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), Y2))), 220.43/34.43 s(tyop_2Emin_2Efun(Y1, X2), Y3)))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['48'])). 220.43/34.43 tff('50', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, Y0), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(Y0, X2), Y2))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, Y0), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, Y0), 220.43/34.43 tyop_2Emin_2Efun(X1, X2))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X3), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(Y0, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, Y0), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), Y1))), 220.43/34.43 s(tyop_2Emin_2Efun(Y0, X2), Y2))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['49'])). 220.43/34.43 tff('51', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y1))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X4, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X3), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X4, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), Y0))), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y1)))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['50'])). 220.43/34.43 tff('52', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y0))) = 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X4, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X3), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X4, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X5))), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y0))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['51'])). 220.43/34.43 tff('53', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u]: 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(X1, X3), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), X6))) 220.43/34.43 = s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X4, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X3), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X4, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)))), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X5))), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), X6))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['52'])). 220.43/34.43 tff('54', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u]: 220.43/34.43 s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(X3, X1), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X6), s(tyop_2Emin_2Efun(X1, X2), X7))) 220.43/34.43 = s(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(X3, X1), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X6))), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), X7))), 220.43/34.43 inference('demod', [status(thm)], ['46', '53'])). 220.43/34.43 tff('55', plain, 220.43/34.43 ( j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun('#sk2', '#sk3'), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'))), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13')))) 220.43/34.43 | j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk2', 220.43/34.43 tyop_2Emin_2Efun('#sk2', tyop_2Emin_2Ebool)), '#sk6'), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun('#sk3', 220.43/34.43 tyop_2Emin_2Efun('#sk3', tyop_2Emin_2Ebool)), '#sk9'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk12'), 220.43/34.43 s(tyop_2Emin_2Efun('#sk2', '#sk3'), '#sk13'))))), 220.43/34.43 inference('lazy_cnf_and', [status(thm)], ['34'])). 220.43/34.43 tff(thm_2Equotient_2EFUN__QUOTIENT, axiom, 220.43/34.43 (![A_27a:d,A_27b:d,A_27c:d,A_27d:d,V0R1_2E0:u,V1abs1_2E0:u,V2rep1_2E0:u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 V0R1_2E0), 220.43/34.43 s(tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27c), 220.43/34.43 V1abs1_2E0), 220.43/34.43 s(tyop_2Emin_2Efun( 220.43/34.43 A_27c,A_27a), 220.43/34.43 V2rep1_2E0)))) => 220.43/34.43 (![V3R2_2E0:u,V4abs2_2E0:u,V5rep2_2E0:u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3(s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 V3R2_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 A_27d), 220.43/34.43 V4abs2_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27d, 220.43/34.43 A_27b), 220.43/34.43 V5rep2_2E0)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3(s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 V0R1_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 V3R2_2E0))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27c, 220.43/34.43 A_27d)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27c, 220.43/34.43 A_27a), 220.43/34.43 V2rep1_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 A_27d), 220.43/34.43 V4abs2_2E0))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27c, 220.43/34.43 A_27d), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27c), 220.43/34.43 V1abs1_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27d, 220.43/34.43 A_27b), 220.43/34.43 V5rep2_2E0))))))))))). 220.43/34.43 tff('56', plain, 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : d]: 220.43/34.43 (!!((^[Y3 : d]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (!!((^[Y6 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), Y5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), Y6)))) => 220.43/34.43 (!!((^[Y7 : u]: 220.43/34.43 (!!((^[Y8 : u]: 220.43/34.43 (!!