%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEO223+1 : TPTP v9.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZbXOaFa9cS true
% Computer : n014.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 Oct 2 04:34:23 PM UTC 2025
% Result : Theorem 3.48s 1.08s
% Output : Refutation 3.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO223+1 : TPTP v9.2.0. Released v3.3.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZbXOaFa9cS true
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 17:37:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.55/0.66 % Total configuration time : 435
% 0.55/0.66 % Estimated wc time : 1092
% 0.55/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 3.48/1.08 % Solved by fo/fo1_av.sh.
% 3.48/1.08 % done 289 iterations in 0.313s
% 3.48/1.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.48/1.08 % SZS output start Refutation
% 3.48/1.08 thf(orthogonal_through_point_type, type, orthogonal_through_point: $i > $i > $i).
% 3.48/1.08 thf(unorthogonal_lines_type, type, unorthogonal_lines: $i > $i > $o).
% 3.48/1.08 thf(distinct_lines_type, type, distinct_lines: $i > $i > $o).
% 3.48/1.08 thf(sk__1_type, type, sk__1: $i).
% 3.48/1.08 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $o).
% 3.48/1.08 thf(parallel_through_point_type, type, parallel_through_point: $i > $i > $i).
% 3.48/1.08 thf(apart_point_and_line_type, type, apart_point_and_line: $i > $i > $o).
% 3.48/1.08 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $o).
% 3.48/1.08 thf(sk__type, type, sk_: $i).
% 3.48/1.08 thf(convergent_lines_type, type, convergent_lines: $i > $i > $o).
% 3.48/1.08 thf(con, conjecture,
% 3.48/1.08 (![A:$i,L:$i]:
% 3.48/1.08 ( ~( distinct_lines @
% 3.48/1.08 ( parallel_through_point @ L @ A ) @
% 3.48/1.08 ( orthogonal_through_point @ ( orthogonal_through_point @ L @ A ) @ A ) ) ))).
% 3.48/1.08 thf(zf_stmt_0, negated_conjecture,
% 3.48/1.08 (~( ![A:$i,L:$i]:
% 3.48/1.08 ( ~( distinct_lines @
% 3.48/1.08 ( parallel_through_point @ L @ A ) @
% 3.48/1.08 ( orthogonal_through_point @
% 3.48/1.08 ( orthogonal_through_point @ L @ A ) @ A ) ) ) )),
% 3.48/1.08 inference('cnf.neg', [status(esa)], [con])).
% 3.48/1.08 thf(zip_derived_cl26, plain,
% 3.48/1.08 ( (distinct_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 3.48/1.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.48/1.08 thf(cup1, axiom,
% 3.48/1.08 (![X:$i,Y:$i,Z:$i]:
% 3.48/1.08 ( ( distinct_lines @ Y @ Z ) =>
% 3.48/1.08 ( ( apart_point_and_line @ X @ Y ) | ( apart_point_and_line @ X @ Z ) |
% 3.48/1.08 ( convergent_lines @ Y @ Z ) ) ))).
% 3.48/1.08 thf(zip_derived_cl16, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @ X1)
% 3.48/1.08 | ~ (distinct_lines @ X1 @ X2)
% 3.48/1.08 | (apart_point_and_line @ X0 @ X2)
% 3.48/1.08 | (convergent_lines @ X1 @ X2))),
% 3.48/1.08 inference('cnf', [status(esa)], [cup1])).
% 3.48/1.08 thf(zip_derived_cl61, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (apart_point_and_line @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 3.48/1.08 | (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl16])).
% 3.48/1.08 thf(zip_derived_cl233, plain,
% 3.48/1.08 (( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))
% 3.48/1.08 <= (( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))))),
% 3.48/1.08 inference('split', [status(esa)], [zip_derived_cl61])).
% 3.48/1.08 thf(zip_derived_cl232, plain,
% 3.48/1.08 ((![X0 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (apart_point_and_line @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))))
% 3.48/1.08 <= ((![X0 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @
% 3.48/1.08 (parallel_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (apart_point_and_line @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))))),
% 3.48/1.08 inference('split', [status(esa)], [zip_derived_cl61])).
% 3.48/1.08 thf(ooc2, axiom,
% 3.48/1.08 (![A:$i,L:$i]:
% 3.48/1.08 ( ~( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) ))).
% 3.48/1.08 thf(zip_derived_cl24, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (apart_point_and_line @ X0 @ (orthogonal_through_point @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [ooc2])).
