0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Lz7xMO2ser true 0.12/0.34 % Computer : n026.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 05:34:34 EDT 2022 0.18/0.34 % CPUTime : 0.18/0.34 % Running portfolio for 960 s 0.18/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.18/0.34 % Number of cores: 8 0.18/0.34 % Python version: Python 3.6.8 0.18/0.34 % Running in FO mode 0.53/0.64 % Total configuration time : 435 0.53/0.64 % Estimated wc time : 845 0.53/0.64 % Estimated cpu time (7 cpus) : 120.71428571428571 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 58s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 58s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 58s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 49s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 39s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 39s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 39s 271.54/39.60 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 39s 271.82/39.61 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 39s 272.10/39.71 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 39s 340.97/49.61 % /export/starexec/sandbox2/solver/bin/fo/fo2.sh running for 29s 402.69/58.62 % /export/starexec/sandbox2/solver/bin/fo/fo14.sh running for 39s 402.69/58.69 % /export/starexec/sandbox2/solver/bin/fo/fo20.sh running for 39s 403.24/58.75 % /export/starexec/sandbox2/solver/bin/fo/fo19.sh running for 39s 413.04/60.15 % Solved by fo/fo1_lcnf.sh. 413.04/60.15 % done 14177 iterations in 20.260s 413.04/60.15 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 413.04/60.15 % SZS output start Refutation 413.04/60.15 thf('#sk33_type', type, '#sk33': $i). 413.04/60.15 thf('#sk39_type', type, '#sk39': $i). 413.04/60.15 thf('#sk25_type', type, '#sk25': $i). 413.04/60.15 thf(cong_type, type, cong: $i > $i > $i > $i > $o). 413.04/60.15 thf('#sk34_type', type, '#sk34': $i). 413.04/60.15 thf('#sk36_type', type, '#sk36': $i). 413.04/60.15 thf('#sk29_type', type, '#sk29': $i). 413.04/60.15 thf('#sk31_type', type, '#sk31': $i). 413.04/60.15 thf('#sk17_type', type, '#sk17': $i > $i > $i > $i > $i > $i > $i). 413.04/60.15 thf(midp_type, type, midp: $i > $i > $i > $o). 413.04/60.15 thf('#sk32_type', type, '#sk32': $i). 413.04/60.15 thf('#sk26_type', type, '#sk26': $i). 413.04/60.15 thf(circle_type, type, circle: $i > $i > $i > $i > $o). 413.04/60.15 thf('#sk30_type', type, '#sk30': $i). 413.04/60.15 thf('#sk22_type', type, '#sk22': $i). 413.04/60.15 thf(perp_type, type, perp: $i > $i > $i > $i > $o). 413.04/60.15 thf('#sk38_type', type, '#sk38': $i). 413.04/60.15 thf(cyclic_type, type, cyclic: $i > $i > $i > $i > $o). 413.04/60.15 thf('#sk21_type', type, '#sk21': $i). 413.04/60.15 thf(eqangle_type, type, eqangle: $i > $i > $i > $i > $i > $i > $i > $i > $o). 413.04/60.15 thf('#sk35_type', type, '#sk35': $i). 413.04/60.15 thf('#sk23_type', type, '#sk23': $i). 413.04/60.15 thf('#sk40_type', type, '#sk40': $i). 413.04/60.15 thf('#sk28_type', type, '#sk28': $i). 413.04/60.15 thf(coll_type, type, coll: $i > $i > $i > $o). 413.04/60.15 thf('#sk24_type', type, '#sk24': $i). 413.04/60.15 thf('#sk27_type', type, '#sk27': $i). 413.04/60.15 thf('#sk37_type', type, '#sk37': $i). 413.04/60.15 thf(para_type, type, para: $i > $i > $i > $i > $o). 413.04/60.15 thf(exemplo6GDDFULL012005, conjecture, 413.04/60.15 (![A:$i,B:$i,C:$i,H:$i,O:$i,C1:$i,B1:$i,A1:$i,MIDPNT1:$i,MIDPNT2:$i, 413.04/60.15 MIDPNT3:$i,MIDPNT4:$i,MIDPNT5:$i,MIDPNT6:$i,MIDPNT7:$i,MIDPNT8:$i, 413.04/60.15 MIDPNT9:$i,MIDPNT01:$i,MIDPNT11:$i,MIDPNT21:$i]: 413.04/60.15 ( ( ( perp @ A @ B @ C @ H ) & ( midp @ MIDPNT1 @ A @ B ) & 413.04/60.15 ( midp @ MIDPNT2 @ A @ C ) & ( perp @ A @ C @ MIDPNT2 @ O ) & 413.04/60.15 ( midp @ MIDPNT3 @ B @ C ) & ( perp @ B @ C @ MIDPNT3 @ O ) & 413.04/60.15 ( midp @ MIDPNT4 @ A @ B ) & ( perp @ A @ B @ MIDPNT4 @ C1 ) & 413.04/60.15 ( midp @ MIDPNT5 @ A @ H ) & ( perp @ A @ H @ MIDPNT5 @ C1 ) & 413.04/60.15 ( midp @ MIDPNT6 @ B @ H ) & ( midp @ MIDPNT7 @ A @ H ) & 413.04/60.15 ( perp @ A @ H @ MIDPNT7 @ B1 ) & ( midp @ MIDPNT01 @ B @ H ) & 413.04/60.15 ( perp @ B @ H @ MIDPNT01 @ A1 ) & ( midp @ MIDPNT11 @ B @ C ) & 413.04/60.15 ( perp @ B @ C @ MIDPNT11 @ A1 ) & ( perp @ H @ C @ MIDPNT21 @ A1 ) & 413.04/60.15 ( midp @ MIDPNT21 @ H @ C ) & ( perp @ H @ C @ MIDPNT9 @ B1 ) & 413.04/60.15 ( midp @ MIDPNT9 @ H @ C ) & ( perp @ A @ C @ MIDPNT8 @ B1 ) & 413.04/60.15 ( midp @ MIDPNT8 @ A @ C ) & ( perp @ B @ H @ MIDPNT6 @ C1 ) & 413.04/60.15 ( perp @ A @ B @ MIDPNT1 @ O ) & ( perp @ B @ C @ A @ H ) & 413.04/60.15 ( perp @ A @ C @ B @ H ) ) => 413.04/60.15 ( perp @ A1 @ O @ B1 @ C1 ) ))). 413.04/60.15 thf(zf_stmt_0, negated_conjecture, 413.04/60.15 (~( ![A:$i,B:$i,C:$i,H:$i,O:$i,C1:$i,B1:$i,A1:$i,MIDPNT1:$i,MIDPNT2:$i, 413.04/60.15 MIDPNT3:$i,MIDPNT4:$i,MIDPNT5:$i,MIDPNT6:$i,MIDPNT7:$i,MIDPNT8:$i, 413.04/60.15 MIDPNT9:$i,MIDPNT01:$i,MIDPNT11:$i,MIDPNT21:$i]: 413.04/60.15 ( ( ( perp @ A @ B @ C @ H ) & ( midp @ MIDPNT1 @ A @ B ) & 413.04/60.15 ( midp @ MIDPNT2 @ A @ C ) & ( perp @ A @ C @ MIDPNT2 @ O ) & 413.04/60.15 ( midp @ MIDPNT3 @ B @ C ) & ( perp @ B @ C @ MIDPNT3 @ O ) & 413.04/60.15 ( midp @ MIDPNT4 @ A @ B ) & ( perp @ A @ B @ MIDPNT4 @ C1 ) & 413.04/60.15 ( midp @ MIDPNT5 @ A @ H ) & ( perp @ A @ H @ MIDPNT5 @ C1 ) & 413.04/60.15 ( midp @ MIDPNT6 @ B @ H ) & ( midp @ MIDPNT7 @ A @ H ) & 413.04/60.15 ( perp @ A @ H @ MIDPNT7 @ B1 ) & ( midp @ MIDPNT01 @ B @ H ) & 413.04/60.15 ( perp @ B @ H @ MIDPNT01 @ A1 ) & ( midp @ MIDPNT11 @ B @ C ) & 413.04/60.15 ( perp @ B @ C @ MIDPNT11 @ A1 ) & 413.04/60.15 ( perp @ H @ C @ MIDPNT21 @ A1 ) & ( midp @ MIDPNT21 @ H @ C ) & 413.04/60.15 ( perp @ H @ C @ MIDPNT9 @ B1 ) & ( midp @ MIDPNT9 @ H @ C ) & 413.04/60.15 ( perp @ A @ C @ MIDPNT8 @ B1 ) & ( midp @ MIDPNT8 @ A @ C ) & 413.04/60.15 ( perp @ B @ H @ MIDPNT6 @ C1 ) & ( perp @ A @ B @ MIDPNT1 @ O ) & 413.04/60.15 ( perp @ B @ C @ A @ H ) & ( perp @ A @ C @ B @ H ) ) => 413.04/60.15 ( perp @ A1 @ O @ B1 @ C1 ) ) )), 413.04/60.15 inference('cnf.neg', [status(esa)], [exemplo6GDDFULL012005])). 413.04/60.15 thf(zip_derived_cl94, plain, 413.04/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.04/60.15 (((!!) @ (^[Y1 : $i]: 413.04/60.15 (((!!) @ (^[Y2 : $i]: 413.04/60.15 (((!!) @ (^[Y3 : $i]: 413.04/60.15 (((!!) @ (^[Y4 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y5 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y6 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y7 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y8 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y9 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y10 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y11 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y12 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y13 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y14 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y15 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y16 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y17 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y18 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y19 : $i]: 413.04/60.15 (( 413.04/60.15 (( 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y1 @ 413.04/60.15 Y2 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y8 @ 413.04/60.15 Y0 @ Y1) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y9 @ 413.04/60.15 Y0 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y2 @ 413.04/60.15 Y9 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y10 @ 413.04/60.15 Y1 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y1 @ 413.04/60.15 Y2 @ 413.04/60.15 Y10 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y11 @ 413.04/60.15 Y0 @ Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y1 @ 413.04/60.15 Y11 @ Y5) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y12 @ 413.04/60.15 Y0 @ Y3) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y3 @ 413.04/60.15 Y12 @ Y5) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y13 @ 413.04/60.15 Y1 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y14 @ 413.04/60.15 Y0 @ Y3) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y3 @ 413.04/60.15 Y14 @ Y6) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y17 @ 413.04/60.15 Y1 @ Y3) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y1 @ 413.04/60.15 Y3 @ 413.04/60.15 Y17 @ Y7) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y18 @ 413.04/60.15 Y1 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y1 @ 413.04/60.15 Y2 @ 413.04/60.15 Y18 @ Y7) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y3 @ 413.04/60.15 Y2 @ 413.04/60.15 Y19 @ Y7) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y19 @ 413.04/60.15 Y3 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y3 @ 413.04/60.15 Y2 @ 413.04/60.15 Y16 @ Y6) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y16 @ 413.04/60.15 Y3 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y2 @ 413.04/60.15 Y15 @ Y6) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y15 @ 413.04/60.15 Y0 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y1 @ 413.04/60.15 Y3 @ 413.04/60.15 Y13 @ Y5) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y1 @ 413.04/60.15 Y8 @ Y4) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y1 @ 413.04/60.15 Y2 @ 413.04/60.15 Y0 @ Y3) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y2 @ 413.04/60.15 Y1 @ Y3))) => 413.04/60.15 (perp @ 413.04/60.15 Y7 @ 413.04/60.15 Y4 @ 413.04/60.15 Y6 @ Y5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 413.04/60.15 inference('cnf', [status(esa)], [zf_stmt_0])). 413.04/60.15 thf(zip_derived_cl1234, plain, 413.04/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.04/60.15 (((!!) @ (^[Y1 : $i]: 413.04/60.15 (((!!) @ (^[Y2 : $i]: 413.04/60.15 (((!!) @ (^[Y3 : $i]: 413.04/60.15 (((!!) @ (^[Y4 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y5 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y6 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y7 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y8 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y9 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y10 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y11 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y12 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y13 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y14 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y15 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y16 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y17 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y18 : $i]: 413.04/60.15 (( 413.04/60.15 (( 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 Y1 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y7 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y8 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1 @ 413.04/60.15 Y8 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y9 @ 413.04/60.15 Y0 @ Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y1 @ 413.04/60.15 Y9 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y10 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 Y10 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y11 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y2 @ 413.04/60.15 Y11 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y12 @ 413.04/60.15 Y0 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y13 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y2 @ 413.04/60.15 Y13 @ Y5) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y16 @ 413.04/60.15 Y0 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y2 @ 413.04/60.15 Y16 @ Y6) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y17 @ 413.04/60.15 Y0 @ Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y1 @ 413.04/60.15 Y17 @ Y6) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y2 @ 413.04/60.15 Y1 @ 413.04/60.15 Y18 @ Y6) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y18 @ 413.04/60.15 Y2 @ Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y2 @ 413.04/60.15 Y1 @ 413.04/60.15 Y15 @ Y5) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y15 @ 413.04/60.15 Y2 @ Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1 @ 413.04/60.15 Y14 @ Y5) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y14 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y2 @ 413.04/60.15 Y12 @ Y4) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 Y7 @ Y3) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 Y1 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1 @ 413.04/60.15 Y0 @ Y2))) => 413.04/60.15 (perp @ 413.04/60.15 Y6 @ 413.04/60.15 Y3 @ 413.04/60.15 Y5 @ Y4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 413.04/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl94])). 