%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEO223+3 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pg813xVJvl true
% Computer : n016.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 0.56s 0.91s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO223+3 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pg813xVJvl true
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 17:46:25 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.53/0.62 % Total configuration time : 435
% 0.53/0.62 % Estimated wc time : 1092
% 0.53/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.56/0.91 % Solved by fo/fo7.sh.
% 0.56/0.91 % done 308 iterations in 0.160s
% 0.56/0.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.56/0.91 % SZS output start Refutation
% 0.56/0.91 thf(sk__type, type, sk_: $i).
% 0.56/0.91 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $o).
% 0.56/0.91 thf(distinct_lines_type, type, distinct_lines: $i > $i > $o).
% 0.56/0.91 thf(orthogonal_through_point_type, type, orthogonal_through_point: $i > $i > $i).
% 0.56/0.91 thf(equal_lines_type, type, equal_lines: $i > $i > $o).
% 0.56/0.91 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $o).
% 0.56/0.91 thf(sk__1_type, type, sk__1: $i).
% 0.56/0.91 thf(parallel_through_point_type, type, parallel_through_point: $i > $i > $i).
% 0.56/0.91 thf(unorthogonal_lines_type, type, unorthogonal_lines: $i > $i > $o).
% 0.56/0.91 thf(convergent_lines_type, type, convergent_lines: $i > $i > $o).
% 0.56/0.91 thf(cotno1, axiom,
% 0.56/0.91 (![L:$i,M:$i,N:$i]:
% 0.56/0.91 ( ( ( ( ~( unorthogonal_lines @ L @ N ) ) |
% 0.56/0.91 ( ~( convergent_lines @ L @ N ) ) ) &
% 0.56/0.91 ( ( ~( unorthogonal_lines @ L @ M ) ) |
% 0.56/0.91 ( ~( convergent_lines @ L @ M ) ) ) ) =>
% 0.56/0.91 ( ( ~( unorthogonal_lines @ M @ N ) ) |
% 0.56/0.91 ( ~( convergent_lines @ M @ N ) ) ) ))).
% 0.56/0.91 thf(zf_stmt_0, axiom,
% 0.56/0.91 (![N:$i,L:$i]:
% 0.56/0.91 ( ( ( ~( convergent_lines @ L @ N ) ) |
% 0.56/0.91 ( ~( unorthogonal_lines @ L @ N ) ) ) =>
% 0.56/0.91 ( zip_tseitin_2 @ N @ L ) ))).
% 0.56/0.91 thf(zip_derived_cl28, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (zip_tseitin_2 @ X0 @ X1) | (convergent_lines @ X1 @ X0))),
% 0.56/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.56/0.91 thf(ax2, axiom,
% 0.56/0.91 (![X:$i,Y:$i]:
% 0.56/0.91 ( ( equal_lines @ X @ Y ) <=> ( ~( distinct_lines @ X @ Y ) ) ))).
% 0.56/0.91 thf(zip_derived_cl41, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (equal_lines @ X0 @ X1) | (distinct_lines @ X0 @ X1))),
% 0.56/0.91 inference('cnf', [status(esa)], [ax2])).
% 0.56/0.91 thf(con, conjecture,
% 0.56/0.91 (![A:$i,L:$i]:
% 0.56/0.91 ( equal_lines @
% 0.56/0.91 ( parallel_through_point @ L @ A ) @
% 0.56/0.91 ( orthogonal_through_point @ ( orthogonal_through_point @ L @ A ) @ A ) ))).
% 0.56/0.91 thf(zf_stmt_1, negated_conjecture,
% 0.56/0.91 (~( ![A:$i,L:$i]:
% 0.56/0.91 ( equal_lines @
% 0.56/0.91 ( parallel_through_point @ L @ A ) @
% 0.56/0.91 ( orthogonal_through_point @ ( orthogonal_through_point @ L @ A ) @ A ) ) )),
% 0.56/0.91 inference('cnf.neg', [status(esa)], [con])).
% 0.56/0.91 thf(zip_derived_cl48, plain,
% 0.56/0.91 (~ (equal_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.56/0.91 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.56/0.91 thf(zip_derived_cl77, plain,
% 0.56/0.91 ( (distinct_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl48])).
% 0.56/0.91 thf(p1, axiom,
% 0.56/0.91 (![X:$i,Y:$i]:
% 0.56/0.91 ( ( distinct_lines @ X @ Y ) => ( convergent_lines @ X @ Y ) ))).
