%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEO222+2 : 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.RPYjLX5VTk true
% Computer : n007.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 0.52s 0.87s
% Output : Refutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO222+2 : TPTP v9.2.0. Released v3.3.0.
% 0.04/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RPYjLX5VTk true
% 0.12/0.35 % Computer : n007.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Wed Oct 1 17:31:23 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Running portfolio for 300 s
% 0.12/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36 % Number of cores: 8
% 0.12/0.36 % Python version: Python 3.6.8
% 0.12/0.36 % Running in FO mode
% 0.43/0.62 % Total configuration time : 435
% 0.43/0.62 % Estimated wc time : 1092
% 0.43/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.68 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.52/0.87 % Solved by fo/fo6_bce.sh.
% 0.52/0.87 % BCE start: 27
% 0.52/0.87 % BCE eliminated: 0
% 0.52/0.87 % PE start: 27
% 0.52/0.87 logic: neq
% 0.52/0.87 % PE eliminated: 1
% 0.52/0.87 % done 149 iterations in 0.169s
% 0.52/0.87 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.52/0.87 % SZS output start Refutation
% 0.52/0.87 thf(unorthogonal_lines_type, type, unorthogonal_lines: $i > $i > $o).
% 0.52/0.87 thf(distinct_lines_type, type, distinct_lines: $i > $i > $o).
% 0.52/0.87 thf(sk__type, type, sk_: $i).
% 0.52/0.87 thf(sk__1_type, type, sk__1: $i).
% 0.52/0.87 thf(orthogonal_through_point_type, type, orthogonal_through_point: $i > $i > $i).
% 0.52/0.87 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $o).
% 0.52/0.87 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $o).
% 0.52/0.87 thf(distinct_points_type, type, distinct_points: $i > $i > $o).
% 0.52/0.87 thf(apart_point_and_line_type, type, apart_point_and_line: $i > $i > $o).
% 0.52/0.87 thf(intersection_point_type, type, intersection_point: $i > $i > $i).
% 0.52/0.87 thf(convergent_lines_type, type, convergent_lines: $i > $i > $o).
% 0.52/0.87 thf(con, conjecture,
% 0.52/0.87 (![A:$i,L:$i]:
% 0.52/0.87 ( ~( convergent_lines @
% 0.52/0.87 L @
% 0.52/0.87 ( orthogonal_through_point @ ( orthogonal_through_point @ L @ A ) @ A ) ) ))).
% 0.52/0.87 thf(zf_stmt_0, negated_conjecture,
% 0.52/0.87 (~( ![A:$i,L:$i]:
% 0.52/0.87 ( ~( convergent_lines @
% 0.52/0.87 L @
% 0.52/0.87 ( orthogonal_through_point @
% 0.52/0.87 ( orthogonal_through_point @ L @ A ) @ A ) ) ) )),
% 0.52/0.87 inference('cnf.neg', [status(esa)], [con])).
% 0.52/0.87 thf(zip_derived_cl26, plain,
% 0.52/0.87 ( (convergent_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.52/0.87 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.52/0.87 thf(ceq3, axiom,
% 0.52/0.87 (![X:$i,Y:$i]:
% 0.52/0.87 ( ( convergent_lines @ X @ Y ) => ( distinct_lines @ X @ Y ) ))).
% 0.52/0.87 thf(zip_derived_cl13, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ( (distinct_lines @ X0 @ X1) | ~ (convergent_lines @ X0 @ X1))),
% 0.52/0.87 inference('cnf', [status(esa)], [ceq3])).
% 0.52/0.87 thf(apart5, axiom,
% 0.52/0.87 (![X:$i,Y:$i,Z:$i]:
% 0.52/0.87 ( ( distinct_lines @ X @ Y ) =>
% 0.52/0.87 ( ( distinct_lines @ X @ Z ) | ( distinct_lines @ Y @ Z ) ) ))).
% 0.52/0.87 thf(zip_derived_cl4, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 (~ (distinct_lines @ X0 @ X1)
% 0.52/0.87 | (distinct_lines @ X0 @ X2)
% 0.52/0.87 | (distinct_lines @ X1 @ X2))),
% 0.52/0.87 inference('cnf', [status(esa)], [apart5])).