413.04/60.15 thf(zip_derived_cl1235, plain, 413.04/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.04/60.15 (((!!) @ (^[Y1 : $i]: 413.04/60.15 (((!!) @ (^[Y2 : $i]: 413.04/60.15 (((!!) @ (^[Y3 : $i]: 413.04/60.15 (((!!) @ (^[Y4 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y5 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y6 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y7 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y8 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y9 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y10 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y11 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y12 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y13 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y14 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y15 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y16 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y17 : $i]: 413.04/60.15 (( 413.04/60.15 (( 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0 @ Y1) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y6 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22') & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y7 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 Y7 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y8 @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0 @ 413.04/60.15 Y8 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y9 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y9 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y10 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1 @ 413.04/60.15 Y10 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y11 @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y1) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y12 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1 @ 413.04/60.15 Y12 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y15 @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y1 @ 413.04/60.15 Y15 @ Y5) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y16 @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0 @ 413.04/60.15 Y16 @ Y5) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y1 @ 413.04/60.15 Y0 @ 413.04/60.15 Y17 @ Y5) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y17 @ 413.04/60.15 Y1 @ Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y1 @ 413.04/60.15 Y0 @ 413.04/60.15 Y14 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y14 @ 413.04/60.15 Y1 @ Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 Y13 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y13 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y1 @ 413.04/60.15 Y11 @ Y3) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y6 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y1))) => 413.04/60.15 (perp @ 413.04/60.15 Y5 @ 413.04/60.15 Y2 @ 413.04/60.15 Y4 @ Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 413.04/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1234])). 413.04/60.15 thf(zip_derived_cl1236, plain, 413.04/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.04/60.15 (((!!) @ (^[Y1 : $i]: 413.04/60.15 (((!!) @ (^[Y2 : $i]: 413.04/60.15 (((!!) @ (^[Y3 : $i]: 413.04/60.15 (((!!) @ (^[Y4 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y5 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y6 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y7 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y8 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y9 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y10 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y11 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y12 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y13 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y14 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y15 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y16 : $i]: 413.04/60.15 (( 413.04/60.15 (( 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y5 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22') & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y6 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y6 @ Y1) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y7 @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y7 @ Y1) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y8 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y8 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y9 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 Y9 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y10 @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y11 @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0 @ 413.04/60.15 Y11 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y14 @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0 @ 413.04/60.15 Y14 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y15 @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y15 @ Y4) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y16 @ Y4) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y16 @ 413.04/60.15 Y0 @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 Y0 @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y13 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y13 @ 413.04/60.15 Y0 @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y12 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y12 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0 @ 413.04/60.15 Y10 @ Y2) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y5 @ Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 '#sk21' @ 413.04/60.15 Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y0))) => 413.04/60.15 (perp @ 413.04/60.15 Y4 @ 413.04/60.15 Y1 @ 413.04/60.15 Y3 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))), 413.04/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1235])). 413.04/60.15 thf(zip_derived_cl1237, plain, 413.04/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.04/60.15 (((!!) @ (^[Y1 : $i]: 413.04/60.15 (((!!) @ (^[Y2 : $i]: 413.04/60.15 (((!!) @ (^[Y3 : $i]: 413.04/60.15 (((!!) @ (^[Y4 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y5 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y6 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y7 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y8 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y9 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y10 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y11 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y12 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y13 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y14 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y15 : $i]: 413.04/60.15 (( 413.04/60.15 (( 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 '#sk24') & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y4 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22') & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y5 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y5 @ Y0) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y6 @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y6 @ Y0) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y7 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y7 @ Y1) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y8 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk24') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk24' @ 413.04/60.15 Y8 @ Y1) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y9 @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk24') & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y10 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk24') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk24' @ 413.04/60.15 Y10 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y13 @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk24') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk24' @ 413.04/60.15 Y13 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y14 @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y14 @ Y3) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk24' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y15 @ Y3) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y15 @ 413.04/60.15 '#sk24' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk24' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y12 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y12 @ 413.04/60.15 '#sk24' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23' @ 413.04/60.15 Y11 @ Y2) & 413.04/60.15 ( 413.04/60.15 midp @ 413.04/60.15 Y11 @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk24' @ 413.04/60.15 Y9 @ Y1) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk22' @ 413.04/60.15 Y4 @ Y0) & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk23' @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk24') & 413.04/60.15 ( 413.04/60.15 perp @ 413.04/60.15 '#sk21' @ 413.04/60.15 '#sk23' @ 413.04/60.15 '#sk22' @ 413.04/60.15 '#sk24'))) => 413.04/60.15 (perp @ 413.04/60.15 Y3 @ 413.04/60.15 Y0 @ 413.04/60.15 Y2 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))), 413.04/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1236])). 413.04/60.15 thf(zip_derived_cl1238, plain, 413.04/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.04/60.15 (((!!) @ (^[Y1 : $i]: 413.04/60.15 (((!!) @ (^[Y2 : $i]: 413.04/60.15 (((!!) @ (^[Y3 : $i]: 413.04/60.15 (((!!) @ (^[Y4 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y5 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y6 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y7 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y8 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y9 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y10 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y11 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y12 : $i]: 413.04/60.15 (( 413.04/60.15 (!!) @ ( 413.04/60.15 ^[Y13 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y14 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y6 @ Y0) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y7 @ Y0) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y9 @ Y1) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y12 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y12 @ Y2) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y13 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y13 @ Y2) & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y14 @ Y2) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y14 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y11 @ Y1) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y11 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y10 @ Y1) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y10 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y8 @ Y0) & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk25' @ 413.42/60.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1237])). 413.42/60.15 thf(zip_derived_cl1239, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y7 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y8 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y9 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y10 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y11 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y12 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y13 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y8 @ Y0) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y11 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y11 @ Y1) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y12 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y12 @ Y1) & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y13 @ Y1) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y13 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y10 @ Y0) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y10 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y9 @ Y0) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk25' @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk26')))))))))))))))))))))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1238])). 413.42/60.15 thf(zip_derived_cl1240, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y7 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y8 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y9 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y10 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y11 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y12 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y10 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y10 @ Y0) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y11 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y11 @ Y0) & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y12 @ Y0) & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y12 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk25' @ 413.42/60.15 '#sk27' @ 413.42/60.15 '#sk26'))))))))))))))))))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1239])). 413.42/60.15 thf(zip_derived_cl1241, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y7 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y8 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y9 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y10 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y11 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y10 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y10 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y11 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y11 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 '#sk28' @ 413.42/60.15 '#sk25' @ 413.42/60.15 '#sk27' @ 413.42/60.15 '#sk26')))))))))))))))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1240])). 413.42/60.15 thf(zip_derived_cl1242, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y7 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y8 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y9 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y10 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y10 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y10 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 '#sk28' @ 413.42/60.15 '#sk25' @ 413.42/60.15 '#sk27' @ 413.42/60.15 '#sk26'))))))))))))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1241])). 413.42/60.15 thf(zip_derived_cl1243, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y7 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y8 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y9 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y9 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 '#sk28' @ 413.42/60.15 '#sk25' @ 413.42/60.15 '#sk27' @ 413.42/60.15 '#sk26')))))))))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1242])). 413.42/60.15 thf(zip_derived_cl1244, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y7 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y8 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk31' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk31' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y8 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 '#sk28' @ 413.42/60.15 '#sk25' @ 413.42/60.15 '#sk27' @ 413.42/60.15 '#sk26'))))))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1243])). 