TSTP Solution File: ALG012-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG012-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6ESuAEeWyL true
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 17:10:03 EDT 2023
% Result : Unsatisfiable 8.85s 1.84s
% Output : Refutation 8.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG012-1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6ESuAEeWyL true
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 02:40:29 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.60 % Total configuration time : 435
% 0.21/0.60 % Estimated wc time : 1092
% 0.21/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 8.85/1.84 % Solved by fo/fo3_bce.sh.
% 8.85/1.84 % BCE start: 11
% 8.85/1.84 % BCE eliminated: 0
% 8.85/1.84 % PE start: 11
% 8.85/1.84 logic: eq
% 8.85/1.84 % PE eliminated: 0
% 8.85/1.84 % done 646 iterations in 1.151s
% 8.85/1.84 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 8.85/1.84 % SZS output start Refutation
% 8.85/1.84 thf(a3_type, type, a3: $i).
% 8.85/1.84 thf(a1_type, type, a1: $i).
% 8.85/1.84 thf(f_type, type, f: $i > $i > $i).
% 8.85/1.84 thf(d2_type, type, d2: $i > $o).
% 8.85/1.84 thf(d1_type, type, d1: $i > $o).
% 8.85/1.84 thf(c_type, type, c: $i > $o).
% 8.85/1.84 thf(conjecture_3, conjecture,
% 8.85/1.84 (~( ( ~( d2 @ Y ) ) | ( ~( d2 @ X ) ) | ( c @ ( f @ X @ Y ) ) ))).
% 8.85/1.84 thf(zf_stmt_0, negated_conjecture,
% 8.85/1.84 (( ~( d2 @ Y ) ) | ( ~( d2 @ X ) ) | ( c @ ( f @ X @ Y ) )),
% 8.85/1.84 inference('cnf.neg', [status(esa)], [conjecture_3])).
% 8.85/1.84 thf(zip_derived_cl10, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d2 @ X0) | ~ (d2 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.85/1.84 thf(f_is_associative, axiom,
% 8.85/1.84 (( f @ X @ ( f @ Y @ Z ) ) = ( f @ ( f @ X @ Y ) @ Z ))).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(conjecture_1, conjecture,
% 8.85/1.84 (~( ( ~( c @ Y ) ) | ( ~( c @ X ) ) | ( d1 @ ( f @ X @ Y ) ) |
% 8.85/1.84 ( d2 @ ( f @ X @ Y ) ) ))).
% 8.85/1.84 thf(zf_stmt_1, negated_conjecture,
% 8.85/1.84 (( ~( c @ Y ) ) | ( ~( c @ X ) ) | ( d1 @ ( f @ X @ Y ) ) |
% 8.85/1.84 ( d2 @ ( f @ X @ Y ) )),
% 8.85/1.84 inference('cnf.neg', [status(esa)], [conjecture_1])).
% 8.85/1.84 thf(zip_derived_cl8, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (d2 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_1])).
% 8.85/1.84 thf(partitions_exclusive_c_d2, axiom, (( ~( c @ X ) ) | ( ~( d2 @ X ) ))).
% 8.85/1.84 thf(zip_derived_cl3, plain, (![X0 : $i]: (~ (c @ X0) | ~ (d2 @ X0))),
% 8.85/1.84 inference('cnf', [status(esa)], [partitions_exclusive_c_d2])).
% 8.85/1.84 thf(zip_derived_cl71, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl3])).
% 8.85/1.84 thf(partitions_exclusive_c_d1, axiom, (( ~( c @ X ) ) | ( ~( d1 @ X ) ))).
% 8.85/1.84 thf(zip_derived_cl2, plain, (![X0 : $i]: (~ (c @ X0) | ~ (d1 @ X0))),
% 8.85/1.84 inference('cnf', [status(esa)], [partitions_exclusive_c_d1])).
% 8.85/1.84 thf(zip_derived_cl97, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (c @ (f @ X1 @ X0)) | ~ (c @ X0) | ~ (c @ X1))),
% 8.85/1.84 inference('clc', [status(thm)], [zip_derived_cl71, zip_derived_cl2])).