% 3.48/1.08 thf(zip_derived_cl236, plain,
% 3.48/1.08 (( (apart_point_and_line @ sk_ @ (parallel_through_point @ sk__1 @ sk_)))
% 3.48/1.08 <= ((![X0 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @
% 3.48/1.08 (parallel_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (apart_point_and_line @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl24])).
% 3.48/1.08 thf(cp2, axiom,
% 3.48/1.08 (![X:$i,Y:$i]:
% 3.48/1.08 ( ~( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) ))).
% 3.48/1.08 thf(zip_derived_cl15, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (apart_point_and_line @ X0 @ (parallel_through_point @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [cp2])).
% 3.48/1.08 thf('0', plain,
% 3.48/1.08 (~
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (apart_point_and_line @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl236, zip_derived_cl15])).
% 3.48/1.08 thf('1', plain,
% 3.48/1.08 (( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))) |
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (apart_point_and_line @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))))),
% 3.48/1.08 inference('split', [status(esa)], [zip_derived_cl61])).
% 3.48/1.08 thf('2', plain,
% 3.48/1.08 (( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 3.48/1.08 inference('sat_resolution*', [status(thm)], ['0', '1'])).
% 3.48/1.08 thf(zip_derived_cl242, plain,
% 3.48/1.08 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 3.48/1.08 inference('simpl_trail', [status(thm)], [zip_derived_cl233, '2'])).
% 3.48/1.08 thf(ax6, axiom,
% 3.48/1.08 (![X:$i,Y:$i,Z:$i]:
% 3.48/1.08 ( ( convergent_lines @ X @ Y ) =>
% 3.48/1.08 ( ( convergent_lines @ X @ Z ) | ( convergent_lines @ Y @ Z ) ) ))).
% 3.48/1.08 thf(zip_derived_cl5, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 (~ (convergent_lines @ X0 @ X1)
% 3.48/1.08 | (convergent_lines @ X0 @ X2)
% 3.48/1.08 | (convergent_lines @ X1 @ X2))),
% 3.48/1.08 inference('cnf', [status(esa)], [ax6])).
% 3.48/1.08 thf(zip_derived_cl243, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0)
% 3.48/1.08 | (convergent_lines @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 3.48/1.08 X0))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl242, zip_derived_cl5])).
% 3.48/1.08 thf(ceq3, axiom,
% 3.48/1.08 (![X:$i,Y:$i,Z:$i]:
% 3.48/1.08 ( ( convergent_lines @ X @ Y ) =>
% 3.48/1.08 ( ( distinct_lines @ Y @ Z ) | ( convergent_lines @ X @ Z ) ) ))).
% 3.48/1.08 thf(zip_derived_cl13, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 (~ (convergent_lines @ X0 @ X1)
% 3.48/1.08 | (distinct_lines @ X1 @ X2)
% 3.48/1.08 | (convergent_lines @ X0 @ X2))),
% 3.48/1.08 inference('cnf', [status(esa)], [ceq3])).
% 3.48/1.08 thf(zip_derived_cl267, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0)
% 3.48/1.08 | (distinct_lines @ X0 @ X1)
% 3.48/1.08 | (convergent_lines @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 3.48/1.08 X1))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl13])).
% 3.48/1.08 thf(apart3, axiom, (![X:$i]: ( ~( convergent_lines @ X @ X ) ))).
% 3.48/1.08 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [apart3])).
% 3.48/1.08 thf(zip_derived_cl544, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (convergent_lines @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 3.48/1.08 X0)
% 3.48/1.08 | (distinct_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl267, zip_derived_cl2])).
% 3.48/1.08 thf(zip_derived_cl5, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 (~ (convergent_lines @ X0 @ X1)
% 3.48/1.08 | (convergent_lines @ X0 @ X2)
% 3.48/1.08 | (convergent_lines @ X1 @ X2))),
% 3.48/1.08 inference('cnf', [status(esa)], [ax6])).
% 3.48/1.08 thf(zip_derived_cl561, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (distinct_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0)
% 3.48/1.08 | (convergent_lines @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 3.48/1.08 X1)
% 3.48/1.08 | (convergent_lines @ X0 @ X1))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl544, zip_derived_cl5])).
% 3.48/1.08 thf(cp1, axiom,
% 3.48/1.08 (![X:$i,Y:$i]:
% 3.48/1.08 ( ~( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) ))).
