0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.XJJGPxozRE true 0.09/0.37 % Computer : n010.cluster.edu 0.09/0.37 % Model : x86_64 x86_64 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.37 % Memory : 8046.5625MB 0.09/0.37 % OS : Linux 6.8.0-71-generic 0.09/0.37 % CPULimit : 1440 0.09/0.37 % WCLimit : 180 0.09/0.37 % DateTime : Mon Jul 27 09:15:04 UTC 2026 0.09/0.37 % CPUTime : 0.09/0.37 % Running portfolio for 1440 s 0.09/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.09/0.37 % Number of cores: 8 0.09/0.38 % Python version: Python 3.12.3 0.09/0.38 % Running in HO mode 0.43/0.65 % Total configuration time : 828 0.43/0.65 % Estimated wc time : 1656 0.43/0.65 % Estimated cpu time (8 cpus) : 207.0 0.47/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.47/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.47/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.47/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.47/0.79 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.47/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.47/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.47/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 3.97/1.18 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 3.97/1.19 % Solved by lams/20_acsne_simpl.sh. 3.97/1.19 % done 230 iterations in 0.326s 3.97/1.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 3.97/1.19 % SZS output start Refutation 3.97/1.19 thf(cQ_1_type, type, cQ_1: $i > $i > $i > $o). 3.97/1.19 thf(d_type, type, d: $i). 3.97/1.19 thf(cQ_2_type, type, cQ_2: $i > $i > $i > $o). 3.97/1.19 thf(cQ_5_type, type, cQ_5: $i > $i > $i > $o). 3.97/1.19 thf(cP_3_type, type, cP_3: $i > $i > $o). 3.97/1.19 thf(cP_4_type, type, cP_4: $i > $i > $o). 3.97/1.19 thf(b_type, type, b: $i). 3.97/1.19 thf(cQ_3_type, type, cQ_3: $i > $i > $i > $o). 3.97/1.19 thf(a_type, type, a: $i). 3.97/1.19 thf(c_type, type, c: $i). 3.97/1.19 thf(cQ_4_type, type, cQ_4: $i > $i > $i > $o). 3.97/1.19 thf(cP_2_type, type, cP_2: $i > $i > $o). 3.97/1.19 thf(f_type, type, f: $i > $i). 3.97/1.19 thf(cP_1_type, type, cP_1: $i > $i > $o). 3.97/1.19 thf(cTHM409_4, conjecture, 3.97/1.19 (~( ( cQ_1 @ a @ b @ c ) & ( cP_1 @ c @ c ) & 3.97/1.19 ( ![Xx:$i]: ( cP_1 @ d @ Xx ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: 3.97/1.19 ( ( cP_2 @ ( f @ Xx ) @ Xy ) | ( ~( cP_2 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( cP_3 @ b @ b ) & ( ![Xx:$i]: ( cP_3 @ d @ Xx ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: 3.97/1.19 ( ( cP_3 @ ( f @ Xx ) @ Xy ) | ( ~( cP_3 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cP_3 @ ( f @ Xx ) @ Xu ) ) | 3.97/1.19 ( ~( cP_3 @ ( f @ Xy ) @ Xv ) ) | ( cQ_4 @ Xu @ Xv @ Xw ) | 3.97/1.19 ( ~( cP_3 @ ( f @ Xz ) @ Xw ) ) | ( ~( cQ_3 @ Xx @ Xy @ Xz ) ) ) ) & 3.97/1.19 ( cP_4 @ c @ c ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cP_4 @ ( f @ Xy ) @ Xv ) ) | 3.97/1.19 ( ~( cP_4 @ ( f @ Xz ) @ Xw ) ) | ( cQ_5 @ Xu @ Xv @ Xw ) | 3.97/1.19 ( ~( cP_4 @ ( f @ Xx ) @ Xu ) ) | ( ~( cQ_4 @ Xx @ Xy @ Xz ) ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i]: ( ~( cQ_5 @ Xx @ Xy @ Xz ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: 3.97/1.19 ( ( cP_4 @ ( f @ Xx ) @ Xy ) | ( ~( cP_4 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( ![Xx:$i]: ( cP_4 @ d @ Xx ) ) & ( cP_4 @ b @ b ) & 3.97/1.19 ( cP_4 @ a @ a ) & ( cP_3 @ c @ c ) & ( cP_3 @ a @ a ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cP_2 @ ( f @ Xx ) @ Xu ) ) | 3.97/1.19 ( ~( cP_2 @ ( f @ Xy ) @ Xv ) ) | 3.97/1.19 ( ~( cP_2 @ ( f @ Xz ) @ Xw ) ) | ( cQ_3 @ Xu @ Xv @ Xw ) | 3.97/1.19 ( ~( cQ_2 @ Xx @ Xy @ Xz ) ) ) ) & 3.97/1.19 ( ![Xx:$i]: ( cP_2 @ d @ Xx ) ) & ( cP_2 @ c @ c ) & 3.97/1.19 ( cP_2 @ b @ b ) & ( cP_2 @ a @ a ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cQ_1 @ Xx @ Xy @ Xz ) ) | ( ~( cP_1 @ ( f @ Xy ) @ Xv ) ) | 3.97/1.19 ( ~( cP_1 @ ( f @ Xz ) @ Xw ) ) | ( cQ_2 @ Xu @ Xv @ Xw ) | 3.97/1.19 ( ~( cP_1 @ ( f @ Xx ) @ Xu ) ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: 3.97/1.19 ( ( cP_1 @ ( f @ Xx ) @ Xy ) | ( ~( cP_1 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( cP_1 @ b @ b ) & ( cP_1 @ a @ a ) ))). 