TSTP Solution File: MSC007-2.005 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : MSC007-2.005 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.dtNHQp0ttF true
% Computer : n022.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 : Thu Aug 31 09:31:47 EDT 2023
% Result : Unsatisfiable 1.68s 1.12s
% Output : Refutation 2.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MSC007-2.005 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.dtNHQp0ttF true
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 13:37:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.67 % Total configuration time : 435
% 0.22/0.67 % Estimated wc time : 1092
% 0.22/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.68/1.12 % Solved by fo/fo1_av.sh.
% 1.68/1.12 % done 726 iterations in 0.318s
% 1.68/1.12 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.68/1.12 % SZS output start Refutation
% 1.68/1.12 thf(hole_1_type, type, hole_1: $i).
% 1.68/1.12 thf(in_type, type, in: $i > $i > $o).
% 1.68/1.12 thf(pigeon_1_type, type, pigeon_1: $i).
% 1.68/1.12 thf(pigeon_5_type, type, pigeon_5: $i).
% 1.68/1.12 thf(pigeon_2_type, type, pigeon_2: $i).
% 1.68/1.12 thf(hole_3_type, type, hole_3: $i).
% 1.68/1.12 thf(pigeon_4_type, type, pigeon_4: $i).
% 1.68/1.12 thf(pigeon_3_type, type, pigeon_3: $i).
% 1.68/1.12 thf(hole_type, type, hole: $i > $o).
% 1.68/1.12 thf(hole_of_type, type, hole_of: $i > $i).
% 1.68/1.12 thf(hole_4_type, type, hole_4: $i).
% 1.68/1.12 thf(pigeon_type, type, pigeon: $i > $o).
% 1.68/1.12 thf(hole_2_type, type, hole_2: $i).
% 1.68/1.12 thf(pigeon_3, axiom, (pigeon @ pigeon_3)).
% 1.68/1.12 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 1.68/1.12 inference('cnf', [status(esa)], [pigeon_3])).
% 1.68/1.12 thf(pigeon_4, axiom, (pigeon @ pigeon_4)).
% 1.68/1.12 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 1.68/1.12 inference('cnf', [status(esa)], [pigeon_4])).
% 1.68/1.12 thf(pigeon_2, axiom, (pigeon @ pigeon_2)).
% 1.68/1.12 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 1.68/1.12 inference('cnf', [status(esa)], [pigeon_2])).
% 1.68/1.12 thf(each_pigeons_hole1, axiom,
% 1.68/1.12 (( ~( pigeon @ X ) ) | ( hole @ ( hole_of @ X ) ))).
% 1.68/1.12 thf(zip_derived_cl29, plain,
% 1.68/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (hole @ (hole_of @ X0)))),
% 1.68/1.12 inference('cnf', [status(esa)], [each_pigeons_hole1])).
% 1.68/1.12 thf(all_holes, axiom,
% 1.68/1.12 (( ~( hole @ Hole ) ) | ( ( Hole ) = ( hole_1 ) ) |
% 1.68/1.12 ( ( Hole ) = ( hole_2 ) ) | ( ( Hole ) = ( hole_3 ) ) |
% 1.68/1.12 ( ( Hole ) = ( hole_4 ) ))).
% 1.68/1.12 thf(zip_derived_cl28, plain,
% 1.68/1.12 (![X0 : $i]:
% 1.68/1.12 (~ (hole @ X0)
% 1.68/1.12 | ((X0) = (hole_1))
% 1.68/1.12 | ((X0) = (hole_2))
% 1.68/1.12 | ((X0) = (hole_3))
% 1.68/1.12 | ((X0) = (hole_4)))),
% 1.68/1.12 inference('cnf', [status(esa)], [all_holes])).
% 1.68/1.12 thf(zip_derived_cl49, plain,
% 1.68/1.12 (![X0 : $i]:
% 1.68/1.12 (~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3))
% 1.68/1.12 | ((hole_of @ X0) = (hole_4)))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl28])).
% 1.68/1.12 thf(each_pigeons_hole2, axiom,
% 1.68/1.12 (( ~( pigeon @ X ) ) | ( in @ X @ ( hole_of @ X ) ))).
% 1.68/1.12 thf(zip_derived_cl30, plain,
% 1.68/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 1.68/1.12 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 1.68/1.12 thf(zip_derived_cl59, plain,
% 1.68/1.12 (![X0 : $i]:
% 1.68/1.12 (((hole_of @ X0) = (hole_3))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | (in @ X0 @ hole_4))),
% 1.68/1.12 inference('s_sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl30])).
% 1.68/1.12 thf(zip_derived_cl66, plain,
% 1.68/1.12 (![X0 : $i]:
% 1.68/1.12 ( (in @ X0 @ hole_4)
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl59])).
% 1.68/1.12 thf(zip_derived_cl49, plain,
% 1.68/1.12 (![X0 : $i]:
% 1.68/1.12 (~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3))
% 1.68/1.12 | ((hole_of @ X0) = (hole_4)))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl28])).
% 1.68/1.12 thf(zip_derived_cl30, plain,
% 1.68/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 1.68/1.12 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 1.68/1.12 thf(only_one_per_hole, conjecture,
% 1.68/1.12 (~( ( ( Pigeon1 ) = ( Pigeon2 ) ) | ( ~( in @ Pigeon2 @ Hole ) ) |
% 1.68/1.12 ( ~( in @ Pigeon1 @ Hole ) ) | ( ~( pigeon @ Pigeon2 ) ) |
% 1.68/1.12 ( ~( pigeon @ Pigeon1 ) ) | ( ~( hole @ Hole ) ) ))).
% 1.68/1.12 thf(zf_stmt_0, negated_conjecture,
% 1.68/1.12 (( ( Pigeon1 ) = ( Pigeon2 ) ) | ( ~( in @ Pigeon2 @ Hole ) ) |
% 1.68/1.12 ( ~( in @ Pigeon1 @ Hole ) ) | ( ~( pigeon @ Pigeon2 ) ) |
% 1.68/1.12 ( ~( pigeon @ Pigeon1 ) ) | ( ~( hole @ Hole ) )),
% 1.68/1.12 inference('cnf.neg', [status(esa)], [only_one_per_hole])).
% 1.68/1.12 thf(zip_derived_cl31, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.68/1.12 (((X1) = (X0))
% 1.68/1.12 | ~ (in @ X0 @ X2)
% 1.68/1.12 | ~ (in @ X1 @ X2)
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ~ (pigeon @ X1)
% 1.68/1.12 | ~ (hole @ X2))),
% 1.68/1.12 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.68/1.12 thf(zip_derived_cl32, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (~ (pigeon @ X0)
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ~ (in @ X1 @ (hole_of @ X0))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ~ (pigeon @ X1)
% 1.68/1.12 | ~ (hole @ (hole_of @ X0)))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl31])).
% 1.68/1.12 thf(zip_derived_cl35, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (~ (hole @ (hole_of @ X0))
% 1.68/1.12 | ~ (pigeon @ X1)
% 1.68/1.12 | ~ (in @ X1 @ (hole_of @ X0))
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ~ (pigeon @ X0))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl32])).