% 0.52/0.87 thf(zip_derived_cl38, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 (~ (convergent_lines @ X1 @ X0)
% 0.52/0.87 | (distinct_lines @ X1 @ X2)
% 0.52/0.87 | (distinct_lines @ X0 @ X2))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 0.52/0.87 thf(zip_derived_cl64, plain,
% 0.52/0.87 (![X0 : $i]:
% 0.52/0.87 ( (distinct_lines @ sk__1 @ X0)
% 0.52/0.87 | (distinct_lines @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.52/0.87 X0))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl38])).
% 0.52/0.87 thf(apart2, axiom, (![X:$i]: ( ~( distinct_lines @ X @ X ) ))).
% 0.52/0.87 thf(zip_derived_cl1, plain, (![X0 : $i]: ~ (distinct_lines @ X0 @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [apart2])).
% 0.52/0.87 thf(zip_derived_cl74, plain,
% 0.52/0.87 ( (distinct_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 0.52/0.87 thf(ouo1, axiom,
% 0.52/0.87 (![A:$i,L:$i,M:$i,N:$i]:
% 0.52/0.87 ( ( distinct_lines @ L @ M ) =>
% 0.52/0.87 ( ( apart_point_and_line @ A @ L ) | ( apart_point_and_line @ A @ M ) |
% 0.52/0.87 ( unorthogonal_lines @ L @ N ) | ( unorthogonal_lines @ M @ N ) ) ))).
% 0.52/0.87 thf(zip_derived_cl25, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.52/0.87 ( (apart_point_and_line @ X0 @ X1)
% 0.52/0.87 | (apart_point_and_line @ X0 @ X2)
% 0.52/0.87 | ~ (distinct_lines @ X2 @ X1)
% 0.52/0.87 | (unorthogonal_lines @ X2 @ X3)
% 0.52/0.87 | (unorthogonal_lines @ X1 @ X3))),
% 0.52/0.87 inference('cnf', [status(esa)], [ouo1])).
% 0.52/0.87 thf(zip_derived_cl81, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ( (apart_point_and_line @ X0 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 0.52/0.87 | (apart_point_and_line @ X0 @ sk__1)
% 0.52/0.87 | (unorthogonal_lines @ sk__1 @ X1)
% 0.52/0.87 | (unorthogonal_lines @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.52/0.87 X1))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl25])).
% 0.52/0.87 thf(ooc1, axiom,
% 0.52/0.87 (![A:$i,L:$i]:
% 0.52/0.87 ( ~( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) ))).
% 0.52/0.87 thf(zip_derived_cl23, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [ooc1])).
% 0.52/0.87 thf(zip_derived_cl250, plain,
% 0.52/0.87 (![X0 : $i]:
% 0.52/0.87 ( (unorthogonal_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_))
% 0.52/0.87 | (apart_point_and_line @ X0 @ sk__1)
% 0.52/0.87 | (apart_point_and_line @ X0 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl23])).
% 0.52/0.87 thf(con2, axiom,
% 0.52/0.87 (![X:$i,Y:$i,Z:$i]:
% 0.52/0.87 ( ( convergent_lines @ X @ Y ) =>
% 0.52/0.87 ( ( ( apart_point_and_line @ Z @ X ) | ( apart_point_and_line @ Z @ Y ) ) =>
% 0.52/0.87 ( distinct_points @ Z @ ( intersection_point @ X @ Y ) ) ) ))).
% 0.52/0.87 thf(zip_derived_cl8, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 (~ (convergent_lines @ X0 @ X1)
% 0.52/0.87 | (distinct_points @ X2 @ (intersection_point @ X0 @ X1))
% 0.52/0.87 | ~ (apart_point_and_line @ X2 @ X1))),
% 0.52/0.87 inference('cnf', [status(esa)], [con2])).
% 0.52/0.87 thf(apart1, axiom, (![X:$i]: ( ~( distinct_points @ X @ X ) ))).
% 0.52/0.87 thf(zip_derived_cl0, plain, (![X0 : $i]: ~ (distinct_points @ X0 @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [apart1])).
% 0.52/0.87 thf(zip_derived_cl51, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 (~ (apart_point_and_line @ (intersection_point @ X1 @ X0) @ X0)
% 0.52/0.87 | ~ (convergent_lines @ X1 @ X0))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl0])).
% 0.52/0.87 thf(zip_derived_cl335, plain,
% 0.52/0.87 (![X0 : $i]:
% 0.52/0.87 ( (apart_point_and_line @
% 0.52/0.87 (intersection_point @ X0 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)) @
% 0.52/0.87 sk__1)
% 0.52/0.87 | (unorthogonal_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_))
% 0.52/0.87 | ~ (convergent_lines @ X0 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl51])).