(( 220.43/34.43 ^[Y9 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y7), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y3), 220.43/34.43 Y8), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y3, Y1), 220.43/34.43 Y9)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y7))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), 220.43/34.43 Y6), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y3), 220.43/34.43 Y8))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y3), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), 220.43/34.43 Y5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y3, Y1), 220.43/34.43 Y9)))))))))))))))))))))))))))))))))))))), 220.43/34.43 inference('cnf', [status(esa)], [thm_2Equotient_2EFUN__QUOTIENT])). 220.43/34.43 tff('57', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : d]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y1), Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, X1), Y5)))) => 220.43/34.43 (!!((^[Y6 : u]: 220.43/34.43 (!!((^[Y7 : u]: 220.43/34.43 (!!(( 220.43/34.43 ^[Y8 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y6), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), 220.43/34.43 Y7), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), 220.43/34.43 Y8)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y6))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, X1), 220.43/34.43 Y5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y2), 220.43/34.43 Y7))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, Y2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y1), 220.43/34.43 Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y2, Y0), 220.43/34.43 Y8))))))))))))))))))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['56'])). 220.43/34.43 tff('58', plain, 220.43/34.43 ![X1 : d, X2 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y2), 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 Y3), 220.43/34.43 s(tyop_2Emin_2Efun(Y0, X1), 220.43/34.43 Y4)))) => 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (!!((^[Y6 : u]: 220.43/34.43 (!!((^[Y7 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, Y1), 220.43/34.43 Y6), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, X2), 220.43/34.43 Y7)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y2), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y5))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, X1), 220.43/34.43 Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, Y1), 220.43/34.43 Y6))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, Y0), 220.43/34.43 Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, X2), 220.43/34.43 Y7)))))))))))))))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['57'])). 220.43/34.43 tff('59', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Ebool)), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), Y2), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), Y3)))) => 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (!!((^[Y6 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, Y0), 220.43/34.43 Y5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, X2), 220.43/34.43 Y6)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y1), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y4))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X3, Y0)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X3, X1), 220.43/34.43 Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, Y0), 220.43/34.43 Y5))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X3, Y0), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X3), 220.43/34.43 Y2), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, X2), 220.43/34.43 Y6))))))))))))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['58'])). 220.43/34.43 tff('60', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Ebool)), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), Y2)))) => 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, X4), Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X4, X2), Y5)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y3))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X3, X1), Y2), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, X4), Y4))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X3, X4), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, X3), Y1), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X4, X2), Y5)))))))))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['59'])). 220.43/34.43 tff('61', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), Y1)))) => 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y2), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, X4), 220.43/34.43 Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X4, X2), 220.43/34.43 Y4)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 X2, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y2))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 X2), 220.43/34.43 tyop_2Emin_2Efun(X3, 220.43/34.43 X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X3, 220.43/34.43 X1), Y1), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 X4), Y3))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, 220.43/34.43 X4), 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 X3), Y0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X4, 220.43/34.43 X2), Y4))))))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['60'])). 220.43/34.43 tff('62', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), Y0)))) => 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Ebool)), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y2), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y3)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Ebool)), X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Ebool)), Y1))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), 220.43/34.43 Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), 220.43/34.43 Y2))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), 220.43/34.43 X6), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), 220.43/34.43 Y3)))))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['61'])). 