% 1.68/1.12 thf(zip_derived_cl29, plain,
% 1.68/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (hole @ (hole_of @ X0)))),
% 1.68/1.12 inference('cnf', [status(esa)], [each_pigeons_hole1])).
% 1.68/1.12 thf(zip_derived_cl36, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (~ (pigeon @ X0)
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ~ (in @ X1 @ (hole_of @ X0))
% 1.68/1.12 | ~ (pigeon @ X1))),
% 1.68/1.12 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 1.68/1.12 thf(zip_derived_cl60, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (((hole_of @ X0) = (hole_3))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ~ (in @ X1 @ hole_4)
% 1.68/1.12 | ~ (pigeon @ X1))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl36])).
% 1.68/1.12 thf(zip_derived_cl67, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (~ (pigeon @ X1)
% 1.68/1.12 | ~ (in @ X1 @ hole_4)
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl60])).
% 1.68/1.12 thf(zip_derived_cl71, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (((hole_of @ X0) = (hole_3))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X0) = (X1))
% 1.68/1.12 | ~ (pigeon @ X1)
% 1.68/1.12 | ((hole_of @ X1) = (hole_1))
% 1.68/1.12 | ((hole_of @ X1) = (hole_2))
% 1.68/1.12 | ((hole_of @ X1) = (hole_3)))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl67])).
% 1.68/1.12 thf(zip_derived_cl72, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (((hole_of @ X1) = (hole_3))
% 1.68/1.12 | ((hole_of @ X1) = (hole_2))
% 1.68/1.12 | ((hole_of @ X1) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X1)
% 1.68/1.12 | ((X0) = (X1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl71])).
% 1.68/1.12 thf(zip_derived_cl74, plain,
% 1.68/1.12 (![X0 : $i]:
% 1.68/1.12 (((hole_of @ pigeon_2) = (hole_3))
% 1.68/1.12 | ((hole_of @ pigeon_2) = (hole_2))
% 1.68/1.12 | ((hole_of @ pigeon_2) = (hole_1))
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl72])).
% 1.68/1.12 thf(zip_derived_cl132, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('split', [status(esa)], [zip_derived_cl74])).
% 1.68/1.12 thf(zip_derived_cl30, plain,
% 1.68/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 1.68/1.12 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 1.68/1.12 thf(zip_derived_cl137, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 (((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | (in @ X0 @ hole_3)))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl30])).
% 1.68/1.12 thf(zip_derived_cl146, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 ( (in @ X0 @ hole_3)
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl137])).
% 1.68/1.12 thf(zip_derived_cl132, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('split', [status(esa)], [zip_derived_cl74])).
% 1.68/1.12 thf(zip_derived_cl36, plain,
% 1.68/1.12 (![X0 : $i, X1 : $i]:
% 1.68/1.12 (~ (pigeon @ X0)
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ~ (in @ X1 @ (hole_of @ X0))
% 1.68/1.12 | ~ (pigeon @ X1))),
% 1.68/1.12 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 1.68/1.12 thf(zip_derived_cl138, plain,
% 1.68/1.12 ((![X0 : $i, X1 : $i]:
% 1.68/1.12 (((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ~ (in @ X1 @ hole_3)
% 1.68/1.12 | ~ (pigeon @ X1)))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl36])).
% 1.68/1.12 thf(zip_derived_cl147, plain,
% 1.68/1.12 ((![X0 : $i, X1 : $i]:
% 1.68/1.12 (~ (pigeon @ X1)
% 1.68/1.12 | ~ (in @ X1 @ hole_3)
% 1.68/1.12 | ((X1) = (X0))
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl138])).
% 1.68/1.12 thf(zip_derived_cl898, plain,
% 1.68/1.12 ((![X0 : $i, X1 : $i]:
% 1.68/1.12 (((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X0) = (X1))
% 1.68/1.12 | ((X1) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X1)
% 1.68/1.12 | ((hole_of @ X1) = (hole_1))
% 1.68/1.12 | ((hole_of @ X1) = (hole_2))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl147])).
% 1.68/1.12 thf(zip_derived_cl905, plain,
% 1.68/1.12 ((![X0 : $i, X1 : $i]:
% 1.68/1.12 (((hole_of @ X1) = (hole_2))
% 1.68/1.12 | ((hole_of @ X1) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X1)
% 1.68/1.12 | ((X1) = (pigeon_2))
% 1.68/1.12 | ((X0) = (X1))
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl898])).
% 1.68/1.12 thf(zip_derived_cl2986, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 (((hole_of @ pigeon_4) = (hole_2))
% 1.68/1.12 | ((hole_of @ pigeon_4) = (hole_1))
% 1.68/1.12 | ((pigeon_4) = (pigeon_2))
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl905])).
% 1.68/1.12 thf(pigeon_2_is_not_pigeon_4, axiom, (( pigeon_2 ) != ( pigeon_4 ))).
% 1.68/1.12 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 1.68/1.12 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 1.68/1.12 thf(zip_derived_cl2991, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 (((hole_of @ pigeon_4) = (hole_2))
% 1.68/1.12 | ((hole_of @ pigeon_4) = (hole_1))
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))
% 1.68/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 1.68/1.12 inference('simplify_reflect-', [status(thm)],
% 1.68/1.12 [zip_derived_cl2986, zip_derived_cl13])).
% 1.68/1.12 thf(zip_derived_cl3138, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 1.68/1.12 inference('split', [status(esa)], [zip_derived_cl2991])).
% 1.68/1.12 thf(zip_derived_cl30, plain,
% 1.68/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 1.68/1.12 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 1.68/1.12 thf(zip_derived_cl3142, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 (((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | (in @ X0 @ hole_2)))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 1.68/1.12 inference('s_sup+', [status(thm)], [zip_derived_cl3138, zip_derived_cl30])).
% 1.68/1.12 thf(zip_derived_cl3162, plain,
% 1.68/1.12 ((![X0 : $i]:
% 1.68/1.12 ( (in @ X0 @ hole_2)
% 1.68/1.12 | ((X0) = (pigeon_2))
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))))
% 1.68/1.12 <= ((![X0 : $i]:
% 1.68/1.12 (((X0) = (pigeon_2))
% 1.68/1.12 | ((X0) = (pigeon_4))
% 1.68/1.12 | ~ (pigeon @ X0)
% 1.68/1.12 | ((hole_of @ X0) = (hole_1))
% 1.68/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 1.68/1.12 inference('simplify', [status(thm)], [zip_derived_cl3142])).
% 2.08/1.12 thf(zip_derived_cl3138, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('split', [status(esa)], [zip_derived_cl2991])).