% 8.85/1.84 thf(zip_derived_cl102, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ (f @ X2 @ (f @ X1 @ X0))) | ~ (c @ (f @ X2 @ X1)) | ~ (c @ X0))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl97])).
% 8.85/1.84 thf(zip_derived_cl10, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d2 @ X0) | ~ (d2 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.85/1.84 thf(zip_derived_cl114, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d2 @ X2)
% 8.85/1.84 | ~ (d2 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl10])).
% 8.85/1.84 thf(zip_derived_cl144, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X1)
% 8.85/1.84 | ~ (d2 @ X0)
% 8.85/1.84 | ~ (d2 @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (d2 @ X1)
% 8.85/1.84 | ~ (c @ X2))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl114])).
% 8.85/1.84 thf(zip_derived_cl148, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X2) | ~ (d2 @ (f @ X0 @ X2)) | ~ (d2 @ X0) | ~ (d2 @ X1))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl144])).
% 8.85/1.84 thf(zip_derived_cl150, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (c @ X0) | ~ (d2 @ (f @ X1 @ X0)) | ~ (d2 @ X1))),
% 8.85/1.84 inference('condensation', [status(thm)], [zip_derived_cl148])).
% 8.85/1.84 thf(partitions_union, axiom, (( c @ X ) | ( d1 @ X ) | ( d2 @ X ))).
% 8.85/1.84 thf(zip_derived_cl1, plain,
% 8.85/1.84 (![X0 : $i]: ( (c @ X0) | (d1 @ X0) | (d2 @ X0))),
% 8.85/1.84 inference('cnf', [status(esa)], [partitions_union])).
% 8.85/1.84 thf(zip_derived_cl151, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 (~ (d2 @ X1)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl150, zip_derived_cl1])).
% 8.85/1.84 thf(zip_derived_cl10, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d2 @ X0) | ~ (d2 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.85/1.84 thf(zip_derived_cl1, plain,
% 8.85/1.84 (![X0 : $i]: ( (c @ X0) | (d1 @ X0) | (d2 @ X0))),
% 8.85/1.84 inference('cnf', [status(esa)], [partitions_union])).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(zip_derived_cl10, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d2 @ X0) | ~ (d2 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.85/1.84 thf(zip_derived_cl70, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (c @ (f @ X2 @ (f @ X1 @ X0)))
% 8.85/1.84 | ~ (d2 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d2 @ X0))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl10])).
% 8.85/1.84 thf(zip_derived_cl97, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (c @ (f @ X1 @ X0)) | ~ (c @ X0) | ~ (c @ X1))),
% 8.85/1.84 inference('clc', [status(thm)], [zip_derived_cl71, zip_derived_cl2])).
% 8.85/1.84 thf(zip_derived_cl181, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X0)
% 8.85/1.84 | ~ (d2 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (c @ X2)
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl97])).
% 8.85/1.84 thf(zip_derived_cl199, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (d2 @ X2))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl181])).
% 8.85/1.84 thf(zip_derived_cl415, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X1)
% 8.85/1.84 | ~ (d2 @ X0)
% 8.85/1.84 | ~ (d2 @ X0)
% 8.85/1.84 | ~ (c @ X2)
% 8.85/1.84 | (c @ (f @ X2 @ X1))
% 8.85/1.84 | (d1 @ (f @ X2 @ X1)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl199])).
% 8.85/1.84 thf(zip_derived_cl422, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | (c @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (c @ X2)
% 8.85/1.84 | ~ (d2 @ X0)
% 8.85/1.84 | ~ (d2 @ X1))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl415])).
% 8.85/1.84 thf(zip_derived_cl536, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (d2 @ X0))),
% 8.85/1.84 inference('condensation', [status(thm)], [zip_derived_cl422])).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(conjecture_2, conjecture,
% 8.85/1.84 (~( ( ~( d1 @ Y ) ) | ( ~( d1 @ X ) ) | ( c @ ( f @ X @ Y ) ) ))).