220.43/34.43 tff('63', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.43 X5), s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7)))) => 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Ebool)), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y2)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Ebool)), X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Ebool)), Y0))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y1))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y2))))))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['62'])). 220.43/34.43 tff('64', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u]: 220.43/34.43 (~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7)))) 220.43/34.43 | (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Ebool)), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y1), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y2)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Ebool)), X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Ebool)), Y0))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y1))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y2))))))))))))))))), 220.43/34.43 inference('lazy_cnf_imply', [status(thm)], ['63'])). 220.43/34.43 tff('65', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u, X8 : u]: 220.43/34.43 ( (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.43 X8), s(tyop_2Emin_2Efun(X2, X4), Y0), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y1)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.43 X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.43 X8))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), Y0))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y1))))))))))))) 220.43/34.43 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['64'])). 220.43/34.43 tff('66', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u, X8 : u, X9 : u]: 220.43/34.43 ( (!!((^[Y0 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X8), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X9), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y0)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X8))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X9))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), Y0)))))))))) 220.43/34.43 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['65'])). 220.43/34.43 tff('67', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u, X8 : u, 220.43/34.43 X9 : u, X10 : u]: 220.43/34.43 ( (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X8), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X9), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), X10)))) => 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X8))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X9))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), X10))))))) 220.43/34.43 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['66'])). 220.43/34.43 tff('68', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : d, X4 : d, X5 : u, X6 : u, X7 : u, X8 : u, 220.43/34.43 X9 : u, X10 : u]: 220.43/34.43 (~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X8), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X9), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), X10)))) 220.43/34.43 | j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X2, 220.43/34.43 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X8))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 tyop_2Emin_2Efun(X3, X4)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7), 220.43/34.43 s(tyop_2Emin_2Efun(X2, X4), X9))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X3, X4), 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 c_2Equotient_2E_2D_2D_3E_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X4, X2), X10)))))) 220.43/34.43 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X5), 220.43/34.43 s(tyop_2Emin_2Efun(X1, X3), X6), 220.43/34.43 s(tyop_2Emin_2Efun(X3, X1), X7))))), 220.43/34.43 inference('lazy_cnf_imply', [status(thm)], ['67'])). 220.43/34.43 tff(thm_2Ecombin_2EW__THM, axiom, 220.43/34.43 (![A_27a:d,A_27b:d,V0f_2E0:u,V1x_2E0:u]: 220.43/34.43 (s(A_27b, 220.43/34.43 c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a, 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 V0f_2E0), 220.43/34.43 s(A_27a,V1x_2E0))) = 220.43/34.43 s(A_27b, 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(A_27a, 220.43/34.43 tyop_2Emin_2Efun(A_27a,A_27b)), 220.43/34.43 V0f_2E0), 220.43/34.43 s(A_27a,V1x_2E0))), 220.43/34.43 s(A_27a,V1x_2E0)))))). 220.43/34.43 tff('69', plain, 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (s(Y1, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), Y2), 220.43/34.43 s(Y0, Y3))) = 220.43/34.43 s(Y1, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(Y0, Y1), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Efun(Y0, Y1)), Y2), 220.43/34.43 s(Y0, Y3))), s(Y0, Y3)))))))))))))))), 220.43/34.43 inference('cnf', [status(esa)], [thm_2Ecombin_2EW__THM])). 220.43/34.43 tff('70', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (s(Y0, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), Y1), 220.43/34.43 s(X1, Y2))) = 220.43/34.43 s(Y0, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, Y0)), Y1), 220.43/34.43 s(X1, Y2))), s(X1, Y2))))))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['69'])). 