413.42/60.15 thf(zip_derived_cl1245, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y7 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk31' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk31' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk32' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk32' @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y7 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 '#sk28' @ 413.42/60.15 '#sk25' @ 413.42/60.15 '#sk27' @ 413.42/60.15 '#sk26')))))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1244])). 413.42/60.15 thf(zip_derived_cl1246, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y6 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk30' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk31' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk31' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk32' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk32' @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 '#sk33' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk33' @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y1 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y4 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y5 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk28') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y6 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y3 @ 413.42/60.15 '#sk24' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk27') & 413.42/60.15 ( 413.42/60.15 midp @ 413.42/60.15 Y2 @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24' @ 413.42/60.15 Y0 @ 413.42/60.15 '#sk26') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk29' @ 413.42/60.15 '#sk25') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk24') & 413.42/60.15 ( 413.42/60.15 perp @ 413.42/60.15 '#sk21' @ 413.42/60.15 '#sk23' @ 413.42/60.15 '#sk22' @ 413.42/60.15 '#sk24'))) => 413.42/60.15 (perp @ 413.42/60.15 '#sk28' @ 413.42/60.15 '#sk25' @ 413.42/60.15 '#sk27' @ 413.42/60.15 '#sk26'))))))))))))))))))))))))), 413.42/60.15 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1245])). 413.42/60.15 thf(zip_derived_cl1247, plain, 413.42/60.15 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.15 (((!!) @ (^[Y1 : $i]: 413.42/60.15 (((!!) @ (^[Y2 : $i]: 413.42/60.15 (((!!) @ (^[Y3 : $i]: 413.42/60.15 (((!!) @ (^[Y4 : $i]: 413.42/60.15 (( 413.42/60.15 (!!) @ ( 413.42/60.15 ^[Y5 : $i]: 413.42/60.15 (( 413.42/60.15 (( 413.42/60.15 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk29' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk30' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk30' @ 413.42/60.16 '#sk25') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk31' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk31' @ 413.42/60.16 '#sk25') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk32' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk32' @ 413.42/60.16 '#sk26') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk33' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk33' @ 413.42/60.16 '#sk26') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk34' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y0 @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24' @ 413.42/60.16 Y0 @ 413.42/60.16 '#sk27') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y3 @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24' @ 413.42/60.16 Y3 @ 413.42/60.16 '#sk28') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y4 @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y4 @ 413.42/60.16 '#sk28') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y5 @ 413.42/60.16 '#sk28') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y5 @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y2 @ 413.42/60.16 '#sk27') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y2 @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y1 @ 413.42/60.16 '#sk27') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y1 @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk34' @ 413.42/60.16 '#sk26') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk29' @ 413.42/60.16 '#sk25') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24'))) => 413.42/60.16 (perp @ 413.42/60.16 '#sk28' @ 413.42/60.16 '#sk25' @ 413.42/60.16 '#sk27' @ 413.42/60.16 '#sk26')))))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1246])). 413.42/60.16 thf(zip_derived_cl1248, plain, 413.42/60.16 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (( 413.42/60.16 (( 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk29' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk30' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk30' @ 413.42/60.16 '#sk25') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk31' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk31' @ 413.42/60.16 '#sk25') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk32' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk32' @ 413.42/60.16 '#sk26') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk33' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk33' @ 413.42/60.16 '#sk26') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk34' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 '#sk35' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk35' @ 413.42/60.16 '#sk27') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y2 @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24' @ 413.42/60.16 Y2 @ 413.42/60.16 '#sk28') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y3 @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y3 @ 413.42/60.16 '#sk28') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y4 @ 413.42/60.16 '#sk28') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y4 @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y1 @ 413.42/60.16 '#sk27') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y1 @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 Y0 @ 413.42/60.16 '#sk27') & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y0 @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk34' @ 413.42/60.16 '#sk26') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk29' @ 413.42/60.16 '#sk25') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 ( 413.42/60.16 perp @ 413.42/60.16 '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk24'))) => 413.42/60.16 (perp @ 413.42/60.16 '#sk28' @ 413.42/60.16 '#sk25' @ 413.42/60.16 '#sk27' @ 413.42/60.16 '#sk26'))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1247])). 413.42/60.16 thf(zip_derived_cl1249, plain, 413.42/60.16 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((perp @ '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk23' @ '#sk24') & 413.42/60.16 (midp @ '#sk29' @ 413.42/60.16 '#sk21' @ '#sk22') & 413.42/60.16 (midp @ '#sk30' @ 413.42/60.16 '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk30' @ '#sk25') & 413.42/60.16 (midp @ '#sk31' @ 413.42/60.16 '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk31' @ '#sk25') & 413.42/60.16 (midp @ '#sk32' @ 413.42/60.16 '#sk21' @ '#sk22') & 413.42/60.16 (perp @ '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk32' @ '#sk26') & 413.42/60.16 (midp @ '#sk33' @ 413.42/60.16 '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk33' @ '#sk26') & 413.42/60.16 (midp @ '#sk34' @ 413.42/60.16 '#sk22' @ '#sk24') & 413.42/60.16 (midp @ '#sk35' @ 413.42/60.16 '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk35' @ '#sk27') & 413.42/60.16 (midp @ Y1 @ 413.42/60.16 '#sk22' @ '#sk24') & 413.42/60.16 (perp @ '#sk22' @ 413.42/60.16 '#sk24' @ Y1 @ 413.42/60.16 '#sk28') & 413.42/60.16 (midp @ Y2 @ 413.42/60.16 '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ 413.42/60.16 '#sk23' @ Y2 @ 413.42/60.16 '#sk28') & 413.42/60.16 (perp @ '#sk24' @ 413.42/60.16 '#sk23' @ Y3 @ 413.42/60.16 '#sk28') & 413.42/60.16 (midp @ Y3 @ 413.42/60.16 '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk24' @ 413.42/60.16 '#sk23' @ Y0 @ 413.42/60.16 '#sk27') & 413.42/60.16 (midp @ Y0 @ 413.42/60.16 '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk36' @ '#sk27') & 413.42/60.16 (midp @ '#sk36' @ 413.42/60.16 '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ 413.42/60.16 '#sk24' @ 413.42/60.16 '#sk34' @ '#sk26') & 413.42/60.16 (perp @ '#sk21' @ 413.42/60.16 '#sk22' @ 413.42/60.16 '#sk29' @ '#sk25') & 413.42/60.16 (perp @ '#sk22' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ 413.42/60.16 '#sk23' @ 413.42/60.16 '#sk22' @ '#sk24'))) => 413.42/60.16 (perp @ '#sk28' @ 413.42/60.16 '#sk25' @ '#sk27' @ 413.42/60.16 '#sk26')))))))))))))))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1248])). 413.42/60.16 thf(zip_derived_cl1250, plain, 413.42/60.16 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((perp @ '#sk21' @ '#sk22' @ 413.42/60.16 '#sk23' @ '#sk24') & 413.42/60.16 (midp @ '#sk29' @ '#sk21' @ 413.42/60.16 '#sk22') & 413.42/60.16 (midp @ '#sk30' @ '#sk21' @ 413.42/60.16 '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ 413.42/60.16 '#sk30' @ '#sk25') & 413.42/60.16 (midp @ '#sk31' @ '#sk22' @ 413.42/60.16 '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ 413.42/60.16 '#sk31' @ '#sk25') & 413.42/60.16 (midp @ '#sk32' @ '#sk21' @ 413.42/60.16 '#sk22') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ 413.42/60.16 '#sk32' @ '#sk26') & 413.42/60.16 (midp @ '#sk33' @ '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ 413.42/60.16 '#sk33' @ '#sk26') & 413.42/60.16 (midp @ '#sk34' @ '#sk22' @ 413.42/60.16 '#sk24') & 413.42/60.16 (midp @ '#sk35' @ '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ 413.42/60.16 '#sk35' @ '#sk27') & 413.42/60.16 (midp @ Y0 @ '#sk22' @ '#sk24') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ 413.42/60.16 Y0 @ '#sk28') & 413.42/60.16 (midp @ Y1 @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ 413.42/60.16 Y1 @ '#sk28') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ 413.42/60.16 Y2 @ '#sk28') & 413.42/60.16 (midp @ Y2 @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ 413.42/60.16 '#sk37' @ '#sk27') & 413.42/60.16 (midp @ '#sk37' @ '#sk24' @ 413.42/60.16 '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ 413.42/60.16 '#sk36' @ '#sk27') & 413.42/60.16 (midp @ '#sk36' @ '#sk21' @ 413.42/60.16 '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ 413.42/60.16 '#sk34' @ '#sk26') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ 413.42/60.16 '#sk29' @ '#sk25') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ 413.42/60.16 '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ 413.42/60.16 '#sk22' @ '#sk24'))) => 413.42/60.16 (perp @ '#sk28' @ '#sk25' @ 413.42/60.16 '#sk27' @ '#sk26'))))))))))))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1249])). 413.42/60.16 thf(zip_derived_cl1251, plain, 413.42/60.16 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((perp @ '#sk21' @ '#sk22' @ '#sk23' @ 413.42/60.16 '#sk24') & 413.42/60.16 (midp @ '#sk29' @ '#sk21' @ '#sk22') & 413.42/60.16 (midp @ '#sk30' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk30' @ 413.42/60.16 '#sk25') & 413.42/60.16 (midp @ '#sk31' @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk31' @ 413.42/60.16 '#sk25') & 413.42/60.16 (midp @ '#sk32' @ '#sk21' @ '#sk22') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk32' @ 413.42/60.16 '#sk26') & 413.42/60.16 (midp @ '#sk33' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk33' @ 413.42/60.16 '#sk26') & 413.42/60.16 (midp @ '#sk34' @ '#sk22' @ '#sk24') & 413.42/60.16 (midp @ '#sk35' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk35' @ 413.42/60.16 '#sk27') & 413.42/60.16 (midp @ '#sk38' @ '#sk22' @ '#sk24') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk38' @ 413.42/60.16 '#sk28') & 413.42/60.16 (midp @ Y0 @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ Y0 @ '#sk28') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ Y1 @ '#sk28') & 413.42/60.16 (midp @ Y1 @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ '#sk37' @ 413.42/60.16 '#sk27') & 413.42/60.16 (midp @ '#sk37' @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk36' @ 413.42/60.16 '#sk27') & 413.42/60.16 (midp @ '#sk36' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk34' @ 413.42/60.16 '#sk26') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk29' @ 413.42/60.16 '#sk25') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk21' @ 413.42/60.16 '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk22' @ 413.42/60.16 '#sk24'))) => 413.42/60.16 (perp @ '#sk28' @ '#sk25' @ '#sk27' @ 413.42/60.16 '#sk26')))))))))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1250])). 413.42/60.16 thf(zip_derived_cl1252, plain, 413.42/60.16 (~ (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((perp @ '#sk21' @ '#sk22' @ '#sk23' @ '#sk24') & 413.42/60.16 (midp @ '#sk29' @ '#sk21' @ '#sk22') & 413.42/60.16 (midp @ '#sk30' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk30' @ '#sk25') & 413.42/60.16 (midp @ '#sk31' @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk31' @ '#sk25') & 413.42/60.16 (midp @ '#sk32' @ '#sk21' @ '#sk22') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk32' @ '#sk26') & 413.42/60.16 (midp @ '#sk33' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk33' @ '#sk26') & 413.42/60.16 (midp @ '#sk34' @ '#sk22' @ '#sk24') & 413.42/60.16 (midp @ '#sk35' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk35' @ '#sk27') & 413.42/60.16 (midp @ '#sk38' @ '#sk22' @ '#sk24') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk38' @ '#sk28') & 413.42/60.16 (midp @ '#sk39' @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk39' @ '#sk28') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ Y0 @ '#sk28') & 413.42/60.16 (midp @ Y0 @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ '#sk37' @ '#sk27') & 413.42/60.16 (midp @ '#sk37' @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk36' @ '#sk27') & 413.42/60.16 (midp @ '#sk36' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk34' @ '#sk26') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk29' @ '#sk25') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk22' @ '#sk24'))) => 413.42/60.16 (perp @ '#sk28' @ '#sk25' @ '#sk27' @ '#sk26'))))))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1251])). 