% 8.85/1.84 thf(zf_stmt_2, negated_conjecture,
% 8.85/1.84 (( ~( d1 @ Y ) ) | ( ~( d1 @ X ) ) | ( c @ ( f @ X @ Y ) )),
% 8.85/1.84 inference('cnf.neg', [status(esa)], [conjecture_2])).
% 8.85/1.84 thf(zip_derived_cl9, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d1 @ X0) | ~ (d1 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_2])).
% 8.85/1.84 thf(zip_derived_cl102, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ (f @ X2 @ (f @ X1 @ X0))) | ~ (c @ (f @ X2 @ X1)) | ~ (c @ X0))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl97])).
% 8.85/1.84 thf(zip_derived_cl9, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d1 @ X0) | ~ (d1 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_2])).
% 8.85/1.84 thf(zip_derived_cl113, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ X2)
% 8.85/1.84 | ~ (d1 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl9])).
% 8.85/1.84 thf(zip_derived_cl123, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d1 @ X1)
% 8.85/1.84 | ~ (d1 @ X0)
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (d1 @ X1)
% 8.85/1.84 | ~ (c @ X2))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl113])).
% 8.85/1.84 thf(zip_derived_cl127, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X2) | ~ (d1 @ (f @ X0 @ X2)) | ~ (d1 @ X0) | ~ (d1 @ X1))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl123])).
% 8.85/1.84 thf(zip_derived_cl128, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (c @ X0) | ~ (d1 @ (f @ X1 @ X0)) | ~ (d1 @ X1))),
% 8.85/1.84 inference('condensation', [status(thm)], [zip_derived_cl127])).
% 8.85/1.84 thf(zip_derived_cl129, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d1 @ (f @ X2 @ (f @ X1 @ X0)))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (c @ X0))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl128])).
% 8.85/1.84 thf(partition_c_not_empty, axiom, (c @ a1)).
% 8.85/1.84 thf(zip_derived_cl5, plain, ( (c @ a1)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_c_not_empty])).
% 8.85/1.84 thf(partition_d2_not_empty, axiom, (d2 @ a3)).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl151, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 (~ (d2 @ X1)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl150, zip_derived_cl1])).
% 8.85/1.84 thf(zip_derived_cl536, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (d2 @ X0))),
% 8.85/1.84 inference('condensation', [status(thm)], [zip_derived_cl422])).
% 8.85/1.84 thf(zip_derived_cl10, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d2 @ X0) | ~ (d2 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.85/1.84 thf(zip_derived_cl8, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (d2 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_1])).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(zip_derived_cl9, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d1 @ X0) | ~ (d1 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_2])).
% 8.85/1.84 thf(zip_derived_cl69, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (c @ (f @ X2 @ (f @ X1 @ X0)))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ X0))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(zip_derived_cl58, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.85/1.84 ((f @ (f @ X2 @ X1) @ (f @ X0 @ X3))
% 8.85/1.84 = (f @ (f @ X2 @ (f @ X1 @ X0)) @ X3))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(zip_derived_cl59, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.85/1.84 ((f @ X2 @ (f @ X1 @ (f @ X0 @ X3)))
% 8.85/1.84 = (f @ (f @ X2 @ (f @ X1 @ X0)) @ X3))),
% 8.85/1.84 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl0])).
% 8.85/1.84 thf(zip_derived_cl114, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d2 @ X2)
% 8.85/1.84 | ~ (d2 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl10])).
% 8.85/1.84 thf(zip_derived_cl147, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 8.85/1.84 (~ (c @ (f @ X3 @ (f @ X2 @ (f @ X1 @ X0))))
% 8.85/1.84 | ~ (d2 @ (f @ X0 @ X4))
% 8.85/1.84 | ~ (d2 @ (f @ X3 @ (f @ X2 @ X1)))
% 8.85/1.84 | ~ (c @ X4))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl114])).