% 2.08/1.12 thf(zip_derived_cl36, plain,
% 2.08/1.12 (![X0 : $i, X1 : $i]:
% 2.08/1.12 (~ (pigeon @ X0)
% 2.08/1.12 | ((X1) = (X0))
% 2.08/1.12 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.12 | ~ (pigeon @ X1))),
% 2.08/1.12 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.12 thf(zip_derived_cl3143, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X1) = (X0))
% 2.08/1.12 | ~ (in @ X1 @ hole_2)
% 2.08/1.12 | ~ (pigeon @ X1)))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl3138, zip_derived_cl36])).
% 2.08/1.12 thf(zip_derived_cl3163, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (~ (pigeon @ X1)
% 2.08/1.12 | ~ (in @ X1 @ hole_2)
% 2.08/1.12 | ((X1) = (X0))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('simplify', [status(thm)], [zip_derived_cl3143])).
% 2.08/1.12 thf(zip_derived_cl3214, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (X1))
% 2.08/1.12 | ((X1) = (pigeon_2))
% 2.08/1.12 | ((X1) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X1)
% 2.08/1.12 | ((hole_of @ X1) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('s_sup-', [status(thm)],
% 2.08/1.12 [zip_derived_cl3162, zip_derived_cl3163])).
% 2.08/1.12 thf(zip_derived_cl3224, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (((hole_of @ X1) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X1)
% 2.08/1.12 | ((X1) = (pigeon_4))
% 2.08/1.12 | ((X1) = (pigeon_2))
% 2.08/1.12 | ((X0) = (X1))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('simplify', [status(thm)], [zip_derived_cl3214])).
% 2.08/1.12 thf(zip_derived_cl4007, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.12 | ((pigeon_3) = (pigeon_4))
% 2.08/1.12 | ((pigeon_3) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl3224])).
% 2.08/1.12 thf(pigeon_2_is_not_pigeon_3, axiom, (( pigeon_2 ) != ( pigeon_3 ))).
% 2.08/1.12 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.12 thf(pigeon_3_is_not_pigeon_4, axiom, (( pigeon_3 ) != ( pigeon_4 ))).
% 2.08/1.12 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.12 thf(zip_derived_cl4012, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('simplify_reflect-', [status(thm)],
% 2.08/1.12 [zip_derived_cl4007, zip_derived_cl12, zip_derived_cl15])).
% 2.08/1.12 thf('0', plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.12 (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.12 ~
% 2.08/1.12 (![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.12 inference('split', [status(esa)], [zip_derived_cl4012])).
% 2.08/1.12 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.12 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.12 thf(zip_derived_cl905, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (((hole_of @ X1) = (hole_2))
% 2.08/1.12 | ((hole_of @ X1) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X1)
% 2.08/1.12 | ((X1) = (pigeon_2))
% 2.08/1.12 | ((X0) = (X1))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))
% 2.08/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.12 inference('simplify', [status(thm)], [zip_derived_cl898])).
% 2.08/1.12 thf(zip_derived_cl2985, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((hole_of @ pigeon_3) = (hole_2))
% 2.08/1.12 | ((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.12 | ((pigeon_3) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))
% 2.08/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl905])).
% 2.08/1.12 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.12 thf(zip_derived_cl2990, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((hole_of @ pigeon_3) = (hole_2))
% 2.08/1.12 | ((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))
% 2.08/1.12 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.12 inference('simplify_reflect-', [status(thm)],
% 2.08/1.12 [zip_derived_cl2985, zip_derived_cl12])).
% 2.08/1.12 thf(zip_derived_cl2996, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('split', [status(esa)], [zip_derived_cl2990])).
% 2.08/1.12 thf(zip_derived_cl30, plain,
% 2.08/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.12 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.12 thf(zip_derived_cl3000, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | (in @ X0 @ hole_2)))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('s_sup+', [status(thm)], [zip_derived_cl2996, zip_derived_cl30])).
% 2.08/1.12 thf(zip_derived_cl3020, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 ( (in @ X0 @ hole_2)
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('simplify', [status(thm)], [zip_derived_cl3000])).
% 2.08/1.12 thf(zip_derived_cl2996, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('split', [status(esa)], [zip_derived_cl2990])).
% 2.08/1.12 thf(zip_derived_cl36, plain,
% 2.08/1.12 (![X0 : $i, X1 : $i]:
% 2.08/1.12 (~ (pigeon @ X0)
% 2.08/1.12 | ((X1) = (X0))
% 2.08/1.12 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.12 | ~ (pigeon @ X1))),
% 2.08/1.12 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.12 thf(zip_derived_cl3001, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X1) = (X0))
% 2.08/1.12 | ~ (in @ X1 @ hole_2)
% 2.08/1.12 | ~ (pigeon @ X1)))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl2996, zip_derived_cl36])).
% 2.08/1.12 thf(zip_derived_cl3021, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (~ (pigeon @ X1)
% 2.08/1.12 | ~ (in @ X1 @ hole_2)
% 2.08/1.12 | ((X1) = (X0))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('simplify', [status(thm)], [zip_derived_cl3001])).
% 2.08/1.12 thf(zip_derived_cl3069, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (X1))
% 2.08/1.12 | ((X1) = (pigeon_2))
% 2.08/1.12 | ((X1) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X1)
% 2.08/1.12 | ((hole_of @ X1) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('s_sup-', [status(thm)],
% 2.08/1.12 [zip_derived_cl3020, zip_derived_cl3021])).
% 2.08/1.12 thf(zip_derived_cl3078, plain,
% 2.08/1.12 ((![X0 : $i, X1 : $i]:
% 2.08/1.12 (((hole_of @ X1) = (hole_1))
% 2.08/1.12 | ~ (pigeon @ X1)
% 2.08/1.12 | ((X1) = (pigeon_3))
% 2.08/1.12 | ((X1) = (pigeon_2))
% 2.08/1.12 | ((X0) = (X1))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('simplify', [status(thm)], [zip_derived_cl3069])).
% 2.08/1.12 thf(zip_derived_cl3391, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.12 | ((pigeon_4) = (pigeon_3))
% 2.08/1.12 | ((pigeon_4) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl3078])).
% 2.08/1.12 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.12 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.12 thf(zip_derived_cl3396, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.12 inference('simplify_reflect-', [status(thm)],
% 2.08/1.12 [zip_derived_cl3391, zip_derived_cl13, zip_derived_cl15])).
% 2.08/1.12 thf('1', plain,
% 2.08/1.12 (~
% 2.08/1.12 (![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))
% 2.08/1.12 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.12 (((hole_of @ pigeon_4) = (hole_1))) |
% 2.08/1.12 (![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))),
% 2.08/1.12 inference('split', [status(esa)], [zip_derived_cl3396])).
% 2.08/1.12 thf(pigeon_5, axiom, (pigeon @ pigeon_5)).
% 2.08/1.12 thf(zip_derived_cl7, plain, ( (pigeon @ pigeon_5)),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_5])).
% 2.08/1.12 thf(pigeon_1, axiom, (pigeon @ pigeon_1)).
% 2.08/1.12 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.12 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.12 thf(zip_derived_cl3458, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.12 inference('split', [status(esa)], [zip_derived_cl3396])).