413.42/60.16 thf(zip_derived_cl1253, plain, 413.42/60.16 (~ (((((perp @ '#sk21' @ '#sk22' @ '#sk23' @ '#sk24') & 413.42/60.16 (midp @ '#sk29' @ '#sk21' @ '#sk22') & 413.42/60.16 (midp @ '#sk30' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk30' @ '#sk25') & 413.42/60.16 (midp @ '#sk31' @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk31' @ '#sk25') & 413.42/60.16 (midp @ '#sk32' @ '#sk21' @ '#sk22') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk32' @ '#sk26') & 413.42/60.16 (midp @ '#sk33' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk33' @ '#sk26') & 413.42/60.16 (midp @ '#sk34' @ '#sk22' @ '#sk24') & 413.42/60.16 (midp @ '#sk35' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk35' @ '#sk27') & 413.42/60.16 (midp @ '#sk38' @ '#sk22' @ '#sk24') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk38' @ '#sk28') & 413.42/60.16 (midp @ '#sk39' @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk39' @ '#sk28') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ '#sk40' @ '#sk28') & 413.42/60.16 (midp @ '#sk40' @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ '#sk37' @ '#sk27') & 413.42/60.16 (midp @ '#sk37' @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk36' @ '#sk27') & 413.42/60.16 (midp @ '#sk36' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk34' @ '#sk26') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk29' @ '#sk25') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk22' @ '#sk24'))) => 413.42/60.16 (perp @ '#sk28' @ '#sk25' @ '#sk27' @ '#sk26')))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1252])). 413.42/60.16 thf(zip_derived_cl1255, plain, 413.42/60.16 (~ (perp @ '#sk28' @ '#sk25' @ '#sk27' @ '#sk26')), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1253])). 413.42/60.16 thf(ruleD56, axiom, 413.42/60.16 (![A:$i,B:$i,P:$i,Q:$i]: 413.42/60.16 ( ( ( cong @ A @ P @ B @ P ) & ( cong @ A @ Q @ B @ Q ) ) => 413.42/60.16 ( perp @ A @ B @ P @ Q ) ))). 413.42/60.16 thf(zip_derived_cl5, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((cong @ Y0 @ Y2 @ 413.42/60.16 Y1 @ Y2) & (cong @ 413.42/60.16 Y0 @ Y3 @ Y1 @ Y3))) => 413.42/60.16 (perp @ Y0 @ Y1 @ 413.42/60.16 Y2 @ Y3)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD56])). 413.42/60.16 thf(zip_derived_cl342, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((cong @ X2 @ Y1 @ Y0 @ Y1) & 413.42/60.16 (cong @ X2 @ Y2 @ Y0 @ Y2))) => 413.42/60.16 (perp @ X2 @ Y0 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 413.42/60.16 thf(zip_derived_cl343, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((cong @ X2 @ Y0 @ X4 @ Y0) & (cong @ 413.42/60.16 X2 @ Y1 @ X4 @ Y1))) => 413.42/60.16 (perp @ X2 @ X4 @ Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl342])). 413.42/60.16 thf(zip_derived_cl344, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((cong @ X2 @ X6 @ X4 @ X6) & (cong @ X2 @ Y0 @ X4 @ 413.42/60.16 Y0))) => 413.42/60.16 (perp @ X2 @ X4 @ X6 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl343])). 413.42/60.16 thf(zip_derived_cl345, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((((cong @ X2 @ X6 @ X4 @ X6) & (cong @ X2 @ X8 @ X4 @ X8))) => 413.42/60.16 (perp @ X2 @ X4 @ X6 @ X8)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl344])). 413.42/60.16 thf(zip_derived_cl346, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (((cong @ X2 @ X6 @ X4 @ X6) & (cong @ X2 @ X8 @ X4 @ X8))) 413.42/60.16 | (perp @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl345])). 413.42/60.16 thf(zip_derived_cl347, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (cong @ X2 @ X6 @ X4 @ X6) 413.42/60.16 | ~ (cong @ X2 @ X8 @ X4 @ X8) 413.42/60.16 | (perp @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl346])). 413.42/60.16 thf(ruleD68, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i]: ( ( midp @ A @ B @ C ) => ( cong @ A @ B @ A @ C ) ))). 413.42/60.16 thf(zip_derived_cl66, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((midp @ Y0 @ Y1 @ Y2) => (cong @ 413.42/60.16 Y0 @ Y1 @ Y0 @ Y2))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD68])). 413.42/60.16 thf(zip_derived_cl128, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((midp @ X2 @ Y0 @ Y1) => (cong @ X2 @ Y0 @ 413.42/60.16 X2 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 413.42/60.16 thf(zip_derived_cl129, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((midp @ X2 @ X4 @ Y0) => (cong @ X2 @ X4 @ X2 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl128])). 413.42/60.16 thf(zip_derived_cl130, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((midp @ X2 @ X4 @ X6) => (cong @ X2 @ X4 @ X2 @ X6)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 413.42/60.16 thf(zip_derived_cl131, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (~ (midp @ X2 @ X4 @ X6) | (cong @ X2 @ X4 @ X2 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 413.42/60.16 thf(zip_derived_cl1254, plain, 413.42/60.16 ( (((perp @ '#sk21' @ '#sk22' @ '#sk23' @ '#sk24') & 413.42/60.16 (midp @ '#sk29' @ '#sk21' @ '#sk22') & 413.42/60.16 (midp @ '#sk30' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk30' @ '#sk25') & 413.42/60.16 (midp @ '#sk31' @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk31' @ '#sk25') & 413.42/60.16 (midp @ '#sk32' @ '#sk21' @ '#sk22') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk32' @ '#sk26') & 413.42/60.16 (midp @ '#sk33' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk33' @ '#sk26') & 413.42/60.16 (midp @ '#sk34' @ '#sk22' @ '#sk24') & 413.42/60.16 (midp @ '#sk35' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk24' @ '#sk35' @ '#sk27') & 413.42/60.16 (midp @ '#sk38' @ '#sk22' @ '#sk24') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk38' @ '#sk28') & 413.42/60.16 (midp @ '#sk39' @ '#sk22' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk39' @ '#sk28') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ '#sk40' @ '#sk28') & 413.42/60.16 (midp @ '#sk40' @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk24' @ '#sk23' @ '#sk37' @ '#sk27') & 413.42/60.16 (midp @ '#sk37' @ '#sk24' @ '#sk23') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk36' @ '#sk27') & 413.42/60.16 (midp @ '#sk36' @ '#sk21' @ '#sk23') & 413.42/60.16 (perp @ '#sk22' @ '#sk24' @ '#sk34' @ '#sk26') & 413.42/60.16 (perp @ '#sk21' @ '#sk22' @ '#sk29' @ '#sk25') & 413.42/60.16 (perp @ '#sk22' @ '#sk23' @ '#sk21' @ '#sk24') & 413.42/60.16 (perp @ '#sk21' @ '#sk23' @ '#sk22' @ '#sk24')))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1253])). 413.42/60.16 thf(zip_derived_cl1257, plain, ( (midp @ '#sk29' @ '#sk21' @ '#sk22')), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1254])). 413.42/60.16 thf(zip_derived_cl1257, plain, ( (midp @ '#sk29' @ '#sk21' @ '#sk22')), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1254])). 413.42/60.16 thf(ruleD11, axiom, 413.42/60.16 (![A:$i,B:$i,M:$i]: ( ( midp @ M @ B @ A ) => ( midp @ M @ A @ B ) ))). 413.42/60.16 thf(zip_derived_cl41, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((midp @ Y2 @ Y1 @ Y0) => (midp @ 413.42/60.16 Y2 @ Y0 @ Y1))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD11])). 413.42/60.16 thf(zip_derived_cl95, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((midp @ Y1 @ Y0 @ X2) => (midp @ Y1 @ X2 @ 413.42/60.16 Y0)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 413.42/60.16 thf(zip_derived_cl96, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((midp @ Y0 @ X4 @ X2) => (midp @ Y0 @ X2 @ X4))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 413.42/60.16 thf(zip_derived_cl97, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((midp @ X6 @ X4 @ X2) => (midp @ X6 @ X2 @ X4)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 413.42/60.16 thf(zip_derived_cl98, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (~ (midp @ X6 @ X4 @ X2) | (midp @ X6 @ X2 @ X4))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 413.42/60.16 thf(zip_derived_cl1283, plain, ( (midp @ '#sk29' @ '#sk22' @ '#sk21')), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl1257, zip_derived_cl98])). 413.42/60.16 thf(ruleX6, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,M:$i,N:$i]: 413.42/60.16 ( ?[P:$i]: 413.42/60.16 ( ( ( midp @ N @ C @ D ) & ( midp @ M @ A @ B ) ) => 413.42/60.16 ( ( midp @ P @ A @ D ) & ( para @ P @ N @ A @ C ) & 413.42/60.16 ( para @ P @ M @ B @ D ) ) ) ))). 413.42/60.16 thf(zip_derived_cl40, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (??) @ ( 413.42/60.16 ^[Y6 : $i]: 413.42/60.16 (( 413.42/60.16 (( 413.42/60.16 (midp @ 413.42/60.16 Y5 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3) & 413.42/60.16 (midp @ 413.42/60.16 Y4 @ 413.42/60.16 Y0 @ Y1))) => 413.42/60.16 (( 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y6 @ 413.42/60.16 Y0 @ Y3) & 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y6 @ 413.42/60.16 Y5 @ 413.42/60.16 Y0 @ Y2) & 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y6 @ 413.42/60.16 Y4 @ 413.42/60.16 Y1 @ Y3))))))))))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleX6])). 413.42/60.16 thf(zip_derived_cl1048, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (??) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (( 413.42/60.16 (midp @ 413.42/60.16 Y4 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2) & 413.42/60.16 (midp @ 413.42/60.16 Y3 @ 413.42/60.16 X2 @ Y0))) => 413.42/60.16 (( 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y5 @ 413.42/60.16 X2 @ Y2) & 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y5 @ 413.42/60.16 Y4 @ 413.42/60.16 X2 @ Y1) & 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y5 @ 413.42/60.16 Y3 @ 413.42/60.16 Y0 @ Y2)))))))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl40])). 413.42/60.16 thf(zip_derived_cl1049, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((??) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (( 413.42/60.16 (midp @ 413.42/60.16 Y3 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1) & 413.42/60.16 (midp @ 413.42/60.16 Y2 @ 413.42/60.16 X2 @ X4))) => 413.42/60.16 (( 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y4 @ 413.42/60.16 X2 @ Y1) & 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y4 @ 413.42/60.16 Y3 @ 413.42/60.16 X2 @ Y0) & 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y4 @ 413.42/60.16 Y2 @ 413.42/60.16 X4 @ Y1))))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1048])). 413.42/60.16 thf(zip_derived_cl1050, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((??) @ (^[Y3 : $i]: 413.42/60.16 (((((midp @ Y2 @ 413.42/60.16 X6 @ Y0) & 413.42/60.16 (midp @ Y1 @ 413.42/60.16 X2 @ X4))) => 413.42/60.16 (((midp @ Y3 @ 413.42/60.16 X2 @ Y0) & 413.42/60.16 (para @ Y3 @ 413.42/60.16 Y2 @ X2 @ X6) & 413.42/60.16 (para @ Y3 @ 413.42/60.16 Y1 @ X4 @ Y0)))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1049])). 413.42/60.16 thf(zip_derived_cl1051, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((??) @ (^[Y2 : $i]: 413.42/60.16 (((((midp @ Y1 @ X6 @ X8) & 413.42/60.16 (midp @ Y0 @ X2 @ X4))) => 413.42/60.16 (((midp @ Y2 @ X2 @ X8) & 413.42/60.16 (para @ Y2 @ Y1 @ X2 @ X6) & 413.42/60.16 (para @ Y2 @ Y0 @ X4 @ X8))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1050])). 413.42/60.16 thf(zip_derived_cl1052, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((??) @ (^[Y1 : $i]: 413.42/60.16 (((((midp @ Y0 @ X6 @ X8) & (midp @ X10 @ 413.42/60.16 X2 @ X4))) => 413.42/60.16 (((midp @ Y1 @ X2 @ X8) & 413.42/60.16 (para @ Y1 @ Y0 @ X2 @ X6) & 413.42/60.16 (para @ Y1 @ X10 @ X4 @ X8)))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1051])). 413.42/60.16 thf(zip_derived_cl1053, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((??) @ (^[Y0 : $i]: 413.42/60.16 (((((midp @ X12 @ X6 @ X8) & (midp @ X10 @ X2 @ X4))) => 413.42/60.16 (((midp @ Y0 @ X2 @ X8) & 413.42/60.16 (para @ Y0 @ X12 @ X2 @ X6) & 413.42/60.16 (para @ Y0 @ X10 @ X4 @ X8))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1052])). 413.42/60.16 thf(zip_derived_cl1054, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((((midp @ X12 @ X6 @ X8) & (midp @ X10 @ X2 @ X4))) => 413.42/60.16 (((midp @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X2 @ X8) & 413.42/60.16 (para @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X12 @ X2 @ X6) & 413.42/60.16 (para @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X10 @ X4 @ X8)))))), 413.42/60.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1053])). 413.42/60.16 thf(zip_derived_cl1055, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (((midp @ X12 @ X6 @ X8) & (midp @ X10 @ X2 @ X4))) 413.42/60.16 | (((midp @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X2 @ X8) & 413.42/60.16 (para @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X12 @ X2 @ 413.42/60.16 X6) & 413.42/60.16 (para @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X10 @ X4 @ 413.42/60.16 X8))))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1054])). 413.42/60.16 thf(zip_derived_cl1056, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (midp @ X12 @ X6 @ X8) 413.42/60.16 | ~ (midp @ X10 @ X2 @ X4) 413.42/60.16 | (((midp @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X2 @ X8) & 413.42/60.16 (para @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X12 @ X2 @ 413.42/60.16 X6) & 413.42/60.16 (para @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X10 @ X4 @ 413.42/60.16 X8))))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1055])). 413.42/60.16 thf(zip_derived_cl1057, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 ( (midp @ ('#sk17' @ X2 @ X4 @ X6 @ X8 @ X10 @ X12) @ X2 @ X8) 413.42/60.16 | ~ (midp @ X10 @ X2 @ X4) 413.42/60.16 | ~ (midp @ X12 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1056])). 413.42/60.16 thf(ruleD63, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,M:$i]: 413.42/60.16 ( ( ( midp @ M @ A @ B ) & ( midp @ M @ C @ D ) ) => 413.42/60.16 ( para @ A @ C @ B @ D ) ))). 