% 3.48/1.08 thf(zip_derived_cl14, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (convergent_lines @ (parallel_through_point @ X0 @ X1) @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [cp1])).
% 3.48/1.08 thf(zip_derived_cl679, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (convergent_lines @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 3.48/1.08 X0)
% 3.48/1.08 | (distinct_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 3.48/1.08 (parallel_through_point @ X0 @ X1)))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl561, zip_derived_cl14])).
% 3.48/1.08 thf(apart2, axiom, (![X:$i]: ( ~( distinct_lines @ X @ X ) ))).
% 3.48/1.08 thf(zip_derived_cl1, plain, (![X0 : $i]: ~ (distinct_lines @ X0 @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [apart2])).
% 3.48/1.08 thf(zip_derived_cl752, plain,
% 3.48/1.08 ( (convergent_lines @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 3.48/1.08 sk__1)),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl679, zip_derived_cl1])).
% 3.48/1.08 thf(occu1, axiom,
% 3.48/1.08 (![L:$i,M:$i]:
% 3.48/1.08 ( ( unorthogonal_lines @ L @ M ) | ( convergent_lines @ L @ M ) ))).
% 3.48/1.08 thf(zip_derived_cl17, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (unorthogonal_lines @ X0 @ X1) | (convergent_lines @ X0 @ X1))),
% 3.48/1.08 inference('cnf', [status(esa)], [occu1])).
% 3.48/1.08 thf(ooc1, axiom,
% 3.48/1.08 (![A:$i,L:$i]:
% 3.48/1.08 ( ~( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) ))).
% 3.48/1.08 thf(zip_derived_cl23, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [ooc1])).
% 3.48/1.08 thf(zip_derived_cl30, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl23])).
% 3.48/1.08 thf(zip_derived_cl13, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 (~ (convergent_lines @ X0 @ X1)
% 3.48/1.08 | (distinct_lines @ X1 @ X2)
% 3.48/1.08 | (convergent_lines @ X0 @ X2))),
% 3.48/1.08 inference('cnf', [status(esa)], [ceq3])).
% 3.48/1.08 thf(zip_derived_cl42, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 ( (distinct_lines @ X0 @ X2)
% 3.48/1.08 | (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X2))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl13])).
% 3.48/1.08 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [apart3])).
% 3.48/1.08 thf(zip_derived_cl44, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 (distinct_lines @ X1 @ (orthogonal_through_point @ X1 @ X0))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl2])).
% 3.48/1.08 thf(ouo1, axiom,
% 3.48/1.08 (![A:$i,L:$i,M:$i,N:$i]:
% 3.48/1.08 ( ( distinct_lines @ L @ M ) =>
% 3.48/1.08 ( ( apart_point_and_line @ A @ L ) | ( apart_point_and_line @ A @ M ) |
% 3.48/1.08 ( unorthogonal_lines @ L @ N ) | ( unorthogonal_lines @ M @ N ) ) ))).
% 3.48/1.08 thf(zip_derived_cl25, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X0 @ X1)
% 3.48/1.08 | (apart_point_and_line @ X0 @ X2)
% 3.48/1.08 | ~ (distinct_lines @ X2 @ X1)
% 3.48/1.08 | (unorthogonal_lines @ X2 @ X3)
% 3.48/1.08 | (unorthogonal_lines @ X1 @ X3))),
% 3.48/1.08 inference('cnf', [status(esa)], [ouo1])).
% 3.48/1.08 thf(zip_derived_cl81, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X2 @ (orthogonal_through_point @ X1 @ X0))
% 3.48/1.08 | (apart_point_and_line @ X2 @ X1)
% 3.48/1.08 | (unorthogonal_lines @ X1 @ X3)
% 3.48/1.08 | (unorthogonal_lines @ (orthogonal_through_point @ X1 @ X0) @ X3))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl25])).
% 3.48/1.08 thf(zip_derived_cl24, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (apart_point_and_line @ X0 @ (orthogonal_through_point @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [ooc2])).
% 3.48/1.08 thf(zip_derived_cl691, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 ( (unorthogonal_lines @ (orthogonal_through_point @ X1 @ X0) @ X2)
% 3.48/1.08 | (unorthogonal_lines @ X1 @ X2)
% 3.48/1.08 | (apart_point_and_line @ X0 @ X1))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl24])).