% 8.85/1.84 thf(zip_derived_cl1395, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 8.85/1.84 (~ (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (d1 @ (f @ X3 @ X2))
% 8.85/1.84 | ~ (c @ X4)
% 8.85/1.84 | ~ (d2 @ (f @ X3 @ (f @ X2 @ X1)))
% 8.85/1.84 | ~ (d2 @ (f @ X0 @ X4)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl147])).
% 8.85/1.84 thf(zip_derived_cl1857, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ (f @ X2 @ (f @ X1 @ X0)))
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2)))),
% 8.85/1.84 inference('eq_fact', [status(thm)], [zip_derived_cl1395])).
% 8.85/1.84 thf(zip_derived_cl1864, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X2 @ (f @ X1 @ X0)))
% 8.85/1.84 | ~ (c @ X2)
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl1857])).
% 8.85/1.84 thf(zip_derived_cl1875, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X2)
% 8.85/1.84 | (d1 @ (f @ X2 @ (f @ X1 @ X0))))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl1864])).
% 8.85/1.84 thf(zip_derived_cl69, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (c @ (f @ X2 @ (f @ X1 @ X0)))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ X0))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 8.85/1.84 thf(zip_derived_cl59, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.85/1.84 ((f @ X2 @ (f @ X1 @ (f @ X0 @ X3)))
% 8.85/1.84 = (f @ (f @ X2 @ (f @ X1 @ X0)) @ X3))),
% 8.85/1.84 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl0])).
% 8.85/1.84 thf(zip_derived_cl113, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ X2)
% 8.85/1.84 | ~ (d1 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl9])).
% 8.85/1.84 thf(zip_derived_cl126, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 8.85/1.84 (~ (c @ (f @ X3 @ (f @ X2 @ (f @ X1 @ X0))))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X4))
% 8.85/1.84 | ~ (d1 @ (f @ X3 @ (f @ X2 @ X1)))
% 8.85/1.84 | ~ (c @ X4))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl113])).
% 8.85/1.84 thf(zip_derived_cl1238, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 8.85/1.84 (~ (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (d1 @ (f @ X3 @ X2))
% 8.85/1.84 | ~ (c @ X4)
% 8.85/1.84 | ~ (d1 @ (f @ X3 @ (f @ X2 @ X1)))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X4)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl126])).
% 8.85/1.84 thf(zip_derived_cl1367, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d1 @ (f @ X2 @ (f @ X1 @ X0)))
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2)))),
% 8.85/1.84 inference('eq_fact', [status(thm)], [zip_derived_cl1238])).
% 8.85/1.84 thf(zip_derived_cl4230, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X2)
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1)))),
% 8.85/1.84 inference('clc', [status(thm)], [zip_derived_cl1875, zip_derived_cl1367])).
% 8.85/1.84 thf(zip_derived_cl4232, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X1)
% 8.85/1.84 | ~ (d2 @ X0)
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (c @ X2))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl4230])).
% 8.85/1.84 thf(zip_derived_cl4262, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X0)
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d2 @ X2)
% 8.85/1.84 | ~ (d2 @ X0))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl536, zip_derived_cl4232])).
% 8.85/1.84 thf(zip_derived_cl4275, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X2)
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1))
% 8.85/1.84 | (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (d2 @ X0))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl4262])).
% 8.85/1.84 thf(zip_derived_cl4279, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | ~ (d2 @ X1)
% 8.85/1.84 | ~ (d2 @ X2)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | (c @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (d2 @ X1))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl4275])).
% 8.85/1.84 thf(zip_derived_cl4291, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (c @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (d2 @ X2)
% 8.85/1.84 | ~ (d2 @ X1)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl4279])).
% 8.85/1.84 thf(zip_derived_cl4305, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 ( (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | ~ (d2 @ X1)
% 8.85/1.84 | (c @ (f @ X0 @ a3)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl4291])).
% 8.85/1.84 thf(zip_derived_cl4406, plain,
% 8.85/1.84 (![X0 : $i]: ( (c @ (f @ X0 @ a3)) | ~ (c @ X0) | (c @ (f @ a3 @ X0)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl4305])).
% 8.85/1.84 thf(zip_derived_cl4424, plain,
% 8.85/1.84 (( (c @ (f @ a3 @ a1)) | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl4406])).