% 0.56/0.91 thf(zip_derived_cl14, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (convergent_lines @ X0 @ X1) | ~ (distinct_lines @ X0 @ X1))),
% 0.56/0.91 inference('cnf', [status(esa)], [p1])).
% 0.56/0.91 thf(ax6, axiom,
% 0.56/0.91 (![X:$i,Y:$i,Z:$i]:
% 0.56/0.91 ( ( convergent_lines @ X @ Y ) =>
% 0.56/0.91 ( ( convergent_lines @ X @ Z ) | ( convergent_lines @ Y @ Z ) ) ))).
% 0.56/0.91 thf(zip_derived_cl5, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 (~ (convergent_lines @ X0 @ X1)
% 0.56/0.91 | (convergent_lines @ X0 @ X2)
% 0.56/0.91 | (convergent_lines @ X1 @ X2))),
% 0.56/0.91 inference('cnf', [status(esa)], [ax6])).
% 0.56/0.91 thf(zip_derived_cl56, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 (~ (distinct_lines @ X1 @ X0)
% 0.56/0.91 | (convergent_lines @ X0 @ X2)
% 0.56/0.91 | (convergent_lines @ X1 @ X2))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl5])).
% 0.56/0.91 thf(zip_derived_cl92, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0)
% 0.56/0.91 | (convergent_lines @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.56/0.91 X0))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl56])).
% 0.56/0.91 thf(occu1, axiom,
% 0.56/0.91 (![L:$i,M:$i]:
% 0.56/0.91 ( ( unorthogonal_lines @ L @ M ) | ( convergent_lines @ L @ M ) ))).
% 0.56/0.91 thf(zip_derived_cl18, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X0 @ X1) | (convergent_lines @ X0 @ X1))),
% 0.56/0.91 inference('cnf', [status(esa)], [occu1])).
% 0.56/0.91 thf(ooc1, axiom,
% 0.56/0.91 (![A:$i,L:$i]:
% 0.56/0.91 ( ~( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) ))).
% 0.56/0.91 thf(zip_derived_cl24, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [ooc1])).
% 0.56/0.91 thf(zip_derived_cl63, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl24])).
% 0.56/0.91 thf(couo1, axiom,
% 0.56/0.91 (![L:$i,M:$i,N:$i]:
% 0.56/0.91 ( ( ( ~( unorthogonal_lines @ L @ M ) ) &
% 0.56/0.91 ( ~( unorthogonal_lines @ L @ N ) ) ) =>
% 0.56/0.91 ( ~( convergent_lines @ M @ N ) ) ))).
% 0.56/0.91 thf(zip_derived_cl33, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X0 @ X1)
% 0.56/0.91 | (unorthogonal_lines @ X0 @ X2)
% 0.56/0.91 | ~ (convergent_lines @ X1 @ X2))),
% 0.56/0.91 inference('cnf', [status(esa)], [couo1])).
% 0.56/0.91 thf(zip_derived_cl72, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X2 @ X0)
% 0.56/0.91 | (unorthogonal_lines @ X2 @ (orthogonal_through_point @ X0 @ X1)))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl33])).
% 0.56/0.91 thf(zip_derived_cl24, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [ooc1])).
% 0.56/0.91 thf(zip_derived_cl150, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 (unorthogonal_lines @
% 0.56/0.91 (orthogonal_through_point @ (orthogonal_through_point @ X1 @ X0) @
% 0.56/0.91 X2) @
% 0.56/0.91 X1)),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl24])).
% 0.56/0.91 thf(zf_stmt_2, axiom,
% 0.56/0.91 (![M:$i,L:$i]:
% 0.56/0.91 ( ( ( ~( convergent_lines @ L @ M ) ) |
% 0.56/0.91 ( ~( unorthogonal_lines @ L @ M ) ) ) =>
% 0.56/0.91 ( zip_tseitin_3 @ M @ L ) ))).
% 0.56/0.91 thf(zip_derived_cl30, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (zip_tseitin_3 @ X0 @ X1) | (convergent_lines @ X1 @ X0))),
% 0.56/0.91 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.56/0.91 thf(zf_stmt_3, type, zip_tseitin_3 : $i > $i > $o).
% 0.56/0.91 thf(zf_stmt_4, type, zip_tseitin_2 : $i > $i > $o).