% 2.08/1.12 thf(zip_derived_cl30, plain,
% 2.08/1.12 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.12 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.12 thf(zip_derived_cl3461, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 (~ (pigeon @ X0)
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | (in @ X0 @ hole_1)))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.12 inference('s_sup+', [status(thm)], [zip_derived_cl3458, zip_derived_cl30])).
% 2.08/1.12 thf(zip_derived_cl3490, plain,
% 2.08/1.12 ((![X0 : $i]:
% 2.08/1.12 ( (in @ X0 @ hole_1)
% 2.08/1.12 | ((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)))
% 2.08/1.12 <= ((![X0 : $i]:
% 2.08/1.12 (((X0) = (pigeon_2))
% 2.08/1.12 | ((X0) = (pigeon_3))
% 2.08/1.12 | ((X0) = (pigeon_4))
% 2.08/1.12 | ~ (pigeon @ X0)
% 2.08/1.12 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl3461])).
% 2.08/1.13 thf(zip_derived_cl3458, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl3396])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl3462, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3458, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl3491, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl3462])).
% 2.08/1.13 thf(zip_derived_cl3603, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl3490, zip_derived_cl3491])).
% 2.08/1.13 thf(zip_derived_cl3609, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl3603])).
% 2.08/1.13 thf(zip_derived_cl3724, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((pigeon_1) = (pigeon_4))
% 2.08/1.13 | ((pigeon_1) = (pigeon_3))
% 2.08/1.13 | ((pigeon_1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl3609])).
% 2.08/1.13 thf(pigeon_1_is_not_pigeon_2, axiom, (( pigeon_1 ) != ( pigeon_2 ))).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(pigeon_1_is_not_pigeon_3, axiom, (( pigeon_1 ) != ( pigeon_3 ))).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(pigeon_1_is_not_pigeon_4, axiom, (( pigeon_1 ) != ( pigeon_4 ))).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl3731, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl3724, zip_derived_cl8, zip_derived_cl9,
% 2.08/1.13 zip_derived_cl10])).
% 2.08/1.13 thf(zip_derived_cl3803, plain,
% 2.08/1.13 (((((pigeon_5) = (pigeon_1))
% 2.08/1.13 | ((pigeon_5) = (pigeon_2))
% 2.08/1.13 | ((pigeon_5) = (pigeon_3))
% 2.08/1.13 | ((pigeon_5) = (pigeon_4))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl3731])).
% 2.08/1.13 thf(pigeon_4_is_not_pigeon_5, axiom, (( pigeon_4 ) != ( pigeon_5 ))).
% 2.08/1.13 thf(zip_derived_cl17, plain, (((pigeon_4) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4_is_not_pigeon_5])).
% 2.08/1.13 thf(pigeon_3_is_not_pigeon_5, axiom, (( pigeon_3 ) != ( pigeon_5 ))).
% 2.08/1.13 thf(zip_derived_cl16, plain, (((pigeon_3) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_5])).
% 2.08/1.13 thf(pigeon_2_is_not_pigeon_5, axiom, (( pigeon_2 ) != ( pigeon_5 ))).
% 2.08/1.13 thf(zip_derived_cl14, plain, (((pigeon_2) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_5])).
% 2.08/1.13 thf(pigeon_1_is_not_pigeon_5, axiom, (( pigeon_1 ) != ( pigeon_5 ))).
% 2.08/1.13 thf(zip_derived_cl11, plain, (((pigeon_1) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_5])).
% 2.08/1.13 thf('2', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl3803, zip_derived_cl17, zip_derived_cl16,
% 2.08/1.13 zip_derived_cl14, zip_derived_cl11])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl72, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_3))
% 2.08/1.13 | ((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl71])).
% 2.08/1.13 thf(zip_derived_cl75, plain,
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_3))
% 2.08/1.13 | ((hole_of @ pigeon_3) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl72])).
% 2.08/1.13 thf(zip_derived_cl199, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl204, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_3)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl199, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl215, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_3)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl204])).
% 2.08/1.13 thf(zip_derived_cl199, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl205, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_3)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl216, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_3)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl205])).
% 2.08/1.13 thf(zip_derived_cl937, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ((hole_of @ X1) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl215, zip_derived_cl216])).
% 2.08/1.13 thf(zip_derived_cl945, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl937])).
% 2.08/1.13 thf(zip_derived_cl4391, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((pigeon_4) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl945])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl4396, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl4391, zip_derived_cl15])).
% 2.08/1.13 thf(zip_derived_cl4477, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4396])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl4481, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_2)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl4477, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl4502, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_2)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl4481])).
% 2.08/1.13 thf(zip_derived_cl4477, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4396])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl4482, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4477, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl4503, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl4482])).
% 2.08/1.13 thf(zip_derived_cl4562, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl4502, zip_derived_cl4503])).
% 2.08/1.13 thf(zip_derived_cl4574, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl4562])).
% 2.08/1.13 thf(zip_derived_cl4768, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((pigeon_2) = (pigeon_4))
% 2.08/1.13 | ((pigeon_2) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl4574])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl4773, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl4768, zip_derived_cl12, zip_derived_cl13])).
% 2.08/1.13 thf('3', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4773])).
% 2.08/1.13 thf(zip_derived_cl135, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl134, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl187, plain,
% 2.08/1.13 ((((hole_1) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl134])).
% 2.08/1.13 thf(hole_1_is_not_hole_2, axiom, (( hole_1 ) != ( hole_2 ))).
% 2.08/1.13 thf(zip_derived_cl22, plain, (((hole_1) != (hole_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [hole_1_is_not_hole_2])).
% 2.08/1.13 thf('4', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_2) = (hole_1)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl187, zip_derived_cl22])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl72, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_3))
% 2.08/1.13 | ((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl71])).
% 2.08/1.13 thf(zip_derived_cl76, plain,
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_3))
% 2.08/1.13 | ((hole_of @ pigeon_4) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl72])).
% 2.08/1.13 thf(zip_derived_cl280, plain,
% 2.08/1.13 ((((hole_of @ pigeon_4) = (hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl76])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl313, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_4) | (in @ pigeon_4 @ hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl280, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl317, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_3)) <= ((((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl313, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl200, plain,
% 2.08/1.13 ((((hole_of @ pigeon_3) = (hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl228, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_3)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (in @ X0 @ hole_3)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl200, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl232, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3)) | ~ (in @ X0 @ hole_3) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl228, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl645, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_3)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl232])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl653, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl645, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf('5', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_4) = (hole_3))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_3) = (hole_3)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl653, zip_derived_cl15])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl279, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl76])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl284, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_3)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl279, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl297, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_3)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl284])).
% 2.08/1.13 thf(zip_derived_cl279, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl76])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl285, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_3)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl279, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl298, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_3)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl285])).
% 2.08/1.13 thf(zip_derived_cl999, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ((hole_of @ X1) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl297, zip_derived_cl298])).