220.43/34.43 tff('71', plain, 220.43/34.43 ![X1 : d, X2 : d]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (s(X2, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), 220.43/34.43 Y0), s(X1, Y1))) = 220.43/34.43 s(X2, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, X2)), Y0), s(X1, Y1))), 220.43/34.43 s(X1, Y1)))))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['70'])). 220.43/34.43 tff('72', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u]: 220.43/34.43 (!!((^[Y0 : u]: 220.43/34.43 (s(X2, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), 220.43/34.43 s(X1, Y0))) = 220.43/34.43 s(X2, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), 220.43/34.43 s(X1, Y0))), s(X1, Y0))))))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['71'])). 220.43/34.43 tff('73', plain, 220.43/34.43 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.43 s(X2, 220.43/34.43 c_2Ecombin_2EW_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), s(X1, X4))) 220.43/34.43 = s(X2, 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), 220.43/34.43 s(X1, X4))), s(X1, X4))), 220.43/34.43 inference('lazy_cnf_forall', [status(thm)], ['72'])). 220.43/34.43 tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b, axiom, 220.43/34.43 (![A_27a:d,A_27b:d,X0_2E0:u,X1_2E0:u,X2_2E0:u,X3_2E0:u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4(s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 X0_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 X1_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b), 220.43/34.43 X2_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b), 220.43/34.43 X3_2E0)))) = 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Ebool), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 app_2E2(s(tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b), 220.43/34.43 tyop_2Emin_2Ebool))), 220.43/34.43 app_2E2( 220.43/34.43 s(tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 A_27b), 220.43/34.43 tyop_2Emin_2Ebool)))), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.43 s(tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27a, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 X0_2E0))), 220.43/34.43 s(tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 A_27b, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 X1_2E0))), 220.43/34.43 s(tyop_2Emin_2Efun( 220.43/34.43 A_27a,A_27b),X2_2E0))), 220.43/34.43 s(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.43 X3_2E0))))))). 220.43/34.43 tff('74', plain, 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : d]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (!!((^[Y5 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y2), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y3), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 Y1), Y4), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 Y1), Y5)))) = 220.43/34.43 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool))), 220.43/34.43 app_2E2( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), 220.43/34.43 tyop_2Emin_2Ebool)))), 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y2))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y3))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun( 220.43/34.43 Y0, Y1), Y4))), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 Y1), Y5))))))))))))))))))))))), 220.43/34.43 inference('cnf', [status(esa)], 220.43/34.43 [arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b])). 220.43/34.43 tff('75', plain, 220.43/34.43 ![X1 : d]: 220.43/34.43 (!!((^[Y0 : d]: 220.43/34.43 (!!((^[Y1 : u]: 220.43/34.43 (!!((^[Y2 : u]: 220.43/34.43 (!!((^[Y3 : u]: 220.43/34.43 (!!((^[Y4 : u]: 220.43/34.43 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.43 s(tyop_2Emin_2Ebool, 220.43/34.43 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Efun(X1, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y1), 220.43/34.43 s( 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Efun(Y0, 220.43/34.43 tyop_2Emin_2Ebool)), 220.43/34.43 Y2), 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), 220.43/34.43 Y3), 220.43/34.43 s(tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 Y4)))) = 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y1))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y2))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 Y0), Y3))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 Y4)))))))))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['74'])). 220.43/34.44 tff('76', plain, 220.43/34.44 ![X1 : d, X2 : d]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (!!((^[Y3 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), Y0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), Y1), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y2), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y3)))) = 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X2, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y0))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y1))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y2))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y3))))))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['75'])). 220.43/34.44 tff('77', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), Y0), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y1), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y2)))) = 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), Y0))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y1))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y2)))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['76'])). 