% 8.85/1.84 thf(zip_derived_cl8, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (d2 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_1])).
% 8.85/1.84 thf(zip_derived_cl4424, plain,
% 8.85/1.84 (( (c @ (f @ a3 @ a1)) | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl4406])).
% 8.85/1.84 thf(zip_derived_cl114, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (d2 @ X2)
% 8.85/1.84 | ~ (d2 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl102, zip_derived_cl10])).
% 8.85/1.84 thf(zip_derived_cl4446, plain,
% 8.85/1.84 (![X0 : $i]:
% 8.85/1.84 ( (c @ (f @ a1 @ a3))
% 8.85/1.84 | ~ (d2 @ (f @ a1 @ X0))
% 8.85/1.84 | ~ (d2 @ a3)
% 8.85/1.84 | ~ (c @ X0))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl4424, zip_derived_cl114])).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl4465, plain,
% 8.85/1.84 (![X0 : $i]: ( (c @ (f @ a1 @ a3)) | ~ (d2 @ (f @ a1 @ X0)) | ~ (c @ X0))),
% 8.85/1.84 inference('demod', [status(thm)], [zip_derived_cl4446, zip_derived_cl7])).
% 8.85/1.84 thf(zip_derived_cl4475, plain,
% 8.85/1.84 (![X0 : $i]:
% 8.85/1.84 ( (d1 @ (f @ a1 @ X0))
% 8.85/1.84 | ~ (c @ a1)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl4465])).
% 8.85/1.84 thf(zip_derived_cl5, plain, ( (c @ a1)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_c_not_empty])).
% 8.85/1.84 thf(zip_derived_cl4479, plain,
% 8.85/1.84 (![X0 : $i]:
% 8.85/1.84 ( (d1 @ (f @ a1 @ X0))
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('demod', [status(thm)], [zip_derived_cl4475, zip_derived_cl5])).
% 8.85/1.84 thf(zip_derived_cl4480, plain,
% 8.85/1.84 (![X0 : $i]: ( (c @ (f @ a1 @ a3)) | ~ (c @ X0) | (d1 @ (f @ a1 @ X0)))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl4479])).
% 8.85/1.84 thf(zip_derived_cl4494, plain,
% 8.85/1.84 (( (c @ (f @ a1 @ a3))
% 8.85/1.84 | (d1 @ (f @ a1 @ (f @ a3 @ a1)))
% 8.85/1.84 | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl4424, zip_derived_cl4480])).
% 8.85/1.84 thf(zip_derived_cl4496, plain,
% 8.85/1.84 (( (d1 @ (f @ a1 @ (f @ a3 @ a1))) | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl4494])).
% 8.85/1.84 thf(zip_derived_cl4927, plain,
% 8.85/1.84 ((~ (c @ a1) | ~ (d1 @ (f @ a1 @ a3)) | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl129, zip_derived_cl4496])).
% 8.85/1.84 thf(zip_derived_cl5, plain, ( (c @ a1)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_c_not_empty])).
% 8.85/1.84 thf(zip_derived_cl4929, plain,
% 8.85/1.84 ((~ (d1 @ (f @ a1 @ a3)) | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('demod', [status(thm)], [zip_derived_cl4927, zip_derived_cl5])).
% 8.85/1.84 thf(zip_derived_cl2, plain, (![X0 : $i]: (~ (c @ X0) | ~ (d1 @ X0))),
% 8.85/1.84 inference('cnf', [status(esa)], [partitions_exclusive_c_d1])).
% 8.85/1.84 thf(zip_derived_cl4964, plain, (~ (d1 @ (f @ a1 @ a3))),
% 8.85/1.84 inference('clc', [status(thm)], [zip_derived_cl4929, zip_derived_cl2])).
% 8.85/1.84 thf(zip_derived_cl4968, plain,
% 8.85/1.84 ((~ (d2 @ a3) | ~ (c @ a1) | (c @ (f @ a1 @ a3)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl536, zip_derived_cl4964])).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl5, plain, ( (c @ a1)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_c_not_empty])).