% 0.52/0.87 thf(zip_derived_cl9, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 (~ (convergent_lines @ X0 @ X1)
% 0.52/0.87 | (distinct_points @ X2 @ (intersection_point @ X0 @ X1))
% 0.52/0.87 | ~ (apart_point_and_line @ X2 @ X0))),
% 0.52/0.87 inference('cnf', [status(esa)], [con2])).
% 0.52/0.87 thf(zip_derived_cl0, plain, (![X0 : $i]: ~ (distinct_points @ X0 @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [apart1])).
% 0.52/0.87 thf(zip_derived_cl54, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 (~ (apart_point_and_line @ (intersection_point @ X1 @ X0) @ X1)
% 0.52/0.87 | ~ (convergent_lines @ X1 @ X0))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl0])).
% 0.52/0.87 thf(zip_derived_cl535, plain,
% 0.52/0.87 ((~ (convergent_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 0.52/0.87 | (unorthogonal_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_))
% 0.52/0.87 | ~ (convergent_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl335, zip_derived_cl54])).
% 0.52/0.87 thf(zip_derived_cl26, plain,
% 0.52/0.87 ( (convergent_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.52/0.87 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.52/0.87 thf(zip_derived_cl26, plain,
% 0.52/0.87 ( (convergent_lines @ sk__1 @
% 0.52/0.87 (orthogonal_through_point @
% 0.52/0.87 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.52/0.87 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.52/0.87 thf(zip_derived_cl536, plain,
% 0.52/0.87 ( (unorthogonal_lines @ sk__1 @ (orthogonal_through_point @ sk__1 @ sk_))),
% 0.52/0.87 inference('demod', [status(thm)],
% 0.52/0.87 [zip_derived_cl535, zip_derived_cl26, zip_derived_cl26])).
% 0.52/0.87 thf(occu1, axiom,
% 0.52/0.87 (![L:$i,M:$i]:
% 0.52/0.87 ( ( unorthogonal_lines @ L @ M ) | ( convergent_lines @ L @ M ) ))).
% 0.52/0.87 thf(zip_derived_cl17, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ( (unorthogonal_lines @ X0 @ X1) | (convergent_lines @ X0 @ X1))),
% 0.52/0.87 inference('cnf', [status(esa)], [occu1])).
% 0.52/0.87 thf(zip_derived_cl23, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [ooc1])).
% 0.52/0.87 thf(zip_derived_cl37, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl23])).
% 0.52/0.87 thf(apart6, axiom,
% 0.52/0.87 (![X:$i,Y:$i,Z:$i]:
% 0.52/0.87 ( ( convergent_lines @ X @ Y ) =>
% 0.52/0.87 ( ( convergent_lines @ X @ Z ) | ( convergent_lines @ Y @ Z ) ) ))).
% 0.52/0.87 thf(zip_derived_cl5, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 (~ (convergent_lines @ X0 @ X1)
% 0.52/0.87 | (convergent_lines @ X0 @ X2)
% 0.52/0.87 | (convergent_lines @ X1 @ X2))),
% 0.52/0.87 inference('cnf', [status(esa)], [apart6])).
% 0.52/0.87 thf(zip_derived_cl42, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 ( (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X2)
% 0.52/0.87 | (convergent_lines @ X0 @ X2))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl5])).
% 0.52/0.87 thf(apart3, axiom, (![X:$i]: ( ~( convergent_lines @ X @ X ) ))).
% 0.52/0.87 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [apart3])).
% 0.52/0.87 thf(zip_derived_cl47, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 (convergent_lines @ X1 @ (orthogonal_through_point @ X1 @ X0))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl2])).
% 0.52/0.87 thf(oac1, axiom,
% 0.52/0.87 (![L:$i,M:$i,N:$i]:
% 0.52/0.87 ( ( ( unorthogonal_lines @ L @ M ) & ( convergent_lines @ L @ M ) ) =>
% 0.52/0.87 ( ( ( unorthogonal_lines @ M @ N ) & ( convergent_lines @ M @ N ) ) |
% 0.52/0.87 ( ( unorthogonal_lines @ L @ N ) & ( convergent_lines @ L @ N ) ) ) ))).
% 0.52/0.87 thf(zf_stmt_1, type, zip_tseitin_1 : $i > $i > $o).