220.43/34.44 tff('78', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y0), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y1)))) = 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), X4))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y0))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y1))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['77'])). 220.43/34.44 tff('79', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X5), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y0)))) = 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 X4))), s(tyop_2Emin_2Efun(X1, X2), X5))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y0)))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['78'])). 220.43/34.44 tff('80', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u, X6 : u]: 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), 220.43/34.44 s(tyop_2Emin_2Efun(X2, tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 X4), s(tyop_2Emin_2Efun(X1, X2), X5), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X6)))) 220.43/34.44 = j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X4))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X5))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X6)))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['79'])). 220.43/34.44 tff(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b, axiom, 220.43/34.44 (![A_27a:d,A_27b:d,X0_2E0:u,X1_2E0:u]: 220.43/34.44 (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 X0_2E0), 220.43/34.44 s(tyop_2Emin_2Efun(A_27b, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27b, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 X1_2E0))) = 220.43/34.44 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27b,tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.44 A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun( 220.43/34.44 A_27b, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27b, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a,A_27b), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s(tyop_2Emin_2Efun(A_27a, 220.43/34.44 tyop_2Emin_2Efun(A_27a, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 X0_2E0))), 220.43/34.44 s(tyop_2Emin_2Efun(A_27b, 220.43/34.44 tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)), 220.43/34.44 X1_2E0)))))). 220.43/34.44 tff('81', plain, 220.43/34.44 (!!((^[Y0 : d]: 220.43/34.44 (!!((^[Y1 : d]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (!!((^[Y3 : u]: 220.43/34.44 (s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Ebool)), Y2), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Ebool)), Y3))) = 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Ebool)), Y2))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Efun(Y1, 220.43/34.44 tyop_2Emin_2Ebool)), Y3)))))))))))))))), 220.43/34.44 inference('cnf', [status(esa)], 220.43/34.44 [arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b])). 220.43/34.44 tff('82', plain, 220.43/34.44 ![X1 : d]: 220.43/34.44 (!!((^[Y0 : d]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 Y1), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, tyop_2Emin_2Ebool)), 220.43/34.44 Y2))) = 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, Y0), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), Y1))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, tyop_2Emin_2Ebool)), 220.43/34.44 Y2))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['81'])). 220.43/34.44 tff('83', plain, 220.43/34.44 ![X1 : d, X2 : d]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), Y0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), Y1))) = 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 Y0))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), Y1)))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['82'])). 220.43/34.44 tff('84', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), Y0))) = 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), Y0))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['83'])). 220.43/34.44 tff('85', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), tyop_2Emin_2Ebool)), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), 220.43/34.44 s(tyop_2Emin_2Efun(X2, tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 X4))) 220.43/34.44 = s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), tyop_2Emin_2Ebool)), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool))), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)))), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E0), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3))), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 X4))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['84'])). 220.43/34.44 tff('86', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u, X6 : u]: 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E4( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), 220.43/34.44 s(tyop_2Emin_2Efun(X2, tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), 220.43/34.44 X4), s(tyop_2Emin_2Efun(X1, X2), X5), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X6)))) 220.43/34.44 = j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 c_2Equotient_2E_3D_3D_3D_3E_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X2, 220.43/34.44 tyop_2Emin_2Efun(X2, tyop_2Emin_2Ebool)), X4))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X5))), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X6)))), 220.43/34.44 inference('demod', [status(thm)], ['80', '85'])). 