% 3.48/1.08 thf(oac1, axiom,
% 3.48/1.08 (![L:$i,M:$i,N:$i]:
% 3.48/1.08 ( ( ( unorthogonal_lines @ L @ M ) & ( convergent_lines @ L @ M ) ) =>
% 3.48/1.08 ( ( ( unorthogonal_lines @ M @ N ) & ( convergent_lines @ M @ N ) ) |
% 3.48/1.08 ( ( unorthogonal_lines @ L @ N ) & ( convergent_lines @ L @ N ) ) ) ))).
% 3.48/1.08 thf(zf_stmt_1, type, zip_tseitin_1 : $i > $i > $o).
% 3.48/1.08 thf(zf_stmt_2, axiom,
% 3.48/1.08 (![N:$i,L:$i]:
% 3.48/1.08 ( ( zip_tseitin_1 @ N @ L ) =>
% 3.48/1.08 ( ( convergent_lines @ L @ N ) & ( unorthogonal_lines @ L @ N ) ) ))).
% 3.48/1.08 thf(zf_stmt_3, type, zip_tseitin_0 : $i > $i > $o).
% 3.48/1.08 thf(zf_stmt_4, axiom,
% 3.48/1.08 (![N:$i,M:$i]:
% 3.48/1.08 ( ( zip_tseitin_0 @ N @ M ) =>
% 3.48/1.08 ( ( convergent_lines @ M @ N ) & ( unorthogonal_lines @ M @ N ) ) ))).
% 3.48/1.08 thf(zf_stmt_5, axiom,
% 3.48/1.08 (![L:$i,M:$i,N:$i]:
% 3.48/1.08 ( ( ( convergent_lines @ L @ M ) & ( unorthogonal_lines @ L @ M ) ) =>
% 3.48/1.08 ( ( zip_tseitin_1 @ N @ L ) | ( zip_tseitin_0 @ N @ M ) ) ))).
% 3.48/1.08 thf(zip_derived_cl22, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 (~ (unorthogonal_lines @ X0 @ X1)
% 3.48/1.08 | ~ (convergent_lines @ X0 @ X1)
% 3.48/1.08 | (zip_tseitin_1 @ X2 @ X0)
% 3.48/1.08 | (zip_tseitin_0 @ X2 @ X1))),
% 3.48/1.08 inference('cnf', [status(esa)], [zf_stmt_5])).
% 3.48/1.08 thf(zip_derived_cl696, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ X1 @ X2)
% 3.48/1.08 | (unorthogonal_lines @ X2 @ X0)
% 3.48/1.08 | ~ (convergent_lines @ (orthogonal_through_point @ X2 @ X1) @ X0)
% 3.48/1.08 | (zip_tseitin_1 @ X3 @ (orthogonal_through_point @ X2 @ X1))
% 3.48/1.08 | (zip_tseitin_0 @ X3 @ X0))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl691, zip_derived_cl22])).
% 3.48/1.08 thf(zip_derived_cl856, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (apart_point_and_line @ sk_ @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (unorthogonal_lines @ (orthogonal_through_point @ sk__1 @ sk_) @
% 3.48/1.08 sk__1)
% 3.48/1.08 | (zip_tseitin_1 @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 3.48/1.08 | (zip_tseitin_0 @ X0 @ sk__1))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl752, zip_derived_cl696])).
% 3.48/1.08 thf(zip_derived_cl24, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (apart_point_and_line @ X0 @ (orthogonal_through_point @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [ooc2])).
% 3.48/1.08 thf(zip_derived_cl23, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [ooc1])).
% 3.48/1.08 thf(zip_derived_cl864, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (zip_tseitin_1 @ X0 @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 3.48/1.08 | (zip_tseitin_0 @ X0 @ sk__1))),
% 3.48/1.08 inference('demod', [status(thm)],
% 3.48/1.08 [zip_derived_cl856, zip_derived_cl24, zip_derived_cl23])).
% 3.48/1.08 thf(zip_derived_cl21, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (unorthogonal_lines @ X0 @ X1) | ~ (zip_tseitin_1 @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [zf_stmt_2])).
% 3.48/1.08 thf(zip_derived_cl866, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (zip_tseitin_0 @ X0 @ sk__1)
% 3.48/1.08 | (unorthogonal_lines @
% 3.48/1.08 (orthogonal_through_point @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 3.48/1.08 X0))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl864, zip_derived_cl21])).
% 3.48/1.08 thf(zip_derived_cl23, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [ooc1])).