3.97/1.19 thf(zf_stmt_0, negated_conjecture, 3.97/1.19 (( cQ_1 @ a @ b @ c ) & ( cP_1 @ c @ c ) & 3.97/1.19 ( ![Xx:$i]: ( cP_1 @ d @ Xx ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: ( ( cP_2 @ ( f @ Xx ) @ Xy ) | ( ~( cP_2 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( cP_3 @ b @ b ) & ( ![Xx:$i]: ( cP_3 @ d @ Xx ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: ( ( cP_3 @ ( f @ Xx ) @ Xy ) | ( ~( cP_3 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cP_3 @ ( f @ Xx ) @ Xu ) ) | ( ~( cP_3 @ ( f @ Xy ) @ Xv ) ) | 3.97/1.19 ( cQ_4 @ Xu @ Xv @ Xw ) | ( ~( cP_3 @ ( f @ Xz ) @ Xw ) ) | 3.97/1.19 ( ~( cQ_3 @ Xx @ Xy @ Xz ) ) ) ) & 3.97/1.19 ( cP_4 @ c @ c ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cP_4 @ ( f @ Xy ) @ Xv ) ) | ( ~( cP_4 @ ( f @ Xz ) @ Xw ) ) | 3.97/1.19 ( cQ_5 @ Xu @ Xv @ Xw ) | ( ~( cP_4 @ ( f @ Xx ) @ Xu ) ) | 3.97/1.19 ( ~( cQ_4 @ Xx @ Xy @ Xz ) ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i]: ( ~( cQ_5 @ Xx @ Xy @ Xz ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: ( ( cP_4 @ ( f @ Xx ) @ Xy ) | ( ~( cP_4 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( ![Xx:$i]: ( cP_4 @ d @ Xx ) ) & ( cP_4 @ b @ b ) & ( cP_4 @ a @ a ) & 3.97/1.19 ( cP_3 @ c @ c ) & ( cP_3 @ a @ a ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cP_2 @ ( f @ Xx ) @ Xu ) ) | ( ~( cP_2 @ ( f @ Xy ) @ Xv ) ) | 3.97/1.19 ( ~( cP_2 @ ( f @ Xz ) @ Xw ) ) | ( cQ_3 @ Xu @ Xv @ Xw ) | 3.97/1.19 ( ~( cQ_2 @ Xx @ Xy @ Xz ) ) ) ) & 3.97/1.19 ( ![Xx:$i]: ( cP_2 @ d @ Xx ) ) & ( cP_2 @ c @ c ) & ( cP_2 @ b @ b ) & 3.97/1.19 ( cP_2 @ a @ a ) & 3.97/1.19 ( ![Xx:$i,Xy:$i,Xz:$i,Xu:$i,Xv:$i,Xw:$i]: 3.97/1.19 ( ( ~( cQ_1 @ Xx @ Xy @ Xz ) ) | ( ~( cP_1 @ ( f @ Xy ) @ Xv ) ) | 3.97/1.19 ( ~( cP_1 @ ( f @ Xz ) @ Xw ) ) | ( cQ_2 @ Xu @ Xv @ Xw ) | 3.97/1.19 ( ~( cP_1 @ ( f @ Xx ) @ Xu ) ) ) ) & 3.97/1.19 ( ![Xx:$i,Xy:$i]: ( ( cP_1 @ ( f @ Xx ) @ Xy ) | ( ~( cP_1 @ Xx @ Xy ) ) ) ) & 3.97/1.19 ( cP_1 @ b @ b ) & ( cP_1 @ a @ a )), 3.97/1.19 inference('cnf.neg', [status(esa)], [cTHM409_4])). 3.97/1.19 thf(zip_derived_cl0, plain, 3.97/1.19 ( (((cQ_1 @ a @ b @ c) & (cP_1 @ c @ c) & 3.97/1.19 (((!!) @ (^[Y0 : $i]: (cP_1 @ d @ Y0)))) & 3.97/1.19 (((!!) @ (^[Y0 : $i]: 3.97/1.19 (((!!) @ (^[Y1 : $i]: 3.97/1.19 (((cP_2 @ (f @ Y0) @ Y1) | 3.97/1.19 (((~) @ (cP_2 @ Y0 @ Y1))))))))))) & 3.97/1.19 (cP_3 @ b @ b) & (((!!) @ (^[Y0 : $i]: (cP_3 @ d @ Y0)))) & 3.97/1.19 (((!!) @ (^[Y0 : $i]: 3.97/1.19 (((!!) @ (^[Y1 : $i]: 3.97/1.19 (((cP_3 @ (f @ Y0) @ Y1) | 3.97/1.19 (((~) @ (cP_3 @ Y0 @ Y1))))))))))) & 3.97/1.19 (((!!) @ (^[Y0 : $i]: 3.97/1.19 (((!!) @ (^[Y1 : $i]: 3.97/1.19 (((!!) @ (^[Y2 : $i]: 3.97/1.19 (((!!) @ (^[Y3 : $i]: 3.97/1.19 (((!!) @ (^[Y4 : $i]: 3.97/1.19 ( 3.97/1.19 ( 3.97/1.19 (!!) @ ( 3.97/1.19 ^[Y5 : $i]: 3.97/1.19 (( 3.97/1.19 ( 3.97/1.19 ( 3.97/1.19 (~) @ ( 3.97/1.19 cP_3 @ 3.97/1.19 ( 3.97/1.19 f @ Y0) @ 3.97/1.19 Y3))) | 3.97/1.19 ( 3.97/1.19 ( 3.97/1.19 (~) @ ( 3.97/1.19 cP_3 @ 3.97/1.19 ( 3.97/1.19 f @ Y1) @ 3.97/1.19 Y4))) | 3.97/1.19 ( 3.97/1.19 cQ_4 @ 3.97/1.19 Y3 @ 3.97/1.19 Y4 @ Y5) | 3.97/1.19 ( 3.97/1.19 ( 3.97/1.19 (~) @ ( 3.97/1.19 cP_3 @ 3.97/1.19 ( 3.97/1.19 f @ Y2) @ 3.97/1.19 Y5))) | 3.97/1.19 ( 3.97/1.19 ( 3.97/1.19 (~) @ ( 3.97/1.19 cQ_3 @ 3.97/1.19 Y0 @ 3.97/1.19 Y1 @ Y2))))))))))))))))))))))) & 3.97/1.19 (cP_4 @ c @ c) & 3.97/1.19 (((!!) @ (^[Y0 : $i]: 3.97/1.19 (((!!) @ (^[Y1 : $i]: 3.97/1.19 (((!!) @ (^[Y2 : $i]: 3.97/1.19 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (!!) @ ( 3.97/1.20 ^[Y5 : $i]: 3.97/1.20 (( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y2) @ 3.97/1.20 Y5))) | 3.97/1.20 ( 3.97/1.20 cQ_5 @ 3.97/1.20 Y3 @ 3.97/1.20 Y4 @ Y5) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_4 @ 3.97/1.20 Y0 @ 3.97/1.20 Y1 @ Y2))))))))))))))))))))))) & 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((~) @ (cQ_5 @ Y0 @ Y1 @ Y2)))))))))))) & 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((cP_4 @ (f @ Y0) @ Y1) | 3.97/1.20 (((~) @ (cP_4 @ Y0 @ Y1))))))))))) & 3.97/1.20 (((!!) @ (^[Y0 : $i]: (cP_4 @ d @ Y0)))) & (cP_4 @ b @ b) & 3.97/1.20 (cP_4 @ a @ a) & (cP_3 @ c @ c) & (cP_3 @ a @ a) & 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (!!) @ ( 3.97/1.20 ^[Y5 : $i]: 3.97/1.20 (( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y2) @ 3.97/1.20 Y5))) | 3.97/1.20 ( 3.97/1.20 cQ_3 @ 3.97/1.20 Y3 @ 3.97/1.20 Y4 @ Y5) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_2 @ 3.97/1.20 Y0 @ 3.97/1.20 Y1 @ Y2))))))))))))))))))))))) & 3.97/1.20 (((!!) @ (^[Y0 : $i]: (cP_2 @ d @ Y0)))) & (cP_2 @ c @ c) & 3.97/1.20 (cP_2 @ b @ b) & (cP_2 @ a @ a) & 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (!!) @ ( 3.97/1.20 ^[Y5 : $i]: 3.97/1.20 (( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_1 @ 3.97/1.20 Y0 @ 3.97/1.20 Y1 @ Y2))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y2) @ 3.97/1.20 Y5))) | 3.97/1.20 ( 3.97/1.20 cQ_2 @ 3.97/1.20 Y3 @ 3.97/1.20 Y4 @ Y5) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))))))))))))))))))))))) & 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((cP_1 @ (f @ Y0) @ Y1) | 3.97/1.20 (((~) @ (cP_1 @ Y0 @ Y1))))))))))) & 3.97/1.20 (cP_1 @ b @ b) & (cP_1 @ a @ a)))), 3.97/1.20 inference('cnf', [status(esa)], [zf_stmt_0])). 