220.43/34.44 tff(thm_2Equotient_2EQUOTIENT__REL, axiom, 220.43/34.44 (![A_27a:d,A_27b:d,V0R_2E0:u,V1abs_2E0:u,V2rep_2E0:u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 V0R_2E0), 220.43/34.44 s(tyop_2Emin_2Efun( 220.43/34.44 A_27a,A_27b), 220.43/34.44 V1abs_2E0), 220.43/34.44 s(tyop_2Emin_2Efun( 220.43/34.44 A_27b,A_27a), 220.43/34.44 V2rep_2E0)))) => 220.43/34.44 (![V3r_2E0:u,V4s_2E0:u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(A_27a, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 V0R_2E0), 220.43/34.44 s(A_27a,V4s_2E0))), 220.43/34.44 s(A_27a,V4s_2E0)))) & 220.43/34.44 (s(A_27b, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0), 220.43/34.44 s(A_27a,V3r_2E0))) = 220.43/34.44 s(A_27b, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0), 220.43/34.44 s(A_27a,V4s_2E0)))) & 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(A_27a, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 V0R_2E0), 220.43/34.44 s(A_27a,V3r_2E0))), 220.43/34.44 s(A_27a,V3r_2E0))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(A_27a, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 A_27a, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 V0R_2E0), 220.43/34.44 s(A_27a,V3r_2E0))), 220.43/34.44 s(A_27a,V4s_2E0))))))))). 220.43/34.44 tff('87', plain, 220.43/34.44 (!!((^[Y0 : d]: 220.43/34.44 (!!((^[Y1 : d]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (!!((^[Y3 : u]: 220.43/34.44 (!!((^[Y4 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Efun(Y0, 220.43/34.44 tyop_2Emin_2Ebool)), Y2), 220.43/34.44 s(tyop_2Emin_2Efun(Y0, Y1), 220.43/34.44 Y3), 220.43/34.44 s(tyop_2Emin_2Efun(Y1, Y0), 220.43/34.44 Y4)))) => 220.43/34.44 (!!((^[Y5 : u]: 220.43/34.44 (!!((^[Y6 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y2), 220.43/34.44 s(Y0, Y6))), 220.43/34.44 s(Y0, Y6))))& 220.43/34.44 (s(Y1, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, Y1), 220.43/34.44 Y3), 220.43/34.44 s(Y0, Y5))) = 220.43/34.44 s(Y1, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, Y1), 220.43/34.44 Y3), 220.43/34.44 s(Y0, Y6))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y2), 220.43/34.44 s(Y0, Y5))), 220.43/34.44 s(Y0, Y5))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 Y0, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y2), 220.43/34.44 s(Y0, Y5))), 220.43/34.44 s(Y0, Y6))))))))))))))))))))))))))), 220.43/34.44 inference('cnf', [status(esa)], [thm_2Equotient_2EQUOTIENT__REL])). 220.43/34.44 tff('88', plain, 220.43/34.44 ![X1 : d]: 220.43/34.44 (!!((^[Y0 : d]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (!!((^[Y3 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), Y1), 220.43/34.44 s(tyop_2Emin_2Efun(X1, Y0), Y2), 220.43/34.44 s(tyop_2Emin_2Efun(Y0, X1), Y3)))) => 220.43/34.44 (!!((^[Y4 : u]: 220.43/34.44 (!!((^[Y5 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y1), 220.43/34.44 s(X1, Y5))), 220.43/34.44 s(X1, Y5))))& 220.43/34.44 (s(Y0, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), Y2), 220.43/34.44 s(X1, Y4))) = 220.43/34.44 s(Y0, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, Y0), Y2), 220.43/34.44 s(X1, Y5))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y1), 220.43/34.44 s(X1, Y4))), 220.43/34.44 s(X1, Y4))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y1), 220.43/34.44 s(X1, Y4))), 220.43/34.44 s(X1, Y5)))))))))))))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['87'])). 220.43/34.44 tff('89', plain, 220.43/34.44 ![X1 : d, X2 : d]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), Y0), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y1), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), Y2)))) => 220.43/34.44 (!!((^[Y3 : u]: 220.43/34.44 (!!((^[Y4 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y0), s(X1, Y4))), 220.43/34.44 s(X1, Y4))))& 220.43/34.44 (s(X2, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 Y1), s(X1, Y3))) = 220.43/34.44 s(X2, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, X2), 220.43/34.44 Y1), s(X1, Y4))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y0), s(X1, Y3))), 220.43/34.44 s(X1, Y3))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun( 220.43/34.44 X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 Y0), s(X1, Y3))), 220.43/34.44 s(X1, Y4))))))))))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['88'])). 220.43/34.44 tff('90', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y0), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), Y1)))) => 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 (!!((^[Y3 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(X1, Y3))), 220.43/34.44 s(X1, Y3))))& 220.43/34.44 (s(X2, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y0), 220.43/34.44 s(X1, Y2))) = 220.43/34.44 s(X2, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), Y0), 220.43/34.44 s(X1, Y3))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(X1, Y2))), 220.43/34.44 s(X1, Y2))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, Y2))), s(X1, Y3)))))))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['89'])). 220.43/34.44 tff('91', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), Y0)))) => 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 (!!((^[Y2 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, Y2))), s(X1, Y2))))& 220.43/34.44 (s(X2, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(X1, Y1))) = 220.43/34.44 s(X2, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(X1, Y2))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, Y1))), s(X1, Y1))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, Y1))), s(X1, Y2))))))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['90'])). 