% 3.48/1.08 thf(zip_derived_cl877, plain,
% 3.48/1.08 ( (zip_tseitin_0 @ (orthogonal_through_point @ sk__1 @ sk_) @ sk__1)),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl866, zip_derived_cl23])).
% 3.48/1.08 thf(zip_derived_cl19, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (unorthogonal_lines @ X0 @ X1) | ~ (zip_tseitin_0 @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.48/1.08 thf(zip_derived_cl879, plain,
% 3.48/1.08 ( (unorthogonal_lines @ sk__1 @ (orthogonal_through_point @ sk__1 @ sk_))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl877, zip_derived_cl19])).
% 3.48/1.08 thf(zip_derived_cl22, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 (~ (unorthogonal_lines @ X0 @ X1)
% 3.48/1.08 | ~ (convergent_lines @ X0 @ X1)
% 3.48/1.08 | (zip_tseitin_1 @ X2 @ X0)
% 3.48/1.08 | (zip_tseitin_0 @ X2 @ X1))),
% 3.48/1.08 inference('cnf', [status(esa)], [zf_stmt_5])).
% 3.48/1.08 thf(zip_derived_cl880, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 (~ (convergent_lines @ sk__1 @
% 3.48/1.08 (orthogonal_through_point @ sk__1 @ sk_))
% 3.48/1.08 | (zip_tseitin_1 @ X0 @ sk__1)
% 3.48/1.08 | (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_)))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl879, zip_derived_cl22])).
% 3.48/1.08 thf(zip_derived_cl30, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl23])).
% 3.48/1.08 thf(zip_derived_cl5, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 (~ (convergent_lines @ X0 @ X1)
% 3.48/1.08 | (convergent_lines @ X0 @ X2)
% 3.48/1.08 | (convergent_lines @ X1 @ X2))),
% 3.48/1.08 inference('cnf', [status(esa)], [ax6])).
% 3.48/1.08 thf(zip_derived_cl35, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.48/1.08 ( (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X2)
% 3.48/1.08 | (convergent_lines @ X0 @ X2))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl5])).
% 3.48/1.08 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [apart3])).
% 3.48/1.08 thf(zip_derived_cl51, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 (convergent_lines @ X1 @ (orthogonal_through_point @ X1 @ X0))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl2])).
% 3.48/1.08 thf(zip_derived_cl881, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (zip_tseitin_1 @ X0 @ sk__1)
% 3.48/1.08 | (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_)))),
% 3.48/1.08 inference('demod', [status(thm)], [zip_derived_cl880, zip_derived_cl51])).
% 3.48/1.08 thf(zip_derived_cl19, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (unorthogonal_lines @ X0 @ X1) | ~ (zip_tseitin_0 @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.48/1.08 thf(zip_derived_cl883, plain,
% 3.48/1.08 (![X0 : $i]:
% 3.48/1.08 ( (zip_tseitin_1 @ X0 @ sk__1)
% 3.48/1.08 | (unorthogonal_lines @ (orthogonal_through_point @ sk__1 @ sk_) @
% 3.48/1.08 X0))),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl881, zip_derived_cl19])).
% 3.48/1.08 thf(zip_derived_cl23, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [ooc1])).
% 3.48/1.08 thf(zip_derived_cl891, plain, ( (zip_tseitin_1 @ sk__1 @ sk__1)),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl883, zip_derived_cl23])).
% 3.48/1.08 thf(zip_derived_cl20, plain,
% 3.48/1.08 (![X0 : $i, X1 : $i]:
% 3.48/1.08 ( (convergent_lines @ X0 @ X1) | ~ (zip_tseitin_1 @ X1 @ X0))),
% 3.48/1.08 inference('cnf', [status(esa)], [zf_stmt_2])).
% 3.48/1.08 thf(zip_derived_cl892, plain, ( (convergent_lines @ sk__1 @ sk__1)),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl891, zip_derived_cl20])).
% 3.48/1.08 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 3.48/1.08 inference('cnf', [status(esa)], [apart3])).
% 3.48/1.08 thf(zip_derived_cl894, plain, ($false),
% 3.48/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl892, zip_derived_cl2])).
% 3.48/1.08
% 3.48/1.08 % SZS output end Refutation
% 3.48/1.08
% 3.48/1.08
% 3.48/1.08 % Terminating...
% 3.90/1.17 % Runner terminated.
% 3.90/1.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------