413.42/60.16 thf(zip_derived_cl57, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((( 413.42/60.16 (midp @ 413.42/60.16 Y4 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1) & 413.42/60.16 (midp @ 413.42/60.16 Y4 @ 413.42/60.16 Y2 @ Y3))) => 413.42/60.16 (para @ 413.42/60.16 Y0 @ 413.42/60.16 Y2 @ 413.42/60.16 Y1 @ Y3))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD63])). 413.42/60.16 thf(zip_derived_cl300, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((midp @ Y3 @ 413.42/60.16 X2 @ Y0) & 413.42/60.16 (midp @ Y3 @ 413.42/60.16 Y1 @ Y2))) => 413.42/60.16 (para @ X2 @ Y1 @ 413.42/60.16 Y0 @ Y2)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 413.42/60.16 thf(zip_derived_cl301, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((midp @ Y2 @ X2 @ X4) & 413.42/60.16 (midp @ Y2 @ Y0 @ Y1))) => 413.42/60.16 (para @ X2 @ Y0 @ X4 @ Y1))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl300])). 413.42/60.16 thf(zip_derived_cl302, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((midp @ Y1 @ X2 @ X4) & (midp @ Y1 @ 413.42/60.16 X6 @ Y0))) => 413.42/60.16 (para @ X2 @ X6 @ X4 @ Y0)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl301])). 413.42/60.16 thf(zip_derived_cl303, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((midp @ Y0 @ X2 @ X4) & (midp @ Y0 @ X6 @ X8))) => 413.42/60.16 (para @ X2 @ X6 @ X4 @ X8))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl302])). 413.42/60.16 thf(zip_derived_cl304, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((((midp @ X10 @ X2 @ X4) & (midp @ X10 @ X6 @ X8))) => (para @ 413.42/60.16 X2 @ X6 @ X4 @ X8)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl303])). 413.42/60.16 thf(zip_derived_cl305, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (((midp @ X10 @ X2 @ X4) & (midp @ X10 @ X6 @ X8))) 413.42/60.16 | (para @ X2 @ X6 @ X4 @ X8))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])). 413.42/60.16 thf(zip_derived_cl306, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (midp @ X10 @ X2 @ X4) 413.42/60.16 | ~ (midp @ X10 @ X6 @ X8) 413.42/60.16 | (para @ X2 @ X6 @ X4 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl305])). 413.42/60.16 thf(zip_derived_cl307, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 ( (para @ X1 @ X1 @ X0 @ X0) | ~ (midp @ X2 @ X1 @ X0))), 413.42/60.16 inference('eq_fact', [status(thm)], [zip_derived_cl306])). 413.42/60.16 thf(zip_derived_cl1064, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 413.42/60.16 (~ (midp @ X2 @ X4 @ X0) 413.42/60.16 | ~ (midp @ X3 @ X1 @ X5) 413.42/60.16 | (para @ X1 @ X1 @ X0 @ X0))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl1057, zip_derived_cl307])). 413.42/60.16 thf(zip_derived_cl1649, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (midp @ X2 @ X1 @ X0) | (para @ X1 @ X1 @ '#sk21' @ '#sk21'))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl1283, zip_derived_cl1064])). 413.42/60.16 thf(zip_derived_cl13549, plain, 413.42/60.16 ( (para @ '#sk21' @ '#sk21' @ '#sk21' @ '#sk21')), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl1257, zip_derived_cl1649])). 413.42/60.16 thf(ruleD40, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,P:$i,Q:$i]: 413.42/60.16 ( ( para @ A @ B @ C @ D ) => ( eqangle @ A @ B @ P @ Q @ C @ D @ P @ Q ) ))). 413.42/60.16 thf(zip_derived_cl8, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (para @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3) => 413.42/60.16 (eqangle @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ Y5)))))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD40])). 413.42/60.16 thf(zip_derived_cl324, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (para @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2) => 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ Y4))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 413.42/60.16 thf(zip_derived_cl325, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ 413.42/60.16 Y0 @ Y1) => 413.42/60.16 (eqangle @ X2 @ 413.42/60.16 X4 @ Y2 @ Y3 @ 413.42/60.16 Y0 @ Y1 @ Y2 @ Y3)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl324])). 413.42/60.16 thf(zip_derived_cl326, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X6 @ Y0) => 413.42/60.16 (eqangle @ X2 @ X4 @ Y1 @ Y2 @ 413.42/60.16 X6 @ Y0 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl325])). 413.42/60.16 thf(zip_derived_cl327, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X6 @ X8) => (eqangle @ 413.42/60.16 X2 @ X4 @ Y0 @ Y1 @ X6 @ X8 @ Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl326])). 413.42/60.16 thf(zip_derived_cl328, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X6 @ X8) => (eqangle @ X2 @ X4 @ 413.42/60.16 X10 @ Y0 @ X6 @ X8 @ X10 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl327])). 413.42/60.16 thf(zip_derived_cl329, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X6 @ X8) => (eqangle @ X2 @ X4 @ X10 @ X12 @ 413.42/60.16 X6 @ X8 @ X10 @ X12)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl328])). 413.42/60.16 thf(zip_derived_cl330, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (para @ X2 @ X4 @ X6 @ X8) 413.42/60.16 | (eqangle @ X2 @ X4 @ X10 @ X12 @ X6 @ X8 @ X10 @ X12))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl329])). 413.42/60.16 thf(ruleD19, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,P:$i,Q:$i,U:$i,V:$i]: 413.42/60.16 ( ( eqangle @ A @ B @ C @ D @ P @ Q @ U @ V ) => 413.42/60.16 ( eqangle @ C @ D @ A @ B @ U @ V @ P @ Q ) ))). 413.42/60.16 thf(zip_derived_cl78, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y6 : $i]: 413.42/60.16 (( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y7 : $i]: 413.42/60.16 (( 413.42/60.16 (eqangle @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y6 @ 413.42/60.16 Y7) => 413.42/60.16 (eqangle @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y6 @ 413.42/60.16 Y7 @ 413.42/60.16 Y4 @ Y5)))))))))))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD19])). 413.42/60.16 thf(zip_derived_cl708, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y6 : $i]: 413.42/60.16 (( 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y6) => 413.42/60.16 (eqangle @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y5 @ 413.42/60.16 Y6 @ 413.42/60.16 Y3 @ Y4))))))))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl78])). 413.42/60.16 thf(zip_derived_cl709, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5) => 413.42/60.16 (eqangle @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y2 @ Y3)))))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl708])). 413.42/60.16 thf(zip_derived_cl710, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 X6 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4) => 413.42/60.16 (eqangle @ 413.42/60.16 X6 @ 413.42/60.16 Y0 @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y1 @ Y2))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl709])). 413.42/60.16 thf(zip_derived_cl711, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((eqangle @ X2 @ 413.42/60.16 X4 @ X6 @ X8 @ 413.42/60.16 Y0 @ Y1 @ Y2 @ 413.42/60.16 Y3) => (eqangle @ 413.42/60.16 X6 @ X8 @ X2 @ 413.42/60.16 X4 @ Y2 @ Y3 @ 413.42/60.16 Y0 @ Y1)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl710])). 413.42/60.16 thf(zip_derived_cl712, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ 413.42/60.16 X10 @ Y0 @ Y1 @ Y2) => 413.42/60.16 (eqangle @ X6 @ X8 @ X2 @ X4 @ 413.42/60.16 Y1 @ Y2 @ X10 @ Y0))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl711])). 413.42/60.16 thf(zip_derived_cl713, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ 413.42/60.16 Y0 @ Y1) => (eqangle @ X6 @ X8 @ X2 @ X4 @ 413.42/60.16 Y0 @ Y1 @ X10 @ X12)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl712])). 413.42/60.16 thf(zip_derived_cl714, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ X14 @ Y0) => 413.42/60.16 (eqangle @ X6 @ X8 @ X2 @ X4 @ X14 @ Y0 @ X10 @ X12))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl713])). 413.42/60.16 thf(zip_derived_cl715, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i, 413.42/60.16 X16 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ X14 @ X16) => 413.42/60.16 (eqangle @ X6 @ X8 @ X2 @ X4 @ X14 @ X16 @ X10 @ X12)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl714])). 413.42/60.16 thf(zip_derived_cl716, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i, 413.42/60.16 X16 : $i]: 413.42/60.16 (~ (eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ X14 @ X16) 413.42/60.16 | (eqangle @ X6 @ X8 @ X2 @ X4 @ X14 @ X16 @ X10 @ X12))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl715])). 413.42/60.16 thf(zip_derived_cl717, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 413.42/60.16 (~ (para @ X5 @ X4 @ X3 @ X2) 413.42/60.16 | (eqangle @ X1 @ X0 @ X5 @ X4 @ X1 @ X0 @ X3 @ X2))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl716])). 413.42/60.16 thf(ruleD39, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,P:$i,Q:$i]: 413.42/60.16 ( ( eqangle @ A @ B @ P @ Q @ C @ D @ P @ Q ) => ( para @ A @ B @ C @ D ) ))). 413.42/60.16 thf(zip_derived_cl90, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (eqangle @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5) => 413.42/60.16 (para @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ Y3)))))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD39])). 413.42/60.16 thf(zip_derived_cl416, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4) => 413.42/60.16 (para @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ Y2))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl90])). 413.42/60.16 thf(zip_derived_cl417, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((eqangle @ X2 @ 413.42/60.16 X4 @ Y2 @ Y3 @ 413.42/60.16 Y0 @ Y1 @ Y2 @ 413.42/60.16 Y3) => (para @ 413.42/60.16 X2 @ X4 @ Y0 @ Y1)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl416])). 413.42/60.16 thf(zip_derived_cl418, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ Y1 @ Y2 @ 413.42/60.16 X6 @ Y0 @ Y1 @ Y2) => (para @ 413.42/60.16 X2 @ X4 @ X6 @ Y0))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl417])). 413.42/60.16 thf(zip_derived_cl419, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ Y0 @ Y1 @ X6 @ X8 @ 413.42/60.16 Y0 @ Y1) => (para @ X2 @ X4 @ X6 @ X8)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl418])). 413.42/60.16 thf(zip_derived_cl420, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X10 @ Y0 @ X6 @ X8 @ X10 @ Y0) => 413.42/60.16 (para @ X2 @ X4 @ X6 @ X8))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl419])). 413.42/60.16 thf(zip_derived_cl421, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X10 @ X12 @ X6 @ X8 @ X10 @ X12) => (para @ 413.42/60.16 X2 @ X4 @ X6 @ X8)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl420])). 413.42/60.16 thf(zip_derived_cl422, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (eqangle @ X2 @ X4 @ X10 @ X12 @ X6 @ X8 @ X10 @ X12) 413.42/60.16 | (para @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl421])). 413.42/60.16 thf(zip_derived_cl3400, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 413.42/60.16 (~ (para @ X1 @ X0 @ X1 @ X0) | (para @ X3 @ X2 @ X3 @ X2))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl717, zip_derived_cl422])). 413.42/60.16 thf(zip_derived_cl42678, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (para @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl13549, zip_derived_cl3400])). 413.42/60.16 thf(ruleD4, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i]: 413.42/60.16 ( ( para @ A @ B @ C @ D ) => ( para @ A @ B @ D @ C ) ))). 413.42/60.16 thf(zip_derived_cl54, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((para @ Y0 @ Y1 @ 413.42/60.16 Y2 @ Y3) => (para @ 413.42/60.16 Y0 @ Y1 @ Y3 @ Y2)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD4])). 413.42/60.16 thf(zip_derived_cl168, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((para @ X2 @ Y0 @ Y1 @ Y2) => 413.42/60.16 (para @ X2 @ Y0 @ Y2 @ Y1))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl54])). 413.42/60.16 thf(zip_derived_cl169, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ Y0 @ Y1) => (para @ X2 @ 413.42/60.16 X4 @ Y1 @ Y0)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl168])). 413.42/60.16 thf(zip_derived_cl170, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X6 @ Y0) => (para @ X2 @ X4 @ Y0 @ 413.42/60.16 X6))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl169])). 413.42/60.16 thf(zip_derived_cl171, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X6 @ X8) => (para @ X2 @ X4 @ X8 @ X6)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl170])). 413.42/60.16 thf(zip_derived_cl172, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (para @ X2 @ X4 @ X6 @ X8) | (para @ X2 @ X4 @ X8 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])). 413.42/60.16 thf(zip_derived_cl42695, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (para @ X1 @ X0 @ X0 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl42678, zip_derived_cl172])). 413.42/60.16 thf(zip_derived_cl330, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (para @ X2 @ X4 @ X6 @ X8) 413.42/60.16 | (eqangle @ X2 @ X4 @ X10 @ X12 @ X6 @ X8 @ X10 @ X12))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl329])). 413.42/60.16 thf(ruleD21, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,P:$i,Q:$i,U:$i,V:$i]: 413.42/60.16 ( ( eqangle @ A @ B @ C @ D @ P @ Q @ U @ V ) => 413.42/60.16 ( eqangle @ A @ B @ P @ Q @ C @ D @ U @ V ) ))). 413.42/60.16 thf(zip_derived_cl27, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y6 : $i]: 413.42/60.16 (( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y7 : $i]: 413.42/60.16 (( 413.42/60.16 (eqangle @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y6 @ 413.42/60.16 Y7) => 413.42/60.16 (eqangle @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y6 @ Y7)))))))))))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD21])). 413.42/60.16 thf(zip_derived_cl585, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y6 : $i]: 413.42/60.16 (( 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5 @ 413.42/60.16 Y6) => 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y5 @ Y6))))))))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])). 