% 2.08/1.13 thf(zip_derived_cl1009, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 2.08/1.13 thf(zip_derived_cl5115, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((pigeon_3) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl1009])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl5120, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl5115, zip_derived_cl15])).
% 2.08/1.13 thf('6', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl5120])).
% 2.08/1.13 thf('7', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4396])).
% 2.08/1.13 thf(zip_derived_cl201, plain,
% 2.08/1.13 ((((hole_of @ pigeon_3) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl236, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_3) | (in @ pigeon_3 @ hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl201, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl244, plain,
% 2.08/1.13 (( (in @ pigeon_3 @ hole_2)) <= ((((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl236, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl72, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_3))
% 2.08/1.13 | ((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl71])).
% 2.08/1.13 thf(zip_derived_cl73, plain,
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_3))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl72])).
% 2.08/1.13 thf(zip_derived_cl80, plain,
% 2.08/1.13 ((((hole_of @ pigeon_1) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl73])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl104, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_1)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (in @ X0 @ hole_2)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl110, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_2) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl104, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl534, plain,
% 2.08/1.13 (((((pigeon_3) = (pigeon_1)) | ~ (pigeon @ pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl244, zip_derived_cl110])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl540, plain,
% 2.08/1.13 ((((pigeon_3) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl534, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf('8', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_1) = (hole_2))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_3) = (hole_2)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl540, zip_derived_cl9])).
% 2.08/1.13 thf(zip_derived_cl200, plain,
% 2.08/1.13 ((((hole_of @ pigeon_3) = (hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl227, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_3) | (in @ pigeon_3 @ hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl231, plain,
% 2.08/1.13 (( (in @ pigeon_3 @ hole_3)) <= ((((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl227, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl79, plain,
% 2.08/1.13 ((((hole_of @ pigeon_1) = (hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl73])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl95, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_1)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (in @ X0 @ hole_3)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl99, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_3) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl516, plain,
% 2.08/1.13 (((((pigeon_3) = (pigeon_1)) | ~ (pigeon @ pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl99])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl523, plain,
% 2.08/1.13 ((((pigeon_3) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl516, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf('9', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_1) = (hole_3))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_3) = (hole_3)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl523, zip_derived_cl9])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl945, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl937])).
% 2.08/1.13 thf(zip_derived_cl4388, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((pigeon_1) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl945])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl4393, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl4388, zip_derived_cl9])).
% 2.08/1.13 thf('10', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4393])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl3078, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl3069])).
% 2.08/1.13 thf(zip_derived_cl3388, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((pigeon_1) = (pigeon_3))
% 2.08/1.13 | ((pigeon_1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl3078])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl3393, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl3388, zip_derived_cl8, zip_derived_cl9])).
% 2.08/1.13 thf('11', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl3393])).
% 2.08/1.13 thf(zip_derived_cl282, plain,
% 2.08/1.13 ((((hole_of @ pigeon_4) = (hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl76])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl384, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_4) | (in @ pigeon_4 @ hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl282, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl397, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_1)) <= ((((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl384, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl81, plain,
% 2.08/1.13 ((((hole_of @ pigeon_1) = (hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl73])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl118, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_1)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (in @ X0 @ hole_1)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl125, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_1) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl118, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl564, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_1)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl397, zip_derived_cl125])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl571, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl564, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf('12', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_4) = (hole_1))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_1) = (hole_1)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl571, zip_derived_cl10])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl4574, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl4562])).
% 2.08/1.13 thf(zip_derived_cl4767, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((pigeon_1) = (pigeon_4))
% 2.08/1.13 | ((pigeon_1) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4574])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl4772, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl4767, zip_derived_cl9, zip_derived_cl10])).
% 2.08/1.13 thf('13', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4772])).
% 2.08/1.13 thf(zip_derived_cl135, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl181, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_2) | (in @ pigeon_2 @ hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl189, plain,
% 2.08/1.13 (( (in @ pigeon_2 @ hole_1)) <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl181, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl125, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_1) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl118, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl562, plain,
% 2.08/1.13 (((((pigeon_2) = (pigeon_1)) | ~ (pigeon @ pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl125])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl567, plain,
% 2.08/1.13 ((((pigeon_2) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl562, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf('14', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_1))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_1) = (hole_1)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl567, zip_derived_cl8])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl945, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl937])).
% 2.08/1.13 thf(zip_derived_cl4389, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((pigeon_2) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl945])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl4394, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl4389, zip_derived_cl12])).
% 2.08/1.13 thf('15', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4394])).
% 2.08/1.13 thf('16', plain,
% 2.08/1.13 ((((hole_of @ pigeon_3) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_3))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf('17', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2990])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl1009, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 2.08/1.13 thf(zip_derived_cl5114, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((pigeon_2) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl1009])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl5119, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl5114, zip_derived_cl13])).
% 2.08/1.13 thf('18', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl5119])).
% 2.08/1.13 thf(zip_derived_cl134, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl163, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_2) | (in @ pigeon_2 @ hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl170, plain,
% 2.08/1.13 (( (in @ pigeon_2 @ hole_2)) <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl110, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_2) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl104, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl533, plain,
% 2.08/1.13 (((((pigeon_2) = (pigeon_1)) | ~ (pigeon @ pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl170, zip_derived_cl110])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl538, plain,
% 2.08/1.13 ((((pigeon_2) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl533, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf('19', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_1) = (hole_2)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl538, zip_derived_cl8])).
% 2.08/1.13 thf(zip_derived_cl317, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_3)) <= ((((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl313, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl99, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_3) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl517, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_1)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl99])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl525, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl517, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf('20', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_1) = (hole_3))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_4) = (hole_3)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl525, zip_derived_cl10])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl1009, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl999])).
% 2.08/1.13 thf(zip_derived_cl5113, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((pigeon_1) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1009])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl5118, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl5113, zip_derived_cl10])).
% 2.08/1.13 thf('21', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl5118])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl78, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl73])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl83, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_3)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl78, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl90, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_3)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl83])).
% 2.08/1.13 thf(zip_derived_cl78, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl73])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl84, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_3)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl91, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_3)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl84])).
% 2.08/1.13 thf(zip_derived_cl547, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ((hole_of @ X1) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl91])).
% 2.08/1.13 thf(zip_derived_cl553, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl547])).
% 2.08/1.13 thf(zip_derived_cl1090, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((pigeon_3) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl553])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl1095, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1090, zip_derived_cl9])).
% 2.08/1.13 thf(zip_derived_cl1178, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1095])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl1182, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_2)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl1178, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl1203, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_2)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1182])).
% 2.08/1.13 thf(zip_derived_cl1178, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1095])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl1183, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl1178, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl1204, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1183])).
% 2.08/1.13 thf(zip_derived_cl1247, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1203, zip_derived_cl1204])).
% 2.08/1.13 thf(zip_derived_cl1254, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1247])).
% 2.08/1.13 thf(zip_derived_cl2113, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((pigeon_2) = (pigeon_3))
% 2.08/1.13 | ((pigeon_2) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl1254])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl2118, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2113, zip_derived_cl8, zip_derived_cl12])).