3.97/1.20 thf(zip_derived_cl14, plain, ( (cP_4 @ b @ b)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl15, plain, ( (cP_4 @ a @ a)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl9, plain, ( (cP_4 @ c @ c)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl12, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((cP_4 @ (f @ Y0) @ Y1) | 3.97/1.20 (((~) @ (cP_4 @ Y0 @ Y1)))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl34, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((cP_4 @ (f @ X2) @ Y0) | (((~) @ (cP_4 @ X2 @ Y0))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 3.97/1.20 thf(zip_derived_cl45, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((cP_4 @ (f @ X2) @ X4) | (((~) @ (cP_4 @ X2 @ X4)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 3.97/1.20 thf(zip_derived_cl54, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_4 @ (f @ X2) @ X4) | ~ (cP_4 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])). 3.97/1.20 thf(zip_derived_cl54, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_4 @ (f @ X2) @ X4) | ~ (cP_4 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])). 3.97/1.20 thf(zip_derived_cl54, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_4 @ (f @ X2) @ X4) | ~ (cP_4 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])). 3.97/1.20 thf(zip_derived_cl22, plain, ( (cP_2 @ a @ a)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl5, plain, ( (cP_3 @ b @ b)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl16, plain, ( (cP_3 @ c @ c)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl7, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((cP_3 @ (f @ Y0) @ Y1) | 3.97/1.20 (((~) @ (cP_3 @ Y0 @ Y1)))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl30, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((cP_3 @ (f @ X2) @ Y0) | (((~) @ (cP_3 @ X2 @ Y0))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 3.97/1.20 thf(zip_derived_cl41, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((cP_3 @ (f @ X2) @ X4) | (((~) @ (cP_3 @ X2 @ X4)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])). 3.97/1.20 thf(zip_derived_cl50, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_3 @ (f @ X2) @ X4) | ~ (cP_3 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 3.97/1.20 thf(zip_derived_cl50, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_3 @ (f @ X2) @ X4) | ~ (cP_3 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 3.97/1.20 thf(zip_derived_cl26, plain, ( (cP_1 @ a @ a)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl21, plain, ( (cP_2 @ b @ b)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl20, plain, ( (cP_2 @ c @ c)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl4, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((cP_2 @ (f @ Y0) @ Y1) | 3.97/1.20 (((~) @ (cP_2 @ Y0 @ Y1)))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl28, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((cP_2 @ (f @ X2) @ Y0) | (((~) @ (cP_2 @ X2 @ Y0))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 3.97/1.20 thf(zip_derived_cl40, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((cP_2 @ (f @ X2) @ X4) | (((~) @ (cP_2 @ X2 @ X4)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 3.97/1.20 thf(zip_derived_cl49, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_2 @ (f @ X2) @ X4) | ~ (cP_2 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 3.97/1.20 thf(zip_derived_cl49, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_2 @ (f @ X2) @ X4) | ~ (cP_2 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 3.97/1.20 thf(zip_derived_cl24, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((cP_1 @ (f @ Y0) @ Y1) | 3.97/1.20 (((~) @ (cP_1 @ Y0 @ Y1)))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl39, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((cP_1 @ (f @ X2) @ Y0) | (((~) @ (cP_1 @ X2 @ Y0))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])). 