% 8.85/1.84 thf(zip_derived_cl4971, plain, ( (c @ (f @ a1 @ a3))),
% 8.85/1.84 inference('demod', [status(thm)],
% 8.85/1.84 [zip_derived_cl4968, zip_derived_cl7, zip_derived_cl5])).
% 8.85/1.84 thf(zip_derived_cl8, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 (~ (c @ X0)
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | (d2 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_1])).
% 8.85/1.84 thf(zip_derived_cl181, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X0)
% 8.85/1.84 | ~ (d2 @ (f @ X2 @ X1))
% 8.85/1.84 | ~ (c @ X2)
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl97])).
% 8.85/1.84 thf(zip_derived_cl200, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | ~ (c @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | ~ (d2 @ X2))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl181])).
% 8.85/1.84 thf(zip_derived_cl203, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (d2 @ X2)
% 8.85/1.84 | ~ (c @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (c @ X0)
% 8.85/1.84 | ~ (c @ X1)
% 8.85/1.84 | (d1 @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl200])).
% 8.85/1.84 thf(zip_derived_cl4989, plain,
% 8.85/1.84 (![X0 : $i]:
% 8.85/1.84 ( (d1 @ (f @ X0 @ a1)) | ~ (c @ X0) | ~ (c @ a1) | ~ (d2 @ a3))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl4971, zip_derived_cl203])).
% 8.85/1.84 thf(zip_derived_cl5, plain, ( (c @ a1)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_c_not_empty])).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl5013, plain,
% 8.85/1.84 (![X0 : $i]: ( (d1 @ (f @ X0 @ a1)) | ~ (c @ X0))),
% 8.85/1.84 inference('demod', [status(thm)],
% 8.85/1.84 [zip_derived_cl4989, zip_derived_cl5, zip_derived_cl7])).
% 8.85/1.84 thf(zip_derived_cl4971, plain, ( (c @ (f @ a1 @ a3))),
% 8.85/1.84 inference('demod', [status(thm)],
% 8.85/1.84 [zip_derived_cl4968, zip_derived_cl7, zip_derived_cl5])).
% 8.85/1.84 thf(zip_derived_cl4230, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 (~ (c @ X2)
% 8.85/1.84 | ~ (c @ (f @ X1 @ X0))
% 8.85/1.84 | ~ (d1 @ (f @ X0 @ X2))
% 8.85/1.84 | ~ (d1 @ (f @ X2 @ X1)))),
% 8.85/1.84 inference('clc', [status(thm)], [zip_derived_cl1875, zip_derived_cl1367])).
% 8.85/1.84 thf(zip_derived_cl4981, plain,
% 8.85/1.84 (![X0 : $i]:
% 8.85/1.84 (~ (d1 @ (f @ X0 @ a1)) | ~ (d1 @ (f @ a3 @ X0)) | ~ (c @ X0))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl4971, zip_derived_cl4230])).
% 8.85/1.84 thf(zip_derived_cl5171, plain,
% 8.85/1.84 (![X0 : $i]: (~ (c @ X0) | ~ (c @ X0) | ~ (d1 @ (f @ a3 @ X0)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl5013, zip_derived_cl4981])).
% 8.85/1.84 thf(zip_derived_cl5206, plain,
% 8.85/1.84 (![X0 : $i]: (~ (d1 @ (f @ a3 @ X0)) | ~ (c @ X0))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl5171])).
% 8.85/1.84 thf(zip_derived_cl5358, plain,
% 8.85/1.84 (![X0 : $i]:
% 8.85/1.84 ( (c @ (f @ a3 @ X0)) | ~ (c @ X0) | ~ (d2 @ a3) | ~ (c @ X0))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl5206])).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl5367, plain,
% 8.85/1.84 (![X0 : $i]: ( (c @ (f @ a3 @ X0)) | ~ (c @ X0) | ~ (c @ X0))),
% 8.85/1.84 inference('demod', [status(thm)], [zip_derived_cl5358, zip_derived_cl7])).