% 0.52/0.87 thf(zf_stmt_2, axiom,
% 0.52/0.87 (![N:$i,L:$i]:
% 0.52/0.87 ( ( zip_tseitin_1 @ N @ L ) =>
% 0.52/0.87 ( ( convergent_lines @ L @ N ) & ( unorthogonal_lines @ L @ N ) ) ))).
% 0.52/0.87 thf(zf_stmt_3, type, zip_tseitin_0 : $i > $i > $o).
% 0.52/0.87 thf(zf_stmt_4, axiom,
% 0.52/0.87 (![N:$i,M:$i]:
% 0.52/0.87 ( ( zip_tseitin_0 @ N @ M ) =>
% 0.52/0.87 ( ( convergent_lines @ M @ N ) & ( unorthogonal_lines @ M @ N ) ) ))).
% 0.52/0.87 thf(zf_stmt_5, axiom,
% 0.52/0.87 (![L:$i,M:$i,N:$i]:
% 0.52/0.87 ( ( ( convergent_lines @ L @ M ) & ( unorthogonal_lines @ L @ M ) ) =>
% 0.52/0.87 ( ( zip_tseitin_1 @ N @ L ) | ( zip_tseitin_0 @ N @ M ) ) ))).
% 0.52/0.87 thf(zip_derived_cl22, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 (~ (unorthogonal_lines @ X0 @ X1)
% 0.52/0.87 | ~ (convergent_lines @ X0 @ X1)
% 0.52/0.87 | (zip_tseitin_1 @ X2 @ X0)
% 0.52/0.87 | (zip_tseitin_0 @ X2 @ X1))),
% 0.52/0.87 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.52/0.87 thf(zip_derived_cl19, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ( (unorthogonal_lines @ X0 @ X1) | ~ (zip_tseitin_0 @ X1 @ X0))),
% 0.52/0.87 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.52/0.87 thf(zip_derived_cl28, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 ( (zip_tseitin_1 @ X0 @ X2)
% 0.52/0.87 | ~ (convergent_lines @ X2 @ X1)
% 0.52/0.87 | ~ (unorthogonal_lines @ X2 @ X1)
% 0.52/0.87 | (unorthogonal_lines @ X1 @ X0))),
% 0.52/0.87 inference('dp-resolution', [status(thm)],
% 0.52/0.87 [zip_derived_cl22, zip_derived_cl19])).
% 0.52/0.87 thf(zip_derived_cl82, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.52/0.87 ( (zip_tseitin_1 @ X2 @ X1)
% 0.52/0.87 | ~ (unorthogonal_lines @ X1 @ (orthogonal_through_point @ X1 @ X0))
% 0.52/0.87 | (unorthogonal_lines @ (orthogonal_through_point @ X1 @ X0) @ X2))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl28])).
% 0.52/0.87 thf(zip_derived_cl559, plain,
% 0.52/0.87 (![X0 : $i]:
% 0.52/0.87 ( (zip_tseitin_1 @ X0 @ sk__1)
% 0.52/0.87 | (unorthogonal_lines @ (orthogonal_through_point @ sk__1 @ sk_) @
% 0.52/0.87 X0))),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl536, zip_derived_cl82])).
% 0.52/0.87 thf(zip_derived_cl23, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [ooc1])).
% 0.52/0.87 thf(zip_derived_cl600, plain, ( (zip_tseitin_1 @ sk__1 @ sk__1)),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl559, zip_derived_cl23])).
% 0.52/0.87 thf(zip_derived_cl20, plain,
% 0.52/0.87 (![X0 : $i, X1 : $i]:
% 0.52/0.87 ( (convergent_lines @ X0 @ X1) | ~ (zip_tseitin_1 @ X1 @ X0))),
% 0.52/0.87 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.52/0.87 thf(zip_derived_cl649, plain, ( (convergent_lines @ sk__1 @ sk__1)),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl600, zip_derived_cl20])).
% 0.52/0.87 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 0.52/0.87 inference('cnf', [status(esa)], [apart3])).
% 0.52/0.87 thf(zip_derived_cl651, plain, ($false),
% 0.52/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl649, zip_derived_cl2])).
% 0.52/0.87
% 0.52/0.87 % SZS output end Refutation
% 0.52/0.87
% 0.52/0.87
% 0.52/0.87 % Terminating...
% 1.54/0.93 % Runner terminated.
% 1.54/0.95 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------