3.97/1.20 thf(zip_derived_cl48, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((cP_1 @ (f @ X2) @ X4) | (((~) @ (cP_1 @ X2 @ X4)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 3.97/1.20 thf(zip_derived_cl57, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_1 @ (f @ X2) @ X4) | ~ (cP_1 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 3.97/1.20 thf(zip_derived_cl57, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_1 @ (f @ X2) @ X4) | ~ (cP_1 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 3.97/1.20 thf(zip_derived_cl57, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_1 @ (f @ X2) @ X4) | ~ (cP_1 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 3.97/1.20 thf(zip_derived_cl1, plain, ( (cQ_1 @ a @ b @ c)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl23, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 (((!!) @ ( 3.97/1.20 ^[Y5 : $i]: 3.97/1.20 (( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_1 @ 3.97/1.20 Y0 @ 3.97/1.20 Y1 @ Y2))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y2) @ 3.97/1.20 Y5))) | 3.97/1.20 ( 3.97/1.20 cQ_2 @ 3.97/1.20 Y3 @ 3.97/1.20 Y4 @ Y5) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3)))))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl38, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_1 @ 3.97/1.20 X2 @ 3.97/1.20 Y0 @ Y1))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 cQ_2 @ 3.97/1.20 Y2 @ 3.97/1.20 Y3 @ Y4) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_1 @ 3.97/1.20 ( 3.97/1.20 f @ X2) @ 3.97/1.20 Y2))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl23])). 3.97/1.20 thf(zip_derived_cl47, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((((~) @ (cQ_1 @ 3.97/1.20 X2 @ X4 @ 3.97/1.20 Y0))) | 3.97/1.20 (((~) @ (cP_1 @ 3.97/1.20 (f @ X4) @ 3.97/1.20 Y2))) | 3.97/1.20 (((~) @ (cP_1 @ 3.97/1.20 (f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 (cQ_2 @ Y1 @ Y2 @ 3.97/1.20 Y3) | 3.97/1.20 (((~) @ (cP_1 @ 3.97/1.20 (f @ X2) @ 3.97/1.20 Y1)))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 3.97/1.20 thf(zip_derived_cl56, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((((~) @ (cQ_1 @ X2 @ X4 @ X6))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X4) @ Y1))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X6) @ Y2))) | 3.97/1.20 (cQ_2 @ Y0 @ Y1 @ Y2) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X2) @ Y0))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 3.97/1.20 thf(zip_derived_cl61, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((((~) @ (cQ_1 @ X2 @ X4 @ X6))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X4) @ Y0))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X6) @ Y1))) | 3.97/1.20 (cQ_2 @ X8 @ Y0 @ Y1) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X2) @ X8)))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 3.97/1.20 thf(zip_derived_cl65, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((((~) @ (cQ_1 @ X2 @ X4 @ X6))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X4) @ X10))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X6) @ Y0))) | 3.97/1.20 (cQ_2 @ X8 @ X10 @ Y0) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X2) @ X8))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 3.97/1.20 thf(zip_derived_cl69, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (((((~) @ (cQ_1 @ X2 @ X4 @ X6))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X4) @ X10))) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X6) @ X12))) | (cQ_2 @ X8 @ X10 @ X12) | 3.97/1.20 (((~) @ (cP_1 @ (f @ X2) @ X8)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl65])). 3.97/1.20 thf(zip_derived_cl73, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (~ (cQ_1 @ X2 @ X4 @ X6) 3.97/1.20 | ~ (cP_1 @ (f @ X4) @ X10) 3.97/1.20 | ~ (cP_1 @ (f @ X6) @ X12) 3.97/1.20 | (cQ_2 @ X8 @ X10 @ X12) 3.97/1.20 | ~ (cP_1 @ (f @ X2) @ X8))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl69])). 3.97/1.20 thf(zip_derived_cl87, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i]: 3.97/1.20 (~ (cP_1 @ (f @ a) @ X0) 3.97/1.20 | (cQ_2 @ X0 @ X2 @ X1) 3.97/1.20 | ~ (cP_1 @ (f @ c) @ X1) 3.97/1.20 | ~ (cP_1 @ (f @ b) @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl73])). 3.97/1.20 thf(zip_derived_cl89, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i]: 3.97/1.20 (~ (cP_1 @ a @ X0) 3.97/1.20 | ~ (cP_1 @ (f @ b) @ X1) 3.97/1.20 | ~ (cP_1 @ (f @ c) @ X2) 3.97/1.20 | (cQ_2 @ X0 @ X1 @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl87])). 3.97/1.20 thf(zip_derived_cl91, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i]: 3.97/1.20 (~ (cP_1 @ b @ X0) 3.97/1.20 | (cQ_2 @ X2 @ X0 @ X1) 3.97/1.20 | ~ (cP_1 @ (f @ c) @ X1) 3.97/1.20 | ~ (cP_1 @ a @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl89])). 