% 0.56/0.91 thf(zf_stmt_5, axiom,
% 0.56/0.91 (![L:$i,M:$i,N:$i]:
% 0.56/0.91 ( ( ( zip_tseitin_3 @ M @ L ) & ( zip_tseitin_2 @ N @ L ) ) =>
% 0.56/0.91 ( ( ~( convergent_lines @ M @ N ) ) |
% 0.56/0.91 ( ~( unorthogonal_lines @ M @ N ) ) ) ))).
% 0.56/0.91 thf(zip_derived_cl32, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 (~ (zip_tseitin_3 @ X0 @ X1)
% 0.56/0.91 | ~ (zip_tseitin_2 @ X2 @ X1)
% 0.56/0.91 | ~ (convergent_lines @ X0 @ X2)
% 0.56/0.91 | ~ (unorthogonal_lines @ X0 @ X2))),
% 0.56/0.91 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.56/0.91 thf(zip_derived_cl75, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (convergent_lines @ X0 @ X1)
% 0.56/0.91 | ~ (unorthogonal_lines @ X1 @ X2)
% 0.56/0.91 | ~ (convergent_lines @ X1 @ X2)
% 0.56/0.91 | ~ (zip_tseitin_2 @ X2 @ X0))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl32])).
% 0.56/0.91 thf(zip_derived_cl155, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.91 (~ (zip_tseitin_2 @ X0 @ X3)
% 0.56/0.91 | ~ (convergent_lines @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ X0 @ X2) @ X1) @
% 0.56/0.91 X0)
% 0.56/0.91 | (convergent_lines @ X3 @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ X0 @ X2) @ X1)))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl75])).
% 0.56/0.91 thf(zip_derived_cl244, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ sk__1)
% 0.56/0.91 | (convergent_lines @ X0 @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 0.56/0.91 | ~ (zip_tseitin_2 @ sk__1 @ X0))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl155])).
% 0.56/0.91 thf(cp1, axiom,
% 0.56/0.91 (![X:$i,Y:$i]:
% 0.56/0.91 ( ~( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) ))).
% 0.56/0.91 thf(zip_derived_cl15, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ~ (convergent_lines @ (parallel_through_point @ X0 @ X1) @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [cp1])).
% 0.56/0.91 thf(zip_derived_cl246, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 ( (convergent_lines @ X0 @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 0.56/0.91 | ~ (zip_tseitin_2 @ sk__1 @ X0))),
% 0.56/0.91 inference('demod', [status(thm)], [zip_derived_cl244, zip_derived_cl15])).
% 0.56/0.91 thf(zip_derived_cl247, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 ( (convergent_lines @ X0 @ sk__1)
% 0.56/0.91 | (convergent_lines @ X0 @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl246])).
% 0.56/0.91 thf(apart3, axiom, (![X:$i]: ( ~( convergent_lines @ X @ X ) ))).
% 0.56/0.91 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [apart3])).
% 0.56/0.91 thf(zip_derived_cl255, plain,
% 0.56/0.91 ( (convergent_lines @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.56/0.91 sk__1)),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl247, zip_derived_cl2])).
% 0.56/0.91 thf(zip_derived_cl33, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X0 @ X1)
% 0.56/0.91 | (unorthogonal_lines @ X0 @ X2)
% 0.56/0.91 | ~ (convergent_lines @ X1 @ X2))),
% 0.56/0.91 inference('cnf', [status(esa)], [couo1])).
% 0.56/0.91 thf(zip_derived_cl268, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X0 @ sk__1)
% 0.56/0.91 | (unorthogonal_lines @ X0 @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl255, zip_derived_cl33])).
% 0.56/0.91 thf(zip_derived_cl28, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (zip_tseitin_2 @ X0 @ X1) | (convergent_lines @ X1 @ X0))),
% 0.56/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.56/0.91 thf(zip_derived_cl63, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl24])).
% 0.56/0.91 thf(ceq3, axiom,
% 0.56/0.91 (![X:$i,Y:$i,Z:$i]:
% 0.56/0.91 ( ( convergent_lines @ X @ Y ) =>
% 0.56/0.91 ( ( distinct_lines @ Y @ Z ) | ( convergent_lines @ X @ Z ) ) ))).
% 0.56/0.91 thf(zip_derived_cl13, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 (~ (convergent_lines @ X0 @ X1)
% 0.56/0.91 | (distinct_lines @ X1 @ X2)
% 0.56/0.91 | (convergent_lines @ X0 @ X2))),
% 0.56/0.91 inference('cnf', [status(esa)], [ceq3])).