% 2.08/1.13 thf('22', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2118])).
% 2.08/1.13 thf(zip_derived_cl397, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_1)) <= ((((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl384, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl135, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl182, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_2)
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (in @ X0 @ hole_1)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl190, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2)) | ~ (in @ X0 @ hole_1) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl182, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl623, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_2)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl397, zip_derived_cl190])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl630, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl623, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf('23', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_4) = (hole_1))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_2) = (hole_1)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl630, zip_derived_cl13])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl1254, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1247])).
% 2.08/1.13 thf(zip_derived_cl2115, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((pigeon_4) = (pigeon_3))
% 2.08/1.13 | ((pigeon_4) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl1254])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl2120, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2115, zip_derived_cl10, zip_derived_cl15])).
% 2.08/1.13 thf('24', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2120])).
% 2.08/1.13 thf(zip_derived_cl7, plain, ( (pigeon @ pigeon_5)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl2124, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2120])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl2127, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl2124, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl2154, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_1)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl2127])).
% 2.08/1.13 thf(zip_derived_cl2124, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2120])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl2128, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl2124, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl2155, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl2128])).
% 2.08/1.13 thf(zip_derived_cl2207, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2154, zip_derived_cl2155])).
% 2.08/1.13 thf(zip_derived_cl2213, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl2207])).
% 2.08/1.13 thf(zip_derived_cl2488, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((pigeon_2) = (pigeon_4))
% 2.08/1.13 | ((pigeon_2) = (pigeon_3))
% 2.08/1.13 | ((pigeon_2) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl2213])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl2495, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2488, zip_derived_cl8, zip_derived_cl12,
% 2.08/1.13 zip_derived_cl13])).
% 2.08/1.13 thf(zip_derived_cl2508, plain,
% 2.08/1.13 (((((pigeon_5) = (pigeon_2))
% 2.08/1.13 | ((pigeon_5) = (pigeon_1))
% 2.08/1.13 | ((pigeon_5) = (pigeon_3))
% 2.08/1.13 | ((pigeon_5) = (pigeon_4))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2495])).
% 2.08/1.13 thf(zip_derived_cl17, plain, (((pigeon_4) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl16, plain, (((pigeon_3) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl11, plain, (((pigeon_1) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl14, plain, (((pigeon_2) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_5])).
% 2.08/1.13 thf('25', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2508, zip_derived_cl17, zip_derived_cl16,
% 2.08/1.13 zip_derived_cl11, zip_derived_cl14])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl553, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl547])).
% 2.08/1.13 thf(zip_derived_cl1091, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((pigeon_4) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl553])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl1096, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1091, zip_derived_cl10])).
% 2.08/1.13 thf(zip_derived_cl1262, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1096])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl1266, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_2)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl1262, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl1287, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_2)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1266])).
% 2.08/1.13 thf(zip_derived_cl1262, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1096])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl1267, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl1262, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl1288, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1267])).
% 2.08/1.13 thf(zip_derived_cl1384, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1287, zip_derived_cl1288])).
% 2.08/1.13 thf(zip_derived_cl1392, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1384])).
% 2.08/1.13 thf(zip_derived_cl2716, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((pigeon_3) = (pigeon_4))
% 2.08/1.13 | ((pigeon_3) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl1392])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl2721, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2716, zip_derived_cl9, zip_derived_cl15])).
% 2.08/1.13 thf('26', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2721])).
% 2.08/1.13 thf('27', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1096])).
% 2.08/1.13 thf('28', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1)))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1095])).
% 2.08/1.13 thf(zip_derived_cl244, plain,
% 2.08/1.13 (( (in @ pigeon_3 @ hole_2)) <= ((((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl236, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl134, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl164, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_2)
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (in @ X0 @ hole_2)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl171, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2)) | ~ (in @ X0 @ hole_2) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl164, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl603, plain,
% 2.08/1.13 (((((pigeon_3) = (pigeon_2)) | ~ (pigeon @ pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl244, zip_derived_cl171])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl609, plain,
% 2.08/1.13 ((((pigeon_3) = (pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl603, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf('29', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_3) = (hole_2)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl609, zip_derived_cl12])).
% 2.08/1.13 thf(zip_derived_cl133, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl154, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_2) | (in @ pigeon_2 @ hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl133, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl158, plain,
% 2.08/1.13 (( (in @ pigeon_2 @ hole_3)) <= ((((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl99, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_3) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl515, plain,
% 2.08/1.13 (((((pigeon_2) = (pigeon_1)) | ~ (pigeon @ pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl99])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl521, plain,
% 2.08/1.13 ((((pigeon_2) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl515, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf('30', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_3))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_1) = (hole_3)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl521, zip_derived_cl8])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl905, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl898])).
% 2.08/1.13 thf(zip_derived_cl2983, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((pigeon_1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl905])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl2988, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2983, zip_derived_cl8])).
% 2.08/1.13 thf('31', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2988])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl553, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_2))
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl547])).
% 2.08/1.13 thf(zip_derived_cl1089, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((pigeon_2) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl553])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl1094, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))
% 2.08/1.13 | ((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1089, zip_derived_cl8])).
% 2.08/1.13 thf(zip_derived_cl1098, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1094])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl1102, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_2)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl1098, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl1123, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_2)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1102])).
% 2.08/1.13 thf(zip_derived_cl1098, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1094])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl1103, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl1098, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl1124, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_2)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1103])).
% 2.08/1.13 thf(zip_derived_cl1164, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((hole_of @ X1) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1123, zip_derived_cl1124])).
% 2.08/1.13 thf(zip_derived_cl1170, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1164])).
% 2.08/1.13 thf(zip_derived_cl1595, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((pigeon_4) = (pigeon_2))
% 2.08/1.13 | ((pigeon_4) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl1170])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl1600, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1595, zip_derived_cl10, zip_derived_cl13])).
% 2.08/1.13 thf('32', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1)))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1600])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl1170, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1164])).
% 2.08/1.13 thf(zip_derived_cl1594, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((pigeon_3) = (pigeon_2))
% 2.08/1.13 | ((pigeon_3) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl1170])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl1599, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1594, zip_derived_cl9, zip_derived_cl12])).
% 2.08/1.13 thf('33', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1599])).
% 2.08/1.13 thf(zip_derived_cl7, plain, ( (pigeon @ pigeon_5)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl1602, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1599])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl1605, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl1602, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl1632, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_1)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1605])).
% 2.08/1.13 thf(zip_derived_cl1602, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1599])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl1606, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl1602, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl1633, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1606])).
% 2.08/1.13 thf(zip_derived_cl1737, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1632, zip_derived_cl1633])).
% 2.08/1.13 thf(zip_derived_cl1743, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_3))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1737])).
% 2.08/1.13 thf(zip_derived_cl1967, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((pigeon_4) = (pigeon_3))
% 2.08/1.13 | ((pigeon_4) = (pigeon_2))
% 2.08/1.13 | ((pigeon_4) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl1743])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl1974, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1967, zip_derived_cl10, zip_derived_cl13,
% 2.08/1.13 zip_derived_cl15])).