3.97/1.20 thf(zip_derived_cl93, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i]: 3.97/1.20 (~ (cP_1 @ c @ X0) 3.97/1.20 | ~ (cP_1 @ a @ X1) 3.97/1.20 | (cQ_2 @ X1 @ X2 @ X0) 3.97/1.20 | ~ (cP_1 @ b @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl91])). 3.97/1.20 thf(zip_derived_cl49, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_2 @ (f @ X2) @ X4) | ~ (cP_2 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 3.97/1.20 thf(zip_derived_cl18, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 (((!!) @ ( 3.97/1.20 ^[Y5 : $i]: 3.97/1.20 (( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y2) @ 3.97/1.20 Y5))) | 3.97/1.20 ( 3.97/1.20 cQ_3 @ 3.97/1.20 Y3 @ 3.97/1.20 Y4 @ Y5) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_2 @ 3.97/1.20 Y0 @ 3.97/1.20 Y1 @ Y2)))))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl36, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ X2) @ 3.97/1.20 Y2))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_2 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 cQ_3 @ 3.97/1.20 Y2 @ 3.97/1.20 Y3 @ Y4) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_2 @ 3.97/1.20 X2 @ 3.97/1.20 Y0 @ Y1))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 3.97/1.20 thf(zip_derived_cl46, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((((~) @ (cP_2 @ 3.97/1.20 (f @ X2) @ 3.97/1.20 Y1))) | 3.97/1.20 (((~) @ (cP_2 @ 3.97/1.20 (f @ X4) @ 3.97/1.20 Y2))) | 3.97/1.20 (((~) @ (cP_2 @ 3.97/1.20 (f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 (cQ_3 @ Y1 @ Y2 @ 3.97/1.20 Y3) | 3.97/1.20 (((~) @ (cQ_2 @ 3.97/1.20 X2 @ X4 @ 3.97/1.20 Y0)))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl36])). 3.97/1.20 thf(zip_derived_cl55, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((((~) @ (cP_2 @ (f @ X2) @ Y0))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X4) @ Y1))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X6) @ Y2))) | 3.97/1.20 (cQ_3 @ Y0 @ Y1 @ Y2) | 3.97/1.20 (((~) @ (cQ_2 @ X2 @ X4 @ X6))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])). 3.97/1.20 thf(zip_derived_cl60, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((((~) @ (cP_2 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X4) @ Y0))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X6) @ Y1))) | 3.97/1.20 (cQ_3 @ X8 @ Y0 @ Y1) | 3.97/1.20 (((~) @ (cQ_2 @ X2 @ X4 @ X6)))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 3.97/1.20 thf(zip_derived_cl64, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((((~) @ (cP_2 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X4) @ X10))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X6) @ Y0))) | 3.97/1.20 (cQ_3 @ X8 @ X10 @ Y0) | 3.97/1.20 (((~) @ (cQ_2 @ X2 @ X4 @ X6))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])). 3.97/1.20 thf(zip_derived_cl68, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (((((~) @ (cP_2 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X4) @ X10))) | 3.97/1.20 (((~) @ (cP_2 @ (f @ X6) @ X12))) | (cQ_3 @ X8 @ X10 @ X12) | 3.97/1.20 (((~) @ (cQ_2 @ X2 @ X4 @ X6)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 3.97/1.20 thf(zip_derived_cl72, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (~ (cP_2 @ (f @ X2) @ X8) 3.97/1.20 | ~ (cP_2 @ (f @ X4) @ X10) 3.97/1.20 | ~ (cP_2 @ (f @ X6) @ X12) 3.97/1.20 | (cQ_3 @ X8 @ X10 @ X12) 3.97/1.20 | ~ (cQ_2 @ X2 @ X4 @ X6))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl68])). 3.97/1.20 thf(zip_derived_cl81, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 3.97/1.20 (~ (cP_2 @ X1 @ X0) 3.97/1.20 | ~ (cQ_2 @ X1 @ X3 @ X2) 3.97/1.20 | (cQ_3 @ X0 @ X5 @ X4) 3.97/1.20 | ~ (cP_2 @ (f @ X2) @ X4) 3.97/1.20 | ~ (cP_2 @ (f @ X3) @ X5))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl72])). 3.97/1.20 thf(zip_derived_cl99, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 3.97/1.20 (~ (cP_1 @ b @ X1) 3.97/1.20 | ~ (cP_1 @ a @ X2) 3.97/1.20 | ~ (cP_1 @ c @ X0) 3.97/1.20 | ~ (cP_2 @ (f @ X1) @ X3) 3.97/1.20 | ~ (cP_2 @ (f @ X0) @ X4) 3.97/1.20 | (cQ_3 @ X5 @ X3 @ X4) 3.97/1.20 | ~ (cP_2 @ X2 @ X5))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl81])). 3.97/1.20 thf(zip_derived_cl211, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 3.97/1.20 (~ (cP_2 @ X1 @ X0) 3.97/1.20 | ~ (cP_2 @ X3 @ X2) 3.97/1.20 | (cQ_3 @ X2 @ X0 @ X4) 3.97/1.20 | ~ (cP_2 @ (f @ X5) @ X4) 3.97/1.20 | ~ (cP_1 @ c @ X5) 3.97/1.20 | ~ (cP_1 @ a @ X3) 3.97/1.20 | ~ (cP_1 @ b @ X1))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl99])). 