413.42/60.16 thf(zip_derived_cl586, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ 413.42/60.16 Y5) => 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y4 @ Y5)))))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl585])). 413.42/60.16 thf(zip_derived_cl587, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 X6 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4) => 413.42/60.16 (eqangle @ 413.42/60.16 X2 @ 413.42/60.16 X4 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 X6 @ 413.42/60.16 Y0 @ 413.42/60.16 Y3 @ Y4))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl586])). 413.42/60.16 thf(zip_derived_cl588, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((eqangle @ X2 @ 413.42/60.16 X4 @ X6 @ X8 @ 413.42/60.16 Y0 @ Y1 @ Y2 @ 413.42/60.16 Y3) => (eqangle @ 413.42/60.16 X2 @ X4 @ Y0 @ 413.42/60.16 Y1 @ X6 @ X8 @ 413.42/60.16 Y2 @ Y3)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl587])). 413.42/60.16 thf(zip_derived_cl589, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ 413.42/60.16 X10 @ Y0 @ Y1 @ Y2) => 413.42/60.16 (eqangle @ X2 @ X4 @ X10 @ 413.42/60.16 Y0 @ X6 @ X8 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl588])). 413.42/60.16 thf(zip_derived_cl590, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ 413.42/60.16 Y0 @ Y1) => (eqangle @ X2 @ X4 @ X10 @ 413.42/60.16 X12 @ X6 @ X8 @ Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl589])). 413.42/60.16 thf(zip_derived_cl591, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ X14 @ Y0) => 413.42/60.16 (eqangle @ X2 @ X4 @ X10 @ X12 @ X6 @ X8 @ X14 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl590])). 413.42/60.16 thf(zip_derived_cl592, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i, 413.42/60.16 X16 : $i]: 413.42/60.16 (((eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ X14 @ X16) => 413.42/60.16 (eqangle @ X2 @ X4 @ X10 @ X12 @ X6 @ X8 @ X14 @ X16)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl591])). 413.42/60.16 thf(zip_derived_cl593, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i, 413.42/60.16 X16 : $i]: 413.42/60.16 (~ (eqangle @ X2 @ X4 @ X6 @ X8 @ X10 @ X12 @ X14 @ X16) 413.42/60.16 | (eqangle @ X2 @ X4 @ X10 @ X12 @ X6 @ X8 @ X14 @ X16))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl592])). 413.42/60.16 thf(zip_derived_cl594, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 413.42/60.16 (~ (para @ X5 @ X4 @ X3 @ X2) 413.42/60.16 | (eqangle @ X5 @ X4 @ X3 @ X2 @ X1 @ X0 @ X1 @ X0))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl593])). 413.42/60.16 thf(ruleD43, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,P:$i,Q:$i,R:$i]: 413.42/60.16 ( ( ( cyclic @ A @ B @ C @ R ) & 413.42/60.16 ( eqangle @ C @ A @ C @ B @ R @ P @ R @ Q ) & 413.42/60.16 ( cyclic @ A @ B @ C @ Q ) & ( cyclic @ A @ B @ C @ P ) ) => 413.42/60.16 ( cong @ A @ B @ P @ Q ) ))). 413.42/60.16 thf(zip_derived_cl42, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (( 413.42/60.16 ( 413.42/60.16 cyclic @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ Y5) & 413.42/60.16 ( 413.42/60.16 eqangle @ 413.42/60.16 Y2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y2 @ 413.42/60.16 Y1 @ 413.42/60.16 Y5 @ 413.42/60.16 Y3 @ 413.42/60.16 Y5 @ Y4) & 413.42/60.16 ( 413.42/60.16 cyclic @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ Y4) & 413.42/60.16 ( 413.42/60.16 cyclic @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ Y3))) => 413.42/60.16 (cong @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y3 @ Y4)))))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD43])). 413.42/60.16 thf(zip_derived_cl1139, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (( 413.42/60.16 ( 413.42/60.16 cyclic @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ Y4) & 413.42/60.16 ( 413.42/60.16 eqangle @ 413.42/60.16 Y1 @ 413.42/60.16 X2 @ 413.42/60.16 Y1 @ 413.42/60.16 Y0 @ 413.42/60.16 Y4 @ 413.42/60.16 Y2 @ 413.42/60.16 Y4 @ Y3) & 413.42/60.16 ( 413.42/60.16 cyclic @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ Y3) & 413.42/60.16 ( 413.42/60.16 cyclic @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ Y2))) => 413.42/60.16 (cong @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y2 @ Y3))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 413.42/60.16 thf(zip_derived_cl1140, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((cyclic @ X2 @ 413.42/60.16 X4 @ Y0 @ Y3) & 413.42/60.16 (eqangle @ Y0 @ 413.42/60.16 X2 @ Y0 @ X4 @ 413.42/60.16 Y3 @ Y1 @ Y3 @ 413.42/60.16 Y2) & 413.42/60.16 (cyclic @ X2 @ 413.42/60.16 X4 @ Y0 @ Y2) & 413.42/60.16 (cyclic @ X2 @ 413.42/60.16 X4 @ Y0 @ Y1))) => 413.42/60.16 (cong @ X2 @ X4 @ 413.42/60.16 Y1 @ Y2)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1139])). 413.42/60.16 thf(zip_derived_cl1141, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((cyclic @ X2 @ X4 @ X6 @ Y2) & 413.42/60.16 (eqangle @ X6 @ X2 @ X6 @ 413.42/60.16 X4 @ Y2 @ Y0 @ Y2 @ Y1) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ Y1) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ Y0))) => 413.42/60.16 (cong @ X2 @ X4 @ Y0 @ Y1))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1140])). 413.42/60.16 thf(zip_derived_cl1142, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((cyclic @ X2 @ X4 @ X6 @ Y1) & 413.42/60.16 (eqangle @ X6 @ X2 @ X6 @ X4 @ Y1 @ X8 @ 413.42/60.16 Y1 @ Y0) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ Y0) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ X8))) => 413.42/60.16 (cong @ X2 @ X4 @ X8 @ Y0)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1141])). 413.42/60.16 thf(zip_derived_cl1143, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((cyclic @ X2 @ X4 @ X6 @ Y0) & 413.42/60.16 (eqangle @ X6 @ X2 @ X6 @ X4 @ Y0 @ X8 @ Y0 @ X10) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ X10) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ X8))) => 413.42/60.16 (cong @ X2 @ X4 @ X8 @ X10))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1142])). 413.42/60.16 thf(zip_derived_cl1144, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((((cyclic @ X2 @ X4 @ X6 @ X12) & 413.42/60.16 (eqangle @ X6 @ X2 @ X6 @ X4 @ X12 @ X8 @ X12 @ X10) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ X10) & (cyclic @ X2 @ X4 @ X6 @ X8))) => 413.42/60.16 (cong @ X2 @ X4 @ X8 @ X10)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1143])). 413.42/60.16 thf(zip_derived_cl1145, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (((cyclic @ X2 @ X4 @ X6 @ X12) & 413.42/60.16 (eqangle @ X6 @ X2 @ X6 @ X4 @ X12 @ X8 @ X12 @ X10) & 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ X10) & (cyclic @ X2 @ X4 @ X6 @ X8))) 413.42/60.16 | (cong @ X2 @ X4 @ X8 @ X10))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1144])). 413.42/60.16 thf(zip_derived_cl1146, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (cyclic @ X2 @ X4 @ X6 @ X12) 413.42/60.16 | ~ (eqangle @ X6 @ X2 @ X6 @ X4 @ X12 @ X8 @ X12 @ X10) 413.42/60.16 | ~ (cyclic @ X2 @ X4 @ X6 @ X10) 413.42/60.16 | ~ (cyclic @ X2 @ X4 @ X6 @ X8) 413.42/60.16 | (cong @ X2 @ X4 @ X8 @ X10))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1145])). 413.42/60.16 thf(zip_derived_cl1149, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 413.42/60.16 (~ (para @ X3 @ X4 @ X3 @ X2) 413.42/60.16 | ~ (cyclic @ X4 @ X2 @ X3 @ X1) 413.42/60.16 | ~ (cyclic @ X4 @ X2 @ X3 @ X0) 413.42/60.16 | ~ (cyclic @ X4 @ X2 @ X3 @ X0) 413.42/60.16 | (cong @ X4 @ X2 @ X0 @ X0))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl594, zip_derived_cl1146])). 413.42/60.16 thf(zip_derived_cl1152, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 413.42/60.16 ( (cong @ X4 @ X2 @ X0 @ X0) 413.42/60.16 | ~ (cyclic @ X4 @ X2 @ X3 @ X0) 413.42/60.16 | ~ (cyclic @ X4 @ X2 @ X3 @ X1) 413.42/60.16 | ~ (para @ X3 @ X4 @ X3 @ X2))), 413.42/60.16 inference('simplify', [status(thm)], [zip_derived_cl1149])). 413.42/60.16 thf(zip_derived_cl10222, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 413.42/60.16 ( (cong @ X2 @ X1 @ X0 @ X0) 413.42/60.16 | ~ (para @ X3 @ X2 @ X3 @ X1) 413.42/60.16 | ~ (cyclic @ X2 @ X1 @ X3 @ X0))), 413.42/60.16 inference('condensation', [status(thm)], [zip_derived_cl1152])). 413.42/60.16 thf(zip_derived_cl43659, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: 413.42/60.16 ( (cong @ X0 @ X0 @ X1 @ X1) | ~ (cyclic @ X0 @ X0 @ X0 @ X1))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl42695, zip_derived_cl10222])). 413.42/60.16 thf(zip_derived_cl594, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 413.42/60.16 (~ (para @ X5 @ X4 @ X3 @ X2) 413.42/60.16 | (eqangle @ X5 @ X4 @ X3 @ X2 @ X1 @ X0 @ X1 @ X0))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl593])). 413.42/60.16 thf(ruleD42a, axiom, 413.42/60.16 (![A:$i,B:$i,P:$i,Q:$i]: 413.42/60.16 ( ( ( eqangle @ P @ A @ P @ B @ Q @ A @ Q @ B ) & 413.42/60.16 ( ~( coll @ P @ Q @ A ) ) ) => 413.42/60.16 ( cyclic @ A @ B @ P @ Q ) ))). 413.42/60.16 thf(zip_derived_cl0, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((eqangle @ Y2 @ 413.42/60.16 Y0 @ Y2 @ Y1 @ 413.42/60.16 Y3 @ Y0 @ Y3 @ 413.42/60.16 Y1) & 413.42/60.16 (((~) @ (coll @ 413.42/60.16 Y2 @ Y3 @ 413.42/60.16 Y0))))) => 413.42/60.16 (cyclic @ Y0 @ Y1 @ 413.42/60.16 Y2 @ Y3)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD42a])). 413.42/60.16 thf(zip_derived_cl111, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((eqangle @ Y1 @ X2 @ Y1 @ 413.42/60.16 Y0 @ Y2 @ X2 @ Y2 @ Y0) & 413.42/60.16 (((~) @ (coll @ Y1 @ Y2 @ X2))))) => 413.42/60.16 (cyclic @ X2 @ Y0 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 413.42/60.16 thf(zip_derived_cl112, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((eqangle @ Y0 @ X2 @ Y0 @ X4 @ Y1 @ X2 @ 413.42/60.16 Y1 @ X4) & 413.42/60.16 (((~) @ (coll @ Y0 @ Y1 @ X2))))) => 413.42/60.16 (cyclic @ X2 @ X4 @ Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])). 413.42/60.16 thf(zip_derived_cl113, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((eqangle @ X6 @ X2 @ X6 @ X4 @ Y0 @ X2 @ Y0 @ X4) & 413.42/60.16 (((~) @ (coll @ X6 @ Y0 @ X2))))) => 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])). 413.42/60.16 thf(zip_derived_cl114, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((((eqangle @ X6 @ X2 @ X6 @ X4 @ X8 @ X2 @ X8 @ X4) & 413.42/60.16 (((~) @ (coll @ X6 @ X8 @ X2))))) => 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ X8)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl113])). 413.42/60.16 thf(zip_derived_cl115, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (((eqangle @ X6 @ X2 @ X6 @ X4 @ X8 @ X2 @ X8 @ X4) & 413.42/60.16 (((~) @ (coll @ X6 @ X8 @ X2))))) 413.42/60.16 | (cyclic @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 413.42/60.16 thf(zip_derived_cl116, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (eqangle @ X6 @ X2 @ X6 @ X4 @ X8 @ X2 @ X8 @ X4) 413.42/60.16 | (coll @ X6 @ X8 @ X2) 413.42/60.16 | (cyclic @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl115])). 413.42/60.16 thf(zip_derived_cl838, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (para @ X2 @ X0 @ X2 @ X0) 413.42/60.16 | (coll @ X2 @ X1 @ X0) 413.42/60.16 | (cyclic @ X0 @ X0 @ X2 @ X1))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl594, zip_derived_cl116])). 413.42/60.16 thf(zip_derived_cl594, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 413.42/60.16 (~ (para @ X5 @ X4 @ X3 @ X2) 413.42/60.16 | (eqangle @ X5 @ X4 @ X3 @ X2 @ X1 @ X0 @ X1 @ X0))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl593])). 413.42/60.16 thf(ruleD42b, axiom, 413.42/60.16 (![A:$i,B:$i,P:$i,Q:$i]: 413.42/60.16 ( ( ( coll @ P @ Q @ B ) & ( eqangle @ P @ A @ P @ B @ Q @ A @ Q @ B ) ) => 413.42/60.16 ( cyclic @ A @ B @ P @ Q ) ))). 413.42/60.16 thf(zip_derived_cl12, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((coll @ Y2 @ Y3 @ 413.42/60.16 Y1) & (eqangle @ 413.42/60.16 Y2 @ Y0 @ Y2 @ 413.42/60.16 Y1 @ Y3 @ Y0 @ 413.42/60.16 Y3 @ Y1))) => 413.42/60.16 (cyclic @ Y0 @ Y1 @ 413.42/60.16 Y2 @ Y3)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD42b])). 413.42/60.16 thf(zip_derived_cl432, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((coll @ Y1 @ Y2 @ Y0) & 413.42/60.16 (eqangle @ Y1 @ X2 @ Y1 @ 413.42/60.16 Y0 @ Y2 @ X2 @ Y2 @ Y0))) => 413.42/60.16 (cyclic @ X2 @ Y0 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 413.42/60.16 thf(zip_derived_cl433, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((coll @ Y0 @ Y1 @ X4) & (eqangle @ Y0 @ 413.42/60.16 X2 @ Y0 @ X4 @ Y1 @ X2 @ Y1 @ X4))) => 413.42/60.16 (cyclic @ X2 @ X4 @ Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl432])). 413.42/60.16 thf(zip_derived_cl434, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((coll @ X6 @ Y0 @ X4) & (eqangle @ X6 @ X2 @ X6 @ 413.42/60.16 X4 @ Y0 @ X2 @ Y0 @ X4))) => 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl433])). 413.42/60.16 thf(zip_derived_cl435, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((((coll @ X6 @ X8 @ X4) & (eqangle @ X6 @ X2 @ X6 @ X4 @ X8 @ X2 @ 413.42/60.16 X8 @ X4))) => 413.42/60.16 (cyclic @ X2 @ X4 @ X6 @ X8)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl434])). 413.42/60.16 thf(zip_derived_cl436, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (((coll @ X6 @ X8 @ X4) & (eqangle @ X6 @ X2 @ X6 @ X4 @ X8 @ X2 @ 413.42/60.16 X8 @ X4))) 413.42/60.16 | (cyclic @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl435])). 413.42/60.16 thf(zip_derived_cl437, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (coll @ X6 @ X8 @ X4) 413.42/60.16 | ~ (eqangle @ X6 @ X2 @ X6 @ X4 @ X8 @ X2 @ X8 @ X4) 413.42/60.16 | (cyclic @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl436])). 413.42/60.16 thf(zip_derived_cl839, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (para @ X2 @ X0 @ X2 @ X0) 413.42/60.16 | ~ (coll @ X2 @ X1 @ X0) 413.42/60.16 | (cyclic @ X0 @ X0 @ X2 @ X1))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl594, zip_derived_cl437])). 413.42/60.16 thf(zip_derived_cl913, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 ( (cyclic @ X0 @ X0 @ X2 @ X1) | ~ (para @ X2 @ X0 @ X2 @ X0))), 413.42/60.16 inference('clc', [status(thm)], [zip_derived_cl838, zip_derived_cl839])). 