% 2.08/1.13 thf(zip_derived_cl1985, plain,
% 2.08/1.13 (((((pigeon_5) = (pigeon_4))
% 2.08/1.13 | ((pigeon_5) = (pigeon_1))
% 2.08/1.13 | ((pigeon_5) = (pigeon_2))
% 2.08/1.13 | ((pigeon_5) = (pigeon_3))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1974])).
% 2.08/1.13 thf(zip_derived_cl16, plain, (((pigeon_3) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl14, plain, (((pigeon_2) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl11, plain, (((pigeon_1) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl17, plain, (((pigeon_4) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4_is_not_pigeon_5])).
% 2.08/1.13 thf('34', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1985, zip_derived_cl16, zip_derived_cl14,
% 2.08/1.13 zip_derived_cl11, zip_derived_cl17])).
% 2.08/1.13 thf('35', plain,
% 2.08/1.13 ((((hole_of @ pigeon_1) = (hole_1))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_3))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl73])).
% 2.08/1.13 thf('36', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1)))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1094])).
% 2.08/1.13 thf(zip_derived_cl281, plain,
% 2.08/1.13 ((((hole_of @ pigeon_4) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl76])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl322, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_4) | (in @ pigeon_4 @ hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl331, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_2)) <= ((((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl322, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl171, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2)) | ~ (in @ X0 @ hole_2) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl164, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl604, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_2)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl331, zip_derived_cl171])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl611, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl604, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf('37', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_4) = (hole_2)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl611, zip_derived_cl13])).
% 2.08/1.13 thf(zip_derived_cl331, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_2)) <= ((((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl322, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl110, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_2) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl104, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl535, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_1)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl331, zip_derived_cl110])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl542, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl535, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf('38', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_4) = (hole_2))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_1) = (hole_2)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl542, zip_derived_cl10])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl1392, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1384])).
% 2.08/1.13 thf(zip_derived_cl2715, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((pigeon_2) = (pigeon_4))
% 2.08/1.13 | ((pigeon_2) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl1392])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl2720, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2715, zip_derived_cl8, zip_derived_cl13])).
% 2.08/1.13 thf('39', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2720])).
% 2.08/1.13 thf(zip_derived_cl7, plain, ( (pigeon @ pigeon_5)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl1752, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1600])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl1755, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | (in @ X0 @ hole_1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl1752, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl1783, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 ( (in @ X0 @ hole_1)
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1755])).
% 2.08/1.13 thf(zip_derived_cl1752, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl1600])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl1756, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl1752, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl1784, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ~ (in @ X1 @ hole_1)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1756])).
% 2.08/1.13 thf(zip_derived_cl1840, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X1)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1783, zip_derived_cl1784])).
% 2.08/1.13 thf(zip_derived_cl1847, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X1) = (pigeon_1))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl1840])).
% 2.08/1.13 thf(zip_derived_cl1998, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((pigeon_3) = (pigeon_4))
% 2.08/1.13 | ((pigeon_3) = (pigeon_2))
% 2.08/1.13 | ((pigeon_3) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl1847])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl2005, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl1998, zip_derived_cl9, zip_derived_cl12,
% 2.08/1.13 zip_derived_cl15])).
% 2.08/1.13 thf(zip_derived_cl2017, plain,
% 2.08/1.13 (((((pigeon_5) = (pigeon_3))
% 2.08/1.13 | ((pigeon_5) = (pigeon_1))
% 2.08/1.13 | ((pigeon_5) = (pigeon_2))
% 2.08/1.13 | ((pigeon_5) = (pigeon_4))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2005])).
% 2.08/1.13 thf(zip_derived_cl17, plain, (((pigeon_4) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl14, plain, (((pigeon_2) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl11, plain, (((pigeon_1) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_5])).
% 2.08/1.13 thf(zip_derived_cl16, plain, (((pigeon_3) != (pigeon_5))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_5])).
% 2.08/1.13 thf('40', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl2017, zip_derived_cl17, zip_derived_cl14,
% 2.08/1.13 zip_derived_cl11, zip_derived_cl16])).
% 2.08/1.13 thf(zip_derived_cl3, plain, ( (pigeon @ pigeon_1)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1])).
% 2.08/1.13 thf(zip_derived_cl3224, plain,
% 2.08/1.13 ((![X0 : $i, X1 : $i]:
% 2.08/1.13 (((hole_of @ X1) = (hole_1))
% 2.08/1.13 | ~ (pigeon @ X1)
% 2.08/1.13 | ((X1) = (pigeon_4))
% 2.08/1.13 | ((X1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (X1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify', [status(thm)], [zip_derived_cl3214])).
% 2.08/1.13 thf(zip_derived_cl4005, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((pigeon_1) = (pigeon_4))
% 2.08/1.13 | ((pigeon_1) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl3224])).
% 2.08/1.13 thf(zip_derived_cl8, plain, (((pigeon_1) != (pigeon_2))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl10, plain, (((pigeon_1) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl4010, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))
% 2.08/1.13 | ((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))))
% 2.08/1.13 <= ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl4005, zip_derived_cl8, zip_derived_cl10])).
% 2.08/1.13 thf('41', plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1))
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1)))) |
% 2.08/1.13 (((hole_of @ pigeon_1) = (hole_1))) |
% 2.08/1.13 ~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl4010])).
% 2.08/1.13 thf(zip_derived_cl397, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_1)) <= ((((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl384, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl202, plain,
% 2.08/1.13 ((((hole_of @ pigeon_3) = (hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl259, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_3)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (in @ X0 @ hole_1)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl202, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl268, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3)) | ~ (in @ X0 @ hole_1) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl259, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl691, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_3)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl397, zip_derived_cl268])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl698, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl691, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf('42', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_4) = (hole_1)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl698, zip_derived_cl15])).
% 2.08/1.13 thf(zip_derived_cl202, plain,
% 2.08/1.13 ((((hole_of @ pigeon_3) = (hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl30, plain,
% 2.08/1.13 (![X0 : $i]: (~ (pigeon @ X0) | (in @ X0 @ (hole_of @ X0)))),
% 2.08/1.13 inference('cnf', [status(esa)], [each_pigeons_hole2])).
% 2.08/1.13 thf(zip_derived_cl258, plain,
% 2.08/1.13 (((~ (pigeon @ pigeon_3) | (in @ pigeon_3 @ hole_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('s_sup+', [status(thm)], [zip_derived_cl202, zip_derived_cl30])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl267, plain,
% 2.08/1.13 (( (in @ pigeon_3 @ hole_1)) <= ((((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl258, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl190, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2)) | ~ (in @ X0 @ hole_1) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl182, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl622, plain,
% 2.08/1.13 (((((pigeon_3) = (pigeon_2)) | ~ (pigeon @ pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl267, zip_derived_cl190])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl628, plain,
% 2.08/1.13 ((((pigeon_3) = (pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl622, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf('43', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_2) = (hole_1)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl628, zip_derived_cl12])).