3.97/1.20 thf(zip_derived_cl243, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 3.97/1.20 (~ (cP_2 @ X1 @ X0) 3.97/1.20 | ~ (cP_1 @ b @ X2) 3.97/1.20 | ~ (cP_1 @ a @ X3) 3.97/1.20 | ~ (cP_1 @ c @ X1) 3.97/1.20 | (cQ_3 @ X5 @ X4 @ X0) 3.97/1.20 | ~ (cP_2 @ X3 @ X5) 3.97/1.20 | ~ (cP_2 @ X2 @ X4))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl211])). 3.97/1.20 thf(zip_derived_cl251, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_2 @ X1 @ X0) 3.97/1.20 | ~ (cP_2 @ X3 @ X2) 3.97/1.20 | (cQ_3 @ X2 @ X0 @ c) 3.97/1.20 | ~ (cP_1 @ c @ c) 3.97/1.20 | ~ (cP_1 @ a @ X3) 3.97/1.20 | ~ (cP_1 @ b @ X1))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl243])). 3.97/1.20 thf(zip_derived_cl2, plain, ( (cP_1 @ c @ c)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl263, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_2 @ X1 @ X0) 3.97/1.20 | ~ (cP_2 @ X3 @ X2) 3.97/1.20 | (cQ_3 @ X2 @ X0 @ c) 3.97/1.20 | ~ (cP_1 @ a @ X3) 3.97/1.20 | ~ (cP_1 @ b @ X1))), 3.97/1.20 inference('demod', [status(thm)], [zip_derived_cl251, zip_derived_cl2])). 3.97/1.20 thf(zip_derived_cl266, plain, 3.97/1.20 (![X0 : $i, X1 : $i]: 3.97/1.20 (~ (cP_1 @ b @ b) 3.97/1.20 | ~ (cP_1 @ a @ X0) 3.97/1.20 | (cQ_3 @ X1 @ b @ c) 3.97/1.20 | ~ (cP_2 @ X0 @ X1))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl263])). 3.97/1.20 thf(zip_derived_cl25, plain, ( (cP_1 @ b @ b)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl277, plain, 3.97/1.20 (![X0 : $i, X1 : $i]: 3.97/1.20 (~ (cP_1 @ a @ X0) | (cQ_3 @ X1 @ b @ c) | ~ (cP_2 @ X0 @ X1))), 3.97/1.20 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl25])). 3.97/1.20 thf(zip_derived_cl279, plain, 3.97/1.20 (![X0 : $i]: (~ (cP_2 @ a @ X0) | (cQ_3 @ X0 @ b @ c))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl277])). 3.97/1.20 thf(zip_derived_cl50, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: ( (cP_3 @ (f @ X2) @ X4) | ~ (cP_3 @ X2 @ X4))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 3.97/1.20 thf(zip_derived_cl8, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 (((!!) @ ( 3.97/1.20 ^[Y5 : $i]: 3.97/1.20 (( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_3 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_3 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 cQ_4 @ 3.97/1.20 Y3 @ 3.97/1.20 Y4 @ Y5) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_3 @ 3.97/1.20 ( 3.97/1.20 f @ Y2) @ 3.97/1.20 Y5))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_3 @ 3.97/1.20 Y0 @ 3.97/1.20 Y1 @ Y2)))))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl31, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_3 @ 3.97/1.20 ( 3.97/1.20 f @ X2) @ 3.97/1.20 Y2))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_3 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 cQ_4 @ 3.97/1.20 Y2 @ 3.97/1.20 Y3 @ Y4) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_3 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_3 @ 3.97/1.20 X2 @ 3.97/1.20 Y0 @ Y1))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 3.97/1.20 thf(zip_derived_cl42, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((((~) @ (cP_3 @ 3.97/1.20 (f @ X2) @ 3.97/1.20 Y1))) | 3.97/1.20 (((~) @ (cP_3 @ 3.97/1.20 (f @ X4) @ 3.97/1.20 Y2))) | 3.97/1.20 (cQ_4 @ Y1 @ Y2 @ 3.97/1.20 Y3) | 3.97/1.20 (((~) @ (cP_3 @ 3.97/1.20 (f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 (((~) @ (cQ_3 @ 3.97/1.20 X2 @ X4 @ 3.97/1.20 Y0)))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 3.97/1.20 thf(zip_derived_cl51, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((((~) @ (cP_3 @ (f @ X2) @ Y0))) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X4) @ Y1))) | 3.97/1.20 (cQ_4 @ Y0 @ Y1 @ Y2) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X6) @ Y2))) | 3.97/1.20 (((~) @ (cQ_3 @ X2 @ X4 @ X6))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 3.97/1.20 thf(zip_derived_cl58, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((((~) @ (cP_3 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X4) @ Y0))) | 3.97/1.20 (cQ_4 @ X8 @ Y0 @ Y1) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X6) @ Y1))) | 3.97/1.20 (((~) @ (cQ_3 @ X2 @ X4 @ X6)))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 3.97/1.20 thf(zip_derived_cl62, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((((~) @ (cP_3 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X4) @ X10))) | 3.97/1.20 (cQ_4 @ X8 @ X10 @ Y0) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X6) @ Y0))) | 3.97/1.20 (((~) @ (cQ_3 @ X2 @ X4 @ X6))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl58])). 