220.43/34.44 tff('92', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u]: 220.43/34.44 (j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), X5)))) => 220.43/34.44 (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(X1, Y1))), s(X1, Y1))))& 220.43/34.44 (s(X2, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(X1, Y0))) = 220.43/34.44 s(X2, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(X1, Y1))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(X1, Y0))), s(X1, Y0))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(X1, Y0))), s(X1, Y1)))))))))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['91'])). 220.43/34.44 tff('93', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u]: 220.43/34.44 (~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), X5)))) 220.43/34.44 | (!!((^[Y0 : u]: 220.43/34.44 (!!((^[Y1 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, Y1))), s(X1, Y1))))& 220.43/34.44 (s(X2, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(X1, Y0))) = 220.43/34.44 s(X2, 220.43/34.44 app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(X1, Y1))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, Y0))), s(X1, Y0))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Ebool)), X3), s(X1, Y0))), 220.43/34.44 s(X1, Y1)))))))))))), 220.43/34.44 inference('lazy_cnf_imply', [status(thm)], ['92'])). 220.43/34.44 tff('94', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u, X6 : u]: 220.43/34.44 ( (!!((^[Y0 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, Y0))), s(X1, Y0))))& 220.43/34.44 (s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, X6))) = 220.43/34.44 s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, Y0))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X6))), s(X1, X6))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X6))), s(X1, Y0)))))))) 220.43/34.44 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), X5))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['93'])). 220.43/34.44 tff('95', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u, X6 : u, X7 : u]: 220.43/34.44 ( ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X7))), s(X1, X7))))& 220.43/34.44 (s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, X6))) = 220.43/34.44 s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, X7))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X6))), s(X1, X6))))) <=> 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X6))), s(X1, X7))))) 220.43/34.44 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), X5))))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['94'])). 220.43/34.44 tff('96', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u, X6 : u, X7 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X7))), s(X1, X7))))& 220.43/34.44 (s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, X6))) = 220.43/34.44 s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, X7))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X6))), s(X1, X6))))) 220.43/34.44 = j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X6))), s(X1, X7)))) 220.43/34.44 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), X5))))), 220.43/34.44 inference('simplify nested equalities', [status(thm)], ['95'])). 220.43/34.44 tff('97', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.44 s(X2, 220.43/34.44 c_2Ecombin_2EW_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), s(X1, X4))) 220.43/34.44 = s(X2, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), 220.43/34.44 s(X1, X4))), s(X1, X4))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['72'])). 220.43/34.44 tff('98', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u]: 220.43/34.44 s(X2, 220.43/34.44 c_2Ecombin_2EW_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), s(X1, X4))) 220.43/34.44 = s(X2, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, X2)), X3), 220.43/34.44 s(X1, X4))), s(X1, X4))), 220.43/34.44 inference('lazy_cnf_forall', [status(thm)], ['72'])). 220.43/34.44 tff('99', plain, 220.43/34.44 ![X1 : d, X2 : d, X3 : u, X4 : u, X5 : u, X6 : u, X7 : u]: 220.43/34.44 ((j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Ecombin_2EW_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(X1, X7))))& 220.43/34.44 (s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, X6))) = 220.43/34.44 s(X2, app_2E2(s(tyop_2Emin_2Efun(X1, X2), X4), s(X1, X7))))& 220.43/34.44 j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Ecombin_2EW_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), 220.43/34.44 X3), s(X1, X6))))) 220.43/34.44 = j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 app_2E2( 220.43/34.44 s(tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool), 220.43/34.44 app_2E2( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(X1, X6))), s(X1, X7)))) 220.43/34.44 | ~ j_mono_2Etyop_2Emin_2Ebool( 220.43/34.44 s(tyop_2Emin_2Ebool, 220.43/34.44 c_2Equotient_2EQUOTIENT_2E3( 220.43/34.44 s( 220.43/34.44 tyop_2Emin_2Efun(X1, 220.43/34.44 tyop_2Emin_2Efun(X1, tyop_2Emin_2Ebool)), X3), 220.43/34.44 s(tyop_2Emin_2Efun(X1, X2), X4), 220.43/34.44 s(tyop_2Emin_2Efun(X2, X1), X5))))), 220.43/34.44 inference('demod', [status(thm)], ['96', '97', '98'])). 220.43/34.44 tff('100', plain, $false, 220.43/34.44 inference('eprover', [status(thm)], 220.43/34.44 ['32', '35', '36', '37', '38', '54', '55', '68', '73', '86', 220.43/34.44 '99'])). 220.43/34.44 220.43/34.44 % SZS output end Refutation 220.43/34.44 220.43/34.44 220.43/34.44 % Terminating... 220.79/34.52 % Runner terminated. 220.79/34.54 % Zipperpin 1.5 exiting 220.79/34.55 EOF