413.42/60.16 thf(zip_derived_cl42678, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (para @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl13549, zip_derived_cl3400])). 413.42/60.16 thf(zip_derived_cl42690, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: (cyclic @ X0 @ X0 @ X2 @ X1)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl913, zip_derived_cl42678])). 413.42/60.16 thf(zip_derived_cl43668, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (cong @ X0 @ X0 @ X1 @ X1)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl43659, zip_derived_cl42690])). 413.42/60.16 thf(ruleD67, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i]: 413.42/60.16 ( ( ( coll @ A @ B @ C ) & ( cong @ A @ B @ A @ C ) ) => 413.42/60.16 ( midp @ A @ B @ C ) ))). 413.42/60.16 thf(zip_derived_cl59, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((coll @ Y0 @ Y1 @ Y2) & 413.42/60.16 (cong @ Y0 @ Y1 @ Y0 @ Y2))) => 413.42/60.16 (midp @ Y0 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD67])). 413.42/60.16 thf(zip_derived_cl227, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((coll @ X2 @ Y0 @ Y1) & (cong @ X2 @ 413.42/60.16 Y0 @ X2 @ Y1))) => 413.42/60.16 (midp @ X2 @ Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl59])). 413.42/60.16 thf(zip_derived_cl228, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((coll @ X2 @ X4 @ Y0) & (cong @ X2 @ X4 @ X2 @ Y0))) => 413.42/60.16 (midp @ X2 @ X4 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl227])). 413.42/60.16 thf(zip_derived_cl229, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((((coll @ X2 @ X4 @ X6) & (cong @ X2 @ X4 @ X2 @ X6))) => (midp @ 413.42/60.16 X2 @ X4 @ X6)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl228])). 413.42/60.16 thf(zip_derived_cl230, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (~ (((coll @ X2 @ X4 @ X6) & (cong @ X2 @ X4 @ X2 @ X6))) 413.42/60.16 | (midp @ X2 @ X4 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl229])). 413.42/60.16 thf(zip_derived_cl231, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (~ (coll @ X2 @ X4 @ X6) 413.42/60.16 | ~ (cong @ X2 @ X4 @ X2 @ X6) 413.42/60.16 | (midp @ X2 @ X4 @ X6))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl230])). 413.42/60.16 thf(zip_derived_cl42678, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (para @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl13549, zip_derived_cl3400])). 413.42/60.16 thf(ruleD66, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i]: ( ( para @ A @ B @ A @ C ) => ( coll @ A @ B @ C ) ))). 413.42/60.16 thf(zip_derived_cl15, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((para @ Y0 @ Y1 @ Y0 @ Y2) => 413.42/60.16 (coll @ Y0 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD66])). 413.42/60.16 thf(zip_derived_cl124, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((para @ X2 @ Y0 @ X2 @ Y1) => (coll @ X2 @ 413.42/60.16 Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 413.42/60.16 thf(zip_derived_cl125, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X2 @ Y0) => (coll @ X2 @ X4 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl124])). 413.42/60.16 thf(zip_derived_cl126, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((para @ X2 @ X4 @ X2 @ X6) => (coll @ X2 @ X4 @ X6)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl125])). 413.42/60.16 thf(zip_derived_cl127, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (~ (para @ X2 @ X4 @ X2 @ X6) | (coll @ X2 @ X4 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 413.42/60.16 thf(zip_derived_cl42694, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (coll @ X1 @ X0 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl42678, zip_derived_cl127])). 413.42/60.16 thf(ruleD3, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i]: 413.42/60.16 ( ( ( coll @ A @ B @ C ) & ( coll @ A @ B @ D ) ) => ( coll @ C @ D @ A ) ))). 413.42/60.16 thf(zip_derived_cl48, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((coll @ Y0 @ Y1 @ 413.42/60.16 Y2) & (coll @ Y0 @ 413.42/60.16 Y1 @ Y3))) => 413.42/60.16 (coll @ Y2 @ Y3 @ Y0)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD3])). 413.42/60.16 thf(zip_derived_cl253, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((coll @ X2 @ Y0 @ Y1) & 413.42/60.16 (coll @ X2 @ Y0 @ Y2))) => 413.42/60.16 (coll @ Y1 @ Y2 @ X2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])). 413.42/60.16 thf(zip_derived_cl254, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((coll @ X2 @ X4 @ Y0) & (coll @ X2 @ 413.42/60.16 X4 @ Y1))) => 413.42/60.16 (coll @ Y0 @ Y1 @ X2)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl253])). 413.42/60.16 thf(zip_derived_cl255, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((coll @ X2 @ X4 @ X6) & (coll @ X2 @ X4 @ Y0))) => 413.42/60.16 (coll @ X6 @ Y0 @ X2))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl254])). 413.42/60.16 thf(zip_derived_cl256, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((((coll @ X2 @ X4 @ X6) & (coll @ X2 @ X4 @ X8))) => (coll @ X6 @ 413.42/60.16 X8 @ X2)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl255])). 413.42/60.16 thf(zip_derived_cl257, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (((coll @ X2 @ X4 @ X6) & (coll @ X2 @ X4 @ X8))) 413.42/60.16 | (coll @ X6 @ X8 @ X2))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl256])). 413.42/60.16 thf(zip_derived_cl258, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (coll @ X2 @ X4 @ X6) 413.42/60.16 | ~ (coll @ X2 @ X4 @ X8) 413.42/60.16 | (coll @ X6 @ X8 @ X2))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl257])). 413.42/60.16 thf(zip_derived_cl265, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 ( (coll @ X0 @ X0 @ X2) | ~ (coll @ X2 @ X1 @ X0))), 413.42/60.16 inference('eq_fact', [status(thm)], [zip_derived_cl258])). 413.42/60.16 thf(zip_derived_cl42749, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (coll @ X0 @ X0 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl42694, zip_derived_cl265])). 413.42/60.16 thf(zip_derived_cl258, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (coll @ X2 @ X4 @ X6) 413.42/60.16 | ~ (coll @ X2 @ X4 @ X8) 413.42/60.16 | (coll @ X6 @ X8 @ X2))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl257])). 413.42/60.16 thf(zip_derived_cl43319, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (coll @ X1 @ X1 @ X2) | (coll @ X0 @ X2 @ X1))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl42749, zip_derived_cl258])). 413.42/60.16 thf(zip_derived_cl42749, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (coll @ X0 @ X0 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl42694, zip_derived_cl265])). 413.42/60.16 thf(zip_derived_cl43322, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: (coll @ X0 @ X2 @ X1)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl43319, zip_derived_cl42749])). 413.42/60.16 thf(zip_derived_cl43472, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (~ (cong @ X2 @ X4 @ X2 @ X6) | (midp @ X2 @ X4 @ X6))), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl231, zip_derived_cl43322])). 413.42/60.16 thf(zip_derived_cl44527, plain, (![X0 : $i]: (midp @ X0 @ X0 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl43668, zip_derived_cl43472])). 413.42/60.16 thf(zip_derived_cl42678, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (para @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl13549, zip_derived_cl3400])). 413.42/60.16 thf(ruleD64, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,M:$i]: 413.42/60.16 ( ( ( para @ A @ D @ B @ C ) & ( para @ A @ C @ B @ D ) & 413.42/60.16 ( midp @ M @ A @ B ) ) => 413.42/60.16 ( midp @ M @ C @ D ) ))). 413.42/60.16 thf(zip_derived_cl29, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((( 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y0 @ 413.42/60.16 Y3 @ 413.42/60.16 Y1 @ Y2) & 413.42/60.16 ( 413.42/60.16 para @ 413.42/60.16 Y0 @ 413.42/60.16 Y2 @ 413.42/60.16 Y1 @ Y3) & 413.42/60.16 ( 413.42/60.16 midp @ 413.42/60.16 Y4 @ 413.42/60.16 Y0 @ Y1))) => 413.42/60.16 (midp @ 413.42/60.16 Y4 @ 413.42/60.16 Y2 @ Y3))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD64])). 413.42/60.16 thf(zip_derived_cl597, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((para @ X2 @ 413.42/60.16 Y2 @ Y0 @ Y1) & 413.42/60.16 (para @ X2 @ 413.42/60.16 Y1 @ Y0 @ Y2) & 413.42/60.16 (midp @ Y3 @ 413.42/60.16 X2 @ Y0))) => 413.42/60.16 (midp @ Y3 @ Y1 @ 413.42/60.16 Y2)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 413.42/60.16 thf(zip_derived_cl598, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((para @ X2 @ Y1 @ X4 @ Y0) & 413.42/60.16 (para @ X2 @ Y0 @ X4 @ Y1) & 413.42/60.16 (midp @ Y2 @ X2 @ X4))) => 413.42/60.16 (midp @ Y2 @ Y0 @ Y1))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl597])). 413.42/60.16 thf(zip_derived_cl599, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((para @ X2 @ Y0 @ X4 @ X6) & 413.42/60.16 (para @ X2 @ X6 @ X4 @ Y0) & 413.42/60.16 (midp @ Y1 @ X2 @ X4))) => 413.42/60.16 (midp @ Y1 @ X6 @ Y0)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl598])). 413.42/60.16 thf(zip_derived_cl600, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((para @ X2 @ X8 @ X4 @ X6) & 413.42/60.16 (para @ X2 @ X6 @ X4 @ X8) & (midp @ Y0 @ X2 @ X4))) => 413.42/60.16 (midp @ Y0 @ X6 @ X8))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl599])). 413.42/60.16 thf(zip_derived_cl601, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((((para @ X2 @ X8 @ X4 @ X6) & (para @ X2 @ X6 @ X4 @ X8) & 413.42/60.16 (midp @ X10 @ X2 @ X4))) => 413.42/60.16 (midp @ X10 @ X6 @ X8)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl600])). 413.42/60.16 thf(zip_derived_cl602, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (((para @ X2 @ X8 @ X4 @ X6) & (para @ X2 @ X6 @ X4 @ X8) & 413.42/60.16 (midp @ X10 @ X2 @ X4))) 413.42/60.16 | (midp @ X10 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl601])). 413.42/60.16 thf(zip_derived_cl603, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (para @ X2 @ X8 @ X4 @ X6) 413.42/60.16 | ~ (para @ X2 @ X6 @ X4 @ X8) 413.42/60.16 | ~ (midp @ X10 @ X2 @ X4) 413.42/60.16 | (midp @ X10 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl602])). 413.42/60.16 thf(zip_derived_cl42704, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (midp @ X2 @ X1 @ X1) | (midp @ X2 @ X0 @ X0))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl42678, zip_derived_cl603])). 413.42/60.16 thf(zip_derived_cl44680, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (midp @ X0 @ X1 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44527, zip_derived_cl42704])). 413.42/60.16 thf(zip_derived_cl603, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (para @ X2 @ X8 @ X4 @ X6) 413.42/60.16 | ~ (para @ X2 @ X6 @ X4 @ X8) 413.42/60.16 | ~ (midp @ X10 @ X2 @ X4) 413.42/60.16 | (midp @ X10 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl602])). 413.42/60.16 thf(zip_derived_cl44680, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (midp @ X0 @ X1 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44527, zip_derived_cl42704])). 413.42/60.16 thf(zip_derived_cl131, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (~ (midp @ X2 @ X4 @ X6) | (cong @ X2 @ X4 @ X2 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 413.42/60.16 thf(zip_derived_cl44689, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (cong @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44680, zip_derived_cl131])). 413.42/60.16 thf(ruleD12, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,O:$i]: 413.42/60.16 ( ( ( cong @ O @ A @ O @ B ) & ( cong @ O @ A @ O @ C ) ) => 413.42/60.16 ( circle @ O @ A @ B @ C ) ))). 413.42/60.16 thf(zip_derived_cl33, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((cong @ Y3 @ Y0 @ 413.42/60.16 Y3 @ Y1) & (cong @ 413.42/60.16 Y3 @ Y0 @ Y3 @ Y2))) => 413.42/60.16 (circle @ Y3 @ Y0 @ 413.42/60.16 Y1 @ Y2)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD12])). 413.42/60.16 thf(zip_derived_cl425, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((cong @ Y2 @ X2 @ Y2 @ Y0) & 413.42/60.16 (cong @ Y2 @ X2 @ Y2 @ Y1))) => 413.42/60.16 (circle @ Y2 @ X2 @ Y0 @ Y1))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 413.42/60.16 thf(zip_derived_cl426, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((cong @ Y1 @ X2 @ Y1 @ X4) & (cong @ 413.42/60.16 Y1 @ X2 @ Y1 @ Y0))) => 413.42/60.16 (circle @ Y1 @ X2 @ X4 @ Y0)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl425])). 413.42/60.16 thf(zip_derived_cl427, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((cong @ Y0 @ X2 @ Y0 @ X4) & (cong @ Y0 @ X2 @ Y0 @ 413.42/60.16 X6))) => 413.42/60.16 (circle @ Y0 @ X2 @ X4 @ X6))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl426])). 413.42/60.16 thf(zip_derived_cl428, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((((cong @ X8 @ X2 @ X8 @ X4) & (cong @ X8 @ X2 @ X8 @ X6))) => 413.42/60.16 (circle @ X8 @ X2 @ X4 @ X6)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl427])). 413.42/60.16 thf(zip_derived_cl429, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (((cong @ X8 @ X2 @ X8 @ X4) & (cong @ X8 @ X2 @ X8 @ X6))) 413.42/60.16 | (circle @ X8 @ X2 @ X4 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])). 413.42/60.16 thf(zip_derived_cl430, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (cong @ X8 @ X2 @ X8 @ X4) 413.42/60.16 | ~ (cong @ X8 @ X2 @ X8 @ X6) 413.42/60.16 | (circle @ X8 @ X2 @ X4 @ X6))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl429])). 413.42/60.16 thf(zip_derived_cl431, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 ( (circle @ X1 @ X2 @ X0 @ X0) | ~ (cong @ X1 @ X2 @ X1 @ X0))), 413.42/60.16 inference('eq_fact', [status(thm)], [zip_derived_cl430])). 413.42/60.16 thf(zip_derived_cl44893, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (circle @ X1 @ X0 @ X0 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44689, zip_derived_cl431])). 