3.97/1.20 thf(zip_derived_cl66, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (((((~) @ (cP_3 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X4) @ X10))) | (cQ_4 @ X8 @ X10 @ X12) | 3.97/1.20 (((~) @ (cP_3 @ (f @ X6) @ X12))) | (((~) @ (cQ_3 @ X2 @ X4 @ X6)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 3.97/1.20 thf(zip_derived_cl70, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (~ (cP_3 @ (f @ X2) @ X8) 3.97/1.20 | ~ (cP_3 @ (f @ X4) @ X10) 3.97/1.20 | (cQ_4 @ X8 @ X10 @ X12) 3.97/1.20 | ~ (cP_3 @ (f @ X6) @ X12) 3.97/1.20 | ~ (cQ_3 @ X2 @ X4 @ X6))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl66])). 3.97/1.20 thf(zip_derived_cl75, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 3.97/1.20 (~ (cP_3 @ X1 @ X0) 3.97/1.20 | ~ (cQ_3 @ X1 @ X3 @ X2) 3.97/1.20 | ~ (cP_3 @ (f @ X2) @ X4) 3.97/1.20 | (cQ_4 @ X0 @ X5 @ X4) 3.97/1.20 | ~ (cP_3 @ (f @ X3) @ X5))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl70])). 3.97/1.20 thf(zip_derived_cl283, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_2 @ a @ X0) 3.97/1.20 | ~ (cP_3 @ (f @ b) @ X1) 3.97/1.20 | (cQ_4 @ X3 @ X1 @ X2) 3.97/1.20 | ~ (cP_3 @ (f @ c) @ X2) 3.97/1.20 | ~ (cP_3 @ X0 @ X3))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl279, zip_derived_cl75])). 3.97/1.20 thf(zip_derived_cl291, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_3 @ b @ X0) 3.97/1.20 | ~ (cP_3 @ X2 @ X1) 3.97/1.20 | ~ (cP_3 @ (f @ c) @ X3) 3.97/1.20 | (cQ_4 @ X1 @ X0 @ X3) 3.97/1.20 | ~ (cP_2 @ a @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl283])). 3.97/1.20 thf(zip_derived_cl295, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_3 @ c @ X0) 3.97/1.20 | ~ (cP_2 @ a @ X1) 3.97/1.20 | (cQ_4 @ X3 @ X2 @ X0) 3.97/1.20 | ~ (cP_3 @ X1 @ X3) 3.97/1.20 | ~ (cP_3 @ b @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl291])). 3.97/1.20 thf(zip_derived_cl299, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i]: 3.97/1.20 (~ (cP_3 @ b @ X0) 3.97/1.20 | ~ (cP_3 @ X2 @ X1) 3.97/1.20 | (cQ_4 @ X1 @ X0 @ c) 3.97/1.20 | ~ (cP_2 @ a @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl295])). 3.97/1.20 thf(zip_derived_cl301, plain, 3.97/1.20 (![X0 : $i, X1 : $i]: 3.97/1.20 (~ (cP_2 @ a @ X0) | (cQ_4 @ X1 @ b @ c) | ~ (cP_3 @ X0 @ X1))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl299])). 3.97/1.20 thf(zip_derived_cl303, plain, 3.97/1.20 (![X0 : $i]: (~ (cP_3 @ a @ X0) | (cQ_4 @ X0 @ b @ c))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl301])). 3.97/1.20 thf(zip_derived_cl10, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 (((!!) @ ( 3.97/1.20 ^[Y5 : $i]: 3.97/1.20 (( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y2) @ 3.97/1.20 Y5))) | 3.97/1.20 ( 3.97/1.20 cQ_5 @ 3.97/1.20 Y3 @ 3.97/1.20 Y4 @ Y5) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_4 @ 3.97/1.20 Y0 @ 3.97/1.20 Y1 @ Y2)))))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl32, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((!!) @ (^[Y4 : $i]: 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ Y1) @ 3.97/1.20 Y4))) | 3.97/1.20 ( 3.97/1.20 cQ_5 @ 3.97/1.20 Y2 @ 3.97/1.20 Y3 @ Y4) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cP_4 @ 3.97/1.20 ( 3.97/1.20 f @ X2) @ 3.97/1.20 Y2))) | 3.97/1.20 ( 3.97/1.20 ( 3.97/1.20 (~) @ ( 3.97/1.20 cQ_4 @ 3.97/1.20 X2 @ 3.97/1.20 Y0 @ Y1))))))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 3.97/1.20 thf(zip_derived_cl43, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((!!) @ (^[Y3 : $i]: 3.97/1.20 (((((~) @ (cP_4 @ 3.97/1.20 (f @ X4) @ 3.97/1.20 Y2))) | 3.97/1.20 (((~) @ (cP_4 @ 3.97/1.20 (f @ Y0) @ 3.97/1.20 Y3))) | 3.97/1.20 (cQ_5 @ Y1 @ Y2 @ 3.97/1.20 Y3) | 3.97/1.20 (((~) @ (cP_4 @ 3.97/1.20 (f @ X2) @ 3.97/1.20 Y1))) | 3.97/1.20 (((~) @ (cQ_4 @ 3.97/1.20 X2 @ X4 @ 3.97/1.20 Y0)))))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 3.97/1.20 thf(zip_derived_cl52, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((((~) @ (cP_4 @ (f @ X4) @ Y1))) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X6) @ Y2))) | 3.97/1.20 (cQ_5 @ Y0 @ Y1 @ Y2) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X2) @ Y0))) | 3.97/1.20 (((~) @ (cQ_4 @ X2 @ X4 @ X6))))))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 3.97/1.20 thf(zip_derived_cl59, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((((~) @ (cP_4 @ (f @ X4) @ Y0))) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X6) @ Y1))) | 3.97/1.20 (cQ_5 @ X8 @ Y0 @ Y1) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cQ_4 @ X2 @ X4 @ X6)))))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl52])). 