% 2.08/1.13 thf(zip_derived_cl267, plain,
% 2.08/1.13 (( (in @ pigeon_3 @ hole_1)) <= ((((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl258, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl125, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_1)) | ~ (in @ X0 @ hole_1) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl118, zip_derived_cl3])).
% 2.08/1.13 thf(zip_derived_cl563, plain,
% 2.08/1.13 (((((pigeon_3) = (pigeon_1)) | ~ (pigeon @ pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl267, zip_derived_cl125])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl569, plain,
% 2.08/1.13 ((((pigeon_3) = (pigeon_1)))
% 2.08/1.13 <= ((((hole_of @ pigeon_1) = (hole_1))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_1))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl563, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl9, plain, (((pigeon_1) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_1_is_not_pigeon_3])).
% 2.08/1.13 thf('44', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_3) = (hole_1))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_1) = (hole_1)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl569, zip_derived_cl9])).
% 2.08/1.13 thf('45', plain,
% 2.08/1.13 ((((hole_of @ pigeon_4) = (hole_3))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl76])).
% 2.08/1.13 thf(zip_derived_cl231, plain,
% 2.08/1.13 (( (in @ pigeon_3 @ hole_3)) <= ((((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl227, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl133, plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl155, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_2)
% 2.08/1.13 | ((X0) = (pigeon_2))
% 2.08/1.13 | ~ (in @ X0 @ hole_3)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl4, plain, ( (pigeon @ pigeon_2)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2])).
% 2.08/1.13 thf(zip_derived_cl159, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2)) | ~ (in @ X0 @ hole_3) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl155, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl582, plain,
% 2.08/1.13 (((((pigeon_3) = (pigeon_2)) | ~ (pigeon @ pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl159])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl589, plain,
% 2.08/1.13 ((((pigeon_3) = (pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_3) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl12, plain, (((pigeon_2) != (pigeon_3))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_3])).
% 2.08/1.13 thf('46', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_3))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_3) = (hole_3)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl589, zip_derived_cl12])).
% 2.08/1.13 thf(zip_derived_cl331, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_2)) <= ((((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl322, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl201, plain,
% 2.08/1.13 ((((hole_of @ pigeon_3) = (hole_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl75])).
% 2.08/1.13 thf(zip_derived_cl36, plain,
% 2.08/1.13 (![X0 : $i, X1 : $i]:
% 2.08/1.13 (~ (pigeon @ X0)
% 2.08/1.13 | ((X1) = (X0))
% 2.08/1.13 | ~ (in @ X1 @ (hole_of @ X0))
% 2.08/1.13 | ~ (pigeon @ X1))),
% 2.08/1.13 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl29])).
% 2.08/1.13 thf(zip_derived_cl237, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (~ (pigeon @ pigeon_3)
% 2.08/1.13 | ((X0) = (pigeon_3))
% 2.08/1.13 | ~ (in @ X0 @ hole_2)
% 2.08/1.13 | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl36])).
% 2.08/1.13 thf(zip_derived_cl5, plain, ( (pigeon @ pigeon_3)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3])).
% 2.08/1.13 thf(zip_derived_cl245, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_3)) | ~ (in @ X0 @ hole_2) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl237, zip_derived_cl5])).
% 2.08/1.13 thf(zip_derived_cl669, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_3)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl331, zip_derived_cl245])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl676, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_3)))
% 2.08/1.13 <= ((((hole_of @ pigeon_3) = (hole_2))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl669, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl15, plain, (((pigeon_3) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_3_is_not_pigeon_4])).
% 2.08/1.13 thf('47', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_4) = (hole_2))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_3) = (hole_2)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl676, zip_derived_cl15])).
% 2.08/1.13 thf('48', plain,
% 2.08/1.13 (~
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_2))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ((X0) = (pigeon_4))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2)))) |
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_1)))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl2991])).
% 2.08/1.13 thf('49', plain,
% 2.08/1.13 ((((hole_of @ pigeon_2) = (hole_3))) |
% 2.08/1.13 (![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2))
% 2.08/1.13 | ~ (pigeon @ X0)
% 2.08/1.13 | ((hole_of @ X0) = (hole_1))
% 2.08/1.13 | ((hole_of @ X0) = (hole_2))
% 2.08/1.13 | ((hole_of @ X0) = (hole_3)))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_2))) |
% 2.08/1.13 (((hole_of @ pigeon_2) = (hole_1)))),
% 2.08/1.13 inference('split', [status(esa)], [zip_derived_cl74])).
% 2.08/1.13 thf(zip_derived_cl317, plain,
% 2.08/1.13 (( (in @ pigeon_4 @ hole_3)) <= ((((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl313, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl159, plain,
% 2.08/1.13 ((![X0 : $i]:
% 2.08/1.13 (((X0) = (pigeon_2)) | ~ (in @ X0 @ hole_3) | ~ (pigeon @ X0)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl155, zip_derived_cl4])).
% 2.08/1.13 thf(zip_derived_cl583, plain,
% 2.08/1.13 (((((pigeon_4) = (pigeon_2)) | ~ (pigeon @ pigeon_4)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl159])).
% 2.08/1.13 thf(zip_derived_cl6, plain, ( (pigeon @ pigeon_4)),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_4])).
% 2.08/1.13 thf(zip_derived_cl591, plain,
% 2.08/1.13 ((((pigeon_4) = (pigeon_2)))
% 2.08/1.13 <= ((((hole_of @ pigeon_2) = (hole_3))) &
% 2.08/1.13 (((hole_of @ pigeon_4) = (hole_3))))),
% 2.08/1.13 inference('demod', [status(thm)], [zip_derived_cl583, zip_derived_cl6])).
% 2.08/1.13 thf(zip_derived_cl13, plain, (((pigeon_2) != (pigeon_4))),
% 2.08/1.13 inference('cnf', [status(esa)], [pigeon_2_is_not_pigeon_4])).
% 2.08/1.13 thf('50', plain,
% 2.08/1.13 (~ (((hole_of @ pigeon_2) = (hole_3))) |
% 2.08/1.13 ~ (((hole_of @ pigeon_4) = (hole_3)))),
% 2.08/1.13 inference('simplify_reflect-', [status(thm)],
% 2.08/1.13 [zip_derived_cl591, zip_derived_cl13])).
% 2.08/1.13 thf(zip_derived_cl5160, plain, ($false),
% 2.08/1.13 inference('sat_resolution*', [status(thm)],
% 2.08/1.13 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 2.08/1.13 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 2.08/1.13 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 2.08/1.13 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 2.08/1.13 '42', '43', '44', '45', '46', '47', '48', '49', '50'])).
% 2.08/1.13
% 2.08/1.13 % SZS output end Refutation
% 2.08/1.13
% 2.08/1.13
% 2.08/1.13 % Terminating...
% 2.09/1.20 % Runner terminated.
% 2.09/1.23 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------