% 0.56/0.91 thf(zip_derived_cl69, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X2)
% 0.56/0.91 | (distinct_lines @ X0 @ X2))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 0.56/0.91 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [apart3])).
% 0.56/0.91 thf(zip_derived_cl105, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 (distinct_lines @ X1 @ (orthogonal_through_point @ X1 @ X0))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl2])).
% 0.56/0.91 thf(zip_derived_cl14, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (convergent_lines @ X0 @ X1) | ~ (distinct_lines @ X0 @ X1))),
% 0.56/0.91 inference('cnf', [status(esa)], [p1])).
% 0.56/0.91 thf(zip_derived_cl31, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ( (zip_tseitin_3 @ X0 @ X1) | (unorthogonal_lines @ X1 @ X0))),
% 0.56/0.91 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.56/0.91 thf(zip_derived_cl32, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 (~ (zip_tseitin_3 @ X0 @ X1)
% 0.56/0.91 | ~ (zip_tseitin_2 @ X2 @ X1)
% 0.56/0.91 | ~ (convergent_lines @ X0 @ X2)
% 0.56/0.91 | ~ (unorthogonal_lines @ X0 @ X2))),
% 0.56/0.91 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.56/0.91 thf(zip_derived_cl76, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X0 @ X1)
% 0.56/0.91 | ~ (unorthogonal_lines @ X1 @ X2)
% 0.56/0.91 | ~ (convergent_lines @ X1 @ X2)
% 0.56/0.91 | ~ (zip_tseitin_2 @ X2 @ X0))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl32])).
% 0.56/0.91 thf(zip_derived_cl81, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 (~ (distinct_lines @ X1 @ X0)
% 0.56/0.91 | ~ (zip_tseitin_2 @ X0 @ X2)
% 0.56/0.91 | ~ (unorthogonal_lines @ X1 @ X0)
% 0.56/0.91 | (unorthogonal_lines @ X2 @ X1))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl76])).
% 0.56/0.91 thf(zip_derived_cl119, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X2 @ X1)
% 0.56/0.91 | ~ (unorthogonal_lines @ X1 @ (orthogonal_through_point @ X1 @ X0))
% 0.56/0.91 | ~ (zip_tseitin_2 @ (orthogonal_through_point @ X1 @ X0) @ X2))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl81])).
% 0.56/0.91 thf(zip_derived_cl137, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.91 ( (convergent_lines @ X0 @ (orthogonal_through_point @ X2 @ X1))
% 0.56/0.91 | ~ (unorthogonal_lines @ X2 @ (orthogonal_through_point @ X2 @ X1))
% 0.56/0.91 | (unorthogonal_lines @ X0 @ X2))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl119])).
% 0.56/0.91 thf(zip_derived_cl345, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ (orthogonal_through_point @ sk__1 @ sk_) @
% 0.56/0.91 sk__1)
% 0.56/0.91 | (unorthogonal_lines @ X0 @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_))
% 0.56/0.91 | (convergent_lines @ X0 @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl268, zip_derived_cl137])).
% 0.56/0.91 thf(zip_derived_cl24, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [ooc1])).
% 0.56/0.91 thf(zip_derived_cl350, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 ( (unorthogonal_lines @ X0 @ (orthogonal_through_point @ sk__1 @ sk_))
% 0.56/0.91 | (convergent_lines @ X0 @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.56/0.91 inference('demod', [status(thm)], [zip_derived_cl345, zip_derived_cl24])).
% 0.56/0.91 thf(zip_derived_cl24, plain,
% 0.56/0.91 (![X0 : $i, X1 : $i]:
% 0.56/0.91 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [ooc1])).
% 0.56/0.91 thf(zip_derived_cl767, plain,
% 0.56/0.91 (![X0 : $i]:
% 0.56/0.91 (convergent_lines @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ X0) @
% 0.56/0.91 (orthogonal_through_point @
% 0.56/0.91 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl350, zip_derived_cl24])).
% 0.56/0.91 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 0.56/0.91 inference('cnf', [status(esa)], [apart3])).
% 0.56/0.91 thf(zip_derived_cl782, plain, ($false),
% 0.56/0.91 inference('sup-', [status(thm)], [zip_derived_cl767, zip_derived_cl2])).
% 0.56/0.91
% 0.56/0.91 % SZS output end Refutation
% 0.56/0.91
% 0.56/0.91
% 0.56/0.91 % Terminating...
% 0.57/0.95 % Runner terminated.
% 0.57/0.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------