3.97/1.20 thf(zip_derived_cl63, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((((~) @ (cP_4 @ (f @ X4) @ X10))) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X6) @ Y0))) | 3.97/1.20 (cQ_5 @ X8 @ X10 @ Y0) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X2) @ X8))) | 3.97/1.20 (((~) @ (cQ_4 @ X2 @ X4 @ X6))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl59])). 3.97/1.20 thf(zip_derived_cl67, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (((((~) @ (cP_4 @ (f @ X4) @ X10))) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X6) @ X12))) | (cQ_5 @ X8 @ X10 @ X12) | 3.97/1.20 (((~) @ (cP_4 @ (f @ X2) @ X8))) | (((~) @ (cQ_4 @ X2 @ X4 @ X6)))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 3.97/1.20 thf(zip_derived_cl71, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (~ (cP_4 @ (f @ X4) @ X10) 3.97/1.20 | ~ (cP_4 @ (f @ X6) @ X12) 3.97/1.20 | (cQ_5 @ X8 @ X10 @ X12) 3.97/1.20 | ~ (cP_4 @ (f @ X2) @ X8) 3.97/1.20 | ~ (cQ_4 @ X2 @ X4 @ X6))), 3.97/1.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl67])). 3.97/1.20 thf(zip_derived_cl11, plain, 3.97/1.20 ( (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: 3.97/1.20 (((!!) @ (^[Y2 : $i]: 3.97/1.20 (((~) @ (cQ_5 @ Y0 @ Y1 @ Y2))))))))))))), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl33, plain, 3.97/1.20 (![X2 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: 3.97/1.20 (((!!) @ (^[Y1 : $i]: (((~) @ (cQ_5 @ X2 @ Y0 @ Y1)))))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 3.97/1.20 thf(zip_derived_cl44, plain, 3.97/1.20 (![X2 : $i, X4 : $i]: 3.97/1.20 (((!!) @ (^[Y0 : $i]: (((~) @ (cQ_5 @ X2 @ X4 @ Y0))))))), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 3.97/1.20 thf(zip_derived_cl53, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i]: ~ (cQ_5 @ X2 @ X4 @ X6)), 3.97/1.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 3.97/1.20 thf(zip_derived_cl74, plain, 3.97/1.20 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 3.97/1.20 (~ (cQ_4 @ X2 @ X4 @ X6) 3.97/1.20 | ~ (cP_4 @ (f @ X2) @ X8) 3.97/1.20 | ~ (cP_4 @ (f @ X6) @ X12) 3.97/1.20 | ~ (cP_4 @ (f @ X4) @ X10))), 3.97/1.20 inference('clc', [status(thm)], [zip_derived_cl71, zip_derived_cl53])). 3.97/1.20 thf(zip_derived_cl305, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_3 @ a @ X0) 3.97/1.20 | ~ (cP_4 @ (f @ b) @ X1) 3.97/1.20 | ~ (cP_4 @ (f @ c) @ X2) 3.97/1.20 | ~ (cP_4 @ (f @ X0) @ X3))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl303, zip_derived_cl74])). 3.97/1.20 thf(zip_derived_cl307, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_4 @ b @ X0) 3.97/1.20 | ~ (cP_4 @ (f @ X2) @ X1) 3.97/1.20 | ~ (cP_4 @ (f @ c) @ X3) 3.97/1.20 | ~ (cP_3 @ a @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl305])). 3.97/1.20 thf(zip_derived_cl311, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_4 @ X1 @ X0) 3.97/1.20 | ~ (cP_3 @ a @ X1) 3.97/1.20 | ~ (cP_4 @ (f @ c) @ X2) 3.97/1.20 | ~ (cP_4 @ b @ X3))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl307])). 3.97/1.20 thf(zip_derived_cl315, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 3.97/1.20 (~ (cP_4 @ c @ X0) 3.97/1.20 | ~ (cP_4 @ b @ X1) 3.97/1.20 | ~ (cP_3 @ a @ X2) 3.97/1.20 | ~ (cP_4 @ X2 @ X3))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl311])). 3.97/1.20 thf(zip_derived_cl319, plain, 3.97/1.20 (![X0 : $i, X1 : $i, X2 : $i]: 3.97/1.20 (~ (cP_4 @ X1 @ X0) | ~ (cP_3 @ a @ X1) | ~ (cP_4 @ b @ X2))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl315])). 3.97/1.20 thf(zip_derived_cl323, plain, 3.97/1.20 (![X0 : $i]: (~ (cP_4 @ b @ X0) | ~ (cP_3 @ a @ a))), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl319])). 3.97/1.20 thf(zip_derived_cl17, plain, ( (cP_3 @ a @ a)), 3.97/1.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl0])). 3.97/1.20 thf(zip_derived_cl335, plain, (![X0 : $i]: ~ (cP_4 @ b @ X0)), 3.97/1.20 inference('demod', [status(thm)], [zip_derived_cl323, zip_derived_cl17])). 3.97/1.20 thf(zip_derived_cl337, plain, ($false), 3.97/1.20 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl335])). 3.97/1.20 3.97/1.20 % SZS output end Refutation 3.97/1.20 3.97/1.20 3.97/1.20 % Terminating... 2.07/1.23 % Runner terminated. 2.07/1.24 % Zipperpin 1.5 exiting 2.07/1.26 EOF