% 8.85/1.84 thf(zip_derived_cl5368, plain,
% 8.85/1.84 (![X0 : $i]: (~ (c @ X0) | (c @ (f @ a3 @ X0)))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl5367])).
% 8.85/1.84 thf(zip_derived_cl10, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]: (~ (d2 @ X0) | ~ (d2 @ X1) | (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.85/1.84 thf(zip_derived_cl0, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.85/1.84 ((f @ X0 @ (f @ X1 @ X2)) = (f @ (f @ X0 @ X1) @ X2))),
% 8.85/1.84 inference('cnf', [status(esa)], [f_is_associative])).
% 8.85/1.84 thf(zip_derived_cl5013, plain,
% 8.85/1.84 (![X0 : $i]: ( (d1 @ (f @ X0 @ a1)) | ~ (c @ X0))),
% 8.85/1.84 inference('demod', [status(thm)],
% 8.85/1.84 [zip_derived_cl4989, zip_derived_cl5, zip_derived_cl7])).
% 8.85/1.84 thf(zip_derived_cl2, plain, (![X0 : $i]: (~ (c @ X0) | ~ (d1 @ X0))),
% 8.85/1.84 inference('cnf', [status(esa)], [partitions_exclusive_c_d1])).
% 8.85/1.84 thf(zip_derived_cl5146, plain,
% 8.85/1.84 (![X0 : $i]: (~ (c @ X0) | ~ (c @ (f @ X0 @ a1)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl5013, zip_derived_cl2])).
% 8.85/1.84 thf(zip_derived_cl5344, plain,
% 8.85/1.84 (![X0 : $i, X1 : $i]:
% 8.85/1.84 (~ (c @ (f @ X1 @ (f @ X0 @ a1))) | ~ (c @ (f @ X1 @ X0)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl5146])).
% 8.85/1.84 thf(zip_derived_cl5368, plain,
% 8.85/1.84 (![X0 : $i]: (~ (c @ X0) | (c @ (f @ a3 @ X0)))),
% 8.85/1.84 inference('simplify', [status(thm)], [zip_derived_cl5367])).
% 8.85/1.84 thf(zip_derived_cl6102, plain,
% 8.85/1.84 (![X0 : $i]: (~ (c @ (f @ a3 @ X0)) | ~ (c @ (f @ X0 @ a1)))),
% 8.85/1.84 inference('sup+', [status(thm)], [zip_derived_cl5344, zip_derived_cl5368])).
% 8.85/1.84 thf(zip_derived_cl6139, plain,
% 8.85/1.84 (![X0 : $i]: (~ (d2 @ a3) | ~ (d2 @ X0) | ~ (c @ (f @ X0 @ a1)))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl6102])).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl6155, plain,
% 8.85/1.84 (![X0 : $i]: (~ (d2 @ X0) | ~ (c @ (f @ X0 @ a1)))),
% 8.85/1.84 inference('demod', [status(thm)], [zip_derived_cl6139, zip_derived_cl7])).
% 8.85/1.84 thf(zip_derived_cl6304, plain, ((~ (c @ a1) | ~ (d2 @ a3))),
% 8.85/1.84 inference('sup-', [status(thm)], [zip_derived_cl5368, zip_derived_cl6155])).
% 8.85/1.84 thf(zip_derived_cl5, plain, ( (c @ a1)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_c_not_empty])).
% 8.85/1.84 thf(zip_derived_cl7, plain, ( (d2 @ a3)),
% 8.85/1.84 inference('cnf', [status(esa)], [partition_d2_not_empty])).
% 8.85/1.84 thf(zip_derived_cl6312, plain, ($false),
% 8.85/1.84 inference('demod', [status(thm)],
% 8.85/1.84 [zip_derived_cl6304, zip_derived_cl5, zip_derived_cl7])).
% 8.85/1.84
% 8.85/1.84 % SZS output end Refutation
% 8.85/1.84
% 8.85/1.84
% 8.85/1.84 % Terminating...
% 9.27/1.94 % Runner terminated.
% 9.27/1.95 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------