413.42/60.16 thf(zip_derived_cl717, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 413.42/60.16 (~ (para @ X5 @ X4 @ X3 @ X2) 413.42/60.16 | (eqangle @ X1 @ X0 @ X5 @ X4 @ X1 @ X0 @ X3 @ X2))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl716])). 413.42/60.16 thf(ruleD49, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,O:$i,X:$i]: 413.42/60.16 ( ( ( eqangle @ A @ X @ A @ B @ C @ A @ C @ B ) & 413.42/60.16 ( circle @ O @ A @ B @ C ) ) => 413.42/60.16 ( perp @ O @ A @ A @ X ) ))). 413.42/60.16 thf(zip_derived_cl86, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((( 413.42/60.16 (eqangle @ 413.42/60.16 Y0 @ 413.42/60.16 Y4 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y2 @ 413.42/60.16 Y1) & 413.42/60.16 (circle @ 413.42/60.16 Y3 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ Y2))) => 413.42/60.16 (perp @ 413.42/60.16 Y3 @ 413.42/60.16 Y0 @ 413.42/60.16 Y0 @ Y4))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD49])). 413.42/60.16 thf(zip_derived_cl798, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((eqangle @ X2 @ 413.42/60.16 Y3 @ X2 @ Y0 @ 413.42/60.16 Y1 @ X2 @ Y1 @ 413.42/60.16 Y0) & (circle @ 413.42/60.16 Y2 @ X2 @ Y0 @ 413.42/60.16 Y1))) => 413.42/60.16 (perp @ Y2 @ X2 @ 413.42/60.16 X2 @ Y3)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 413.42/60.16 thf(zip_derived_cl799, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((eqangle @ X2 @ Y2 @ X2 @ 413.42/60.16 X4 @ Y0 @ X2 @ Y0 @ X4) & 413.42/60.16 (circle @ Y1 @ X2 @ X4 @ Y0))) => 413.42/60.16 (perp @ Y1 @ X2 @ X2 @ Y2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl798])). 413.42/60.16 thf(zip_derived_cl800, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((eqangle @ X2 @ Y1 @ X2 @ X4 @ X6 @ X2 @ 413.42/60.16 X6 @ X4) & (circle @ Y0 @ X2 @ X4 @ X6))) => 413.42/60.16 (perp @ Y0 @ X2 @ X2 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl799])). 413.42/60.16 thf(zip_derived_cl801, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((eqangle @ X2 @ Y0 @ X2 @ X4 @ X6 @ X2 @ X6 @ X4) & 413.42/60.16 (circle @ X8 @ X2 @ X4 @ X6))) => 413.42/60.16 (perp @ X8 @ X2 @ X2 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl800])). 413.42/60.16 thf(zip_derived_cl802, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((((eqangle @ X2 @ X10 @ X2 @ X4 @ X6 @ X2 @ X6 @ X4) & (circle @ 413.42/60.16 X8 @ X2 @ X4 @ X6))) => 413.42/60.16 (perp @ X8 @ X2 @ X2 @ X10)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl801])). 413.42/60.16 thf(zip_derived_cl803, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (((eqangle @ X2 @ X10 @ X2 @ X4 @ X6 @ X2 @ X6 @ X4) & (circle @ 413.42/60.16 X8 @ X2 @ X4 @ X6))) 413.42/60.16 | (perp @ X8 @ X2 @ X2 @ X10))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl802])). 413.42/60.16 thf(zip_derived_cl804, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (eqangle @ X2 @ X10 @ X2 @ X4 @ X6 @ X2 @ X6 @ X4) 413.42/60.16 | ~ (circle @ X8 @ X2 @ X4 @ X6) 413.42/60.16 | (perp @ X8 @ X2 @ X2 @ X10))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl803])). 413.42/60.16 thf(zip_derived_cl3406, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (para @ X1 @ X0 @ X1 @ X0) 413.42/60.16 | ~ (circle @ X2 @ X1 @ X0 @ X1) 413.42/60.16 | (perp @ X2 @ X1 @ X1 @ X1))), 413.42/60.16 inference('s_sup-', [status(thm)], [zip_derived_cl717, zip_derived_cl804])). 413.42/60.16 thf(zip_derived_cl42678, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (para @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl13549, zip_derived_cl3400])). 413.42/60.16 thf(zip_derived_cl43603, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (circle @ X2 @ X1 @ X0 @ X1) | (perp @ X2 @ X1 @ X1 @ X1))), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl3406, zip_derived_cl42678])). 413.42/60.16 thf(zip_derived_cl44994, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (perp @ X1 @ X0 @ X0 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44893, zip_derived_cl43603])). 413.42/60.16 thf(ruleD9, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: 413.42/60.16 ( ( ( perp @ A @ B @ C @ D ) & ( perp @ C @ D @ E @ F ) ) => 413.42/60.16 ( para @ A @ B @ E @ F ) ))). 413.42/60.16 thf(zip_derived_cl70, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 (((!!) @ ( 413.42/60.16 ^[Y5 : $i]: 413.42/60.16 (( 413.42/60.16 (( 413.42/60.16 (perp @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3) & 413.42/60.16 (perp @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ 413.42/60.16 Y4 @ Y5))) => 413.42/60.16 (para @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y4 @ Y5)))))))))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD9])). 413.42/60.16 thf(zip_derived_cl504, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((!!) @ (^[Y4 : $i]: 413.42/60.16 ( 413.42/60.16 ( 413.42/60.16 (( 413.42/60.16 (perp @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y1 @ 413.42/60.16 Y2) & 413.42/60.16 (perp @ 413.42/60.16 Y1 @ 413.42/60.16 Y2 @ 413.42/60.16 Y3 @ Y4))) => 413.42/60.16 (para @ 413.42/60.16 X2 @ 413.42/60.16 Y0 @ 413.42/60.16 Y3 @ Y4))))))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 413.42/60.16 thf(zip_derived_cl505, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((((perp @ X2 @ 413.42/60.16 X4 @ Y0 @ Y1) & 413.42/60.16 (perp @ Y0 @ 413.42/60.16 Y1 @ Y2 @ Y3))) => 413.42/60.16 (para @ X2 @ X4 @ 413.42/60.16 Y2 @ Y3)))))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl504])). 413.42/60.16 thf(zip_derived_cl506, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((((perp @ X2 @ X4 @ X6 @ Y0) & 413.42/60.16 (perp @ X6 @ Y0 @ Y1 @ Y2))) => 413.42/60.16 (para @ X2 @ X4 @ Y1 @ Y2))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl505])). 413.42/60.16 thf(zip_derived_cl507, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((((perp @ X2 @ X4 @ X6 @ X8) & (perp @ 413.42/60.16 X6 @ X8 @ Y0 @ Y1))) => 413.42/60.16 (para @ X2 @ X4 @ Y0 @ Y1)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl506])). 413.42/60.16 thf(zip_derived_cl508, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((((perp @ X2 @ X4 @ X6 @ X8) & (perp @ X6 @ X8 @ X10 @ 413.42/60.16 Y0))) => 413.42/60.16 (para @ X2 @ X4 @ X10 @ Y0))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl507])). 413.42/60.16 thf(zip_derived_cl509, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (((((perp @ X2 @ X4 @ X6 @ X8) & (perp @ X6 @ X8 @ X10 @ X12))) => 413.42/60.16 (para @ X2 @ X4 @ X10 @ X12)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl508])). 413.42/60.16 thf(zip_derived_cl510, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (((perp @ X2 @ X4 @ X6 @ X8) & (perp @ X6 @ X8 @ X10 @ X12))) 413.42/60.16 | (para @ X2 @ X4 @ X10 @ X12))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl509])). 413.42/60.16 thf(zip_derived_cl511, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 413.42/60.16 (~ (perp @ X2 @ X4 @ X6 @ X8) 413.42/60.16 | ~ (perp @ X6 @ X8 @ X10 @ X12) 413.42/60.16 | (para @ X2 @ X4 @ X10 @ X12))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl510])). 413.42/60.16 thf(zip_derived_cl45095, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 413.42/60.16 (~ (perp @ X0 @ X0 @ X3 @ X2) | (para @ X1 @ X0 @ X3 @ X2))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44994, zip_derived_cl511])). 413.42/60.16 thf(zip_derived_cl44689, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (cong @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44680, zip_derived_cl131])). 413.42/60.16 thf(zip_derived_cl347, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (cong @ X2 @ X6 @ X4 @ X6) 413.42/60.16 | ~ (cong @ X2 @ X8 @ X4 @ X8) 413.42/60.16 | (perp @ X2 @ X4 @ X6 @ X8))), 413.42/60.16 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl346])). 413.42/60.16 thf(zip_derived_cl44895, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: 413.42/60.16 (~ (cong @ X1 @ X2 @ X1 @ X2) | (perp @ X1 @ X1 @ X0 @ X2))), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44689, zip_derived_cl347])). 413.42/60.16 thf(zip_derived_cl44689, plain, 413.42/60.16 (![X0 : $i, X1 : $i]: (cong @ X1 @ X0 @ X1 @ X0)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44680, zip_derived_cl131])). 413.42/60.16 thf(zip_derived_cl44910, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: (perp @ X1 @ X1 @ X0 @ X2)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl44895, zip_derived_cl44689])). 413.42/60.16 thf(zip_derived_cl45249, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: (para @ X1 @ X0 @ X3 @ X2)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl45095, zip_derived_cl44910])). 413.42/60.16 thf(zip_derived_cl45249, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: (para @ X1 @ X0 @ X3 @ X2)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl45095, zip_derived_cl44910])). 413.42/60.16 thf(zip_derived_cl45430, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 413.42/60.16 (~ (midp @ X10 @ X2 @ X4) | (midp @ X10 @ X6 @ X8))), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl603, zip_derived_cl45249, zip_derived_cl45249])). 413.42/60.16 thf(zip_derived_cl45462, plain, 413.42/60.16 (![X1 : $i, X2 : $i, X3 : $i]: (midp @ X1 @ X3 @ X2)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl44680, zip_derived_cl45430])). 413.42/60.16 thf(zip_derived_cl45518, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: (cong @ X2 @ X4 @ X2 @ X6)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl131, zip_derived_cl45462])). 413.42/60.16 thf(ruleD23, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i]: 413.42/60.16 ( ( cong @ A @ B @ C @ D ) => ( cong @ A @ B @ D @ C ) ))). 413.42/60.16 thf(zip_derived_cl93, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((cong @ Y0 @ Y1 @ 413.42/60.16 Y2 @ Y3) => (cong @ 413.42/60.16 Y0 @ Y1 @ Y3 @ Y2)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD23])). 413.42/60.16 thf(zip_derived_cl213, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((cong @ X2 @ Y0 @ Y1 @ Y2) => 413.42/60.16 (cong @ X2 @ Y0 @ Y2 @ Y1))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 413.42/60.16 thf(zip_derived_cl214, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((cong @ X2 @ X4 @ Y0 @ Y1) => (cong @ X2 @ 413.42/60.16 X4 @ Y1 @ Y0)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl213])). 413.42/60.16 thf(zip_derived_cl215, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((cong @ X2 @ X4 @ X6 @ Y0) => (cong @ X2 @ X4 @ Y0 @ 413.42/60.16 X6))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl214])). 413.42/60.16 thf(zip_derived_cl216, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((cong @ X2 @ X4 @ X6 @ X8) => (cong @ X2 @ X4 @ X8 @ X6)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl215])). 413.42/60.16 thf(zip_derived_cl217, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (cong @ X2 @ X4 @ X6 @ X8) | (cong @ X2 @ X4 @ X8 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])). 413.42/60.16 thf(zip_derived_cl45742, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: (cong @ X1 @ X2 @ X0 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl45518, zip_derived_cl217])). 413.42/60.16 thf(ruleD24, axiom, 413.42/60.16 (![A:$i,B:$i,C:$i,D:$i]: 413.42/60.16 ( ( cong @ A @ B @ C @ D ) => ( cong @ C @ D @ A @ B ) ))). 413.42/60.16 thf(zip_derived_cl63, plain, 413.42/60.16 ( (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((!!) @ (^[Y3 : $i]: 413.42/60.16 (((cong @ Y0 @ Y1 @ 413.42/60.16 Y2 @ Y3) => (cong @ 413.42/60.16 Y2 @ Y3 @ Y0 @ Y1)))))))))))))))), 413.42/60.16 inference('cnf', [status(esa)], [ruleD24])). 413.42/60.16 thf(zip_derived_cl180, plain, 413.42/60.16 (![X2 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((!!) @ (^[Y2 : $i]: 413.42/60.16 (((cong @ X2 @ Y0 @ Y1 @ Y2) => 413.42/60.16 (cong @ Y1 @ Y2 @ X2 @ Y0))))))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 413.42/60.16 thf(zip_derived_cl181, plain, 413.42/60.16 (![X2 : $i, X4 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((!!) @ (^[Y1 : $i]: 413.42/60.16 (((cong @ X2 @ X4 @ Y0 @ Y1) => (cong @ Y0 @ 413.42/60.16 Y1 @ X2 @ X4)))))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl180])). 413.42/60.16 thf(zip_derived_cl182, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i]: 413.42/60.16 (((!!) @ (^[Y0 : $i]: 413.42/60.16 (((cong @ X2 @ X4 @ X6 @ Y0) => (cong @ X6 @ Y0 @ X2 @ 413.42/60.16 X4))))))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl181])). 413.42/60.16 thf(zip_derived_cl183, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (((cong @ X2 @ X4 @ X6 @ X8) => (cong @ X6 @ X8 @ X2 @ X4)))), 413.42/60.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl182])). 413.42/60.16 thf(zip_derived_cl184, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (cong @ X2 @ X4 @ X6 @ X8) | (cong @ X6 @ X8 @ X2 @ X4))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])). 413.42/60.16 thf(zip_derived_cl45787, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: (cong @ X1 @ X0 @ X0 @ X2)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl45742, zip_derived_cl184])). 413.42/60.16 thf(zip_derived_cl217, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 413.42/60.16 (~ (cong @ X2 @ X4 @ X6 @ X8) | (cong @ X2 @ X4 @ X8 @ X6))), 413.42/60.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])). 413.42/60.16 thf(zip_derived_cl45792, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: (cong @ X2 @ X1 @ X0 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl45787, zip_derived_cl217])). 413.42/60.16 thf(zip_derived_cl45792, plain, 413.42/60.16 (![X0 : $i, X1 : $i, X2 : $i]: (cong @ X2 @ X1 @ X0 @ X1)), 413.42/60.16 inference('s_sup-', [status(thm)], 413.42/60.16 [zip_derived_cl45787, zip_derived_cl217])). 413.42/60.16 thf(zip_derived_cl45795, plain, 413.42/60.16 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: (perp @ X2 @ X4 @ X6 @ X8)), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl347, zip_derived_cl45792, zip_derived_cl45792])). 413.42/60.16 thf(zip_derived_cl45799, plain, ($false), 413.42/60.16 inference('demod', [status(thm)], 413.42/60.16 [zip_derived_cl1255, zip_derived_cl45795])). 413.42/60.16 413.42/60.16 % SZS output end Refutation 413.42/60.16 413.42/60.16 413.42/60.16 % Terminating... 413.42/60.20 % Runner terminated. 413.42/60.21 % Zipperpin 1.5 exiting 413.42/60.21 EOF