%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEO223+2 : TPTP v9.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4EfFGaTod9 true
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:34:23 PM UTC 2025
% Result : Theorem 0.55s 0.93s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO223+2 : TPTP v9.2.0. Released v3.3.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4EfFGaTod9 true
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 17:41:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.47/0.62 % Total configuration time : 435
% 0.47/0.62 % Estimated wc time : 1092
% 0.47/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.93 % Solved by fo/fo1_av.sh.
% 0.55/0.93 % done 173 iterations in 0.186s
% 0.55/0.93 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.55/0.93 % SZS output start Refutation
% 0.55/0.93 thf(unorthogonal_lines_type, type, unorthogonal_lines: $i > $i > $o).
% 0.55/0.93 thf(distinct_lines_type, type, distinct_lines: $i > $i > $o).
% 0.55/0.93 thf(sk__type, type, sk_: $i).
% 0.55/0.93 thf(sk__1_type, type, sk__1: $i).
% 0.55/0.93 thf(orthogonal_through_point_type, type, orthogonal_through_point: $i > $i > $i).
% 0.55/0.93 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $o).
% 0.55/0.93 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $o).
% 0.55/0.93 thf(parallel_through_point_type, type, parallel_through_point: $i > $i > $i).
% 0.55/0.93 thf(apart_point_and_line_type, type, apart_point_and_line: $i > $i > $o).
% 0.55/0.93 thf(convergent_lines_type, type, convergent_lines: $i > $i > $o).
% 0.55/0.93 thf(con, conjecture,
% 0.55/0.93 (![A:$i,L:$i]:
% 0.55/0.93 ( ~( distinct_lines @
% 0.55/0.93 ( parallel_through_point @ L @ A ) @
% 0.55/0.93 ( orthogonal_through_point @ ( orthogonal_through_point @ L @ A ) @ A ) ) ))).
% 0.55/0.93 thf(zf_stmt_0, negated_conjecture,
% 0.55/0.93 (~( ![A:$i,L:$i]:
% 0.55/0.93 ( ~( distinct_lines @
% 0.55/0.93 ( parallel_through_point @ L @ A ) @
% 0.55/0.93 ( orthogonal_through_point @
% 0.55/0.93 ( orthogonal_through_point @ L @ A ) @ A ) ) ) )),
% 0.55/0.93 inference('cnf.neg', [status(esa)], [con])).
% 0.55/0.93 thf(zip_derived_cl26, plain,
% 0.55/0.93 ( (distinct_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.55/0.93 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/0.93 thf(ouo1, axiom,
% 0.55/0.93 (![A:$i,L:$i,M:$i,N:$i]:
% 0.55/0.93 ( ( distinct_lines @ L @ M ) =>
% 0.55/0.93 ( ( apart_point_and_line @ A @ L ) | ( apart_point_and_line @ A @ M ) |
% 0.55/0.93 ( unorthogonal_lines @ L @ N ) | ( unorthogonal_lines @ M @ N ) ) ))).
% 0.55/0.93 thf(zip_derived_cl25, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @ X1)
% 0.55/0.93 | (apart_point_and_line @ X0 @ X2)
% 0.55/0.93 | ~ (distinct_lines @ X2 @ X1)
% 0.55/0.93 | (unorthogonal_lines @ X2 @ X3)
% 0.55/0.93 | (unorthogonal_lines @ X1 @ X3))),
% 0.55/0.93 inference('cnf', [status(esa)], [ouo1])).
% 0.55/0.93 thf(zip_derived_cl69, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 0.55/0.93 | (apart_point_and_line @ X0 @
% 0.55/0.93 (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (unorthogonal_lines @ (parallel_through_point @ sk__1 @ sk_) @ X1)
% 0.55/0.93 | (unorthogonal_lines @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.55/0.93 X1))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl25])).
% 0.55/0.93 thf(zip_derived_cl487, plain,
% 0.55/0.93 ((![X1 : $i]:
% 0.55/0.93 ( (unorthogonal_lines @ (parallel_through_point @ sk__1 @ sk_) @ X1)
% 0.55/0.93 | (unorthogonal_lines @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.55/0.93 X1)))
% 0.55/0.93 <= ((![X1 : $i]:
% 0.55/0.93 ( (unorthogonal_lines @
% 0.55/0.93 (parallel_through_point @ sk__1 @ sk_) @ X1)
% 0.55/0.93 | (unorthogonal_lines @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.55/0.93 X1))))),
% 0.55/0.93 inference('split', [status(esa)], [zip_derived_cl69])).
% 0.55/0.93 thf(ooc1, axiom,
% 0.55/0.93 (![A:$i,L:$i]:
% 0.55/0.93 ( ~( unorthogonal_lines @ ( orthogonal_through_point @ L @ A ) @ L ) ))).
% 0.55/0.93 thf(zip_derived_cl23, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.55/0.93 inference('cnf', [status(esa)], [ooc1])).
% 0.55/0.93 thf(zip_derived_cl490, plain,
% 0.55/0.93 (( (unorthogonal_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_)))
% 0.55/0.93 <= ((![X1 : $i]:
% 0.55/0.93 ( (unorthogonal_lines @
% 0.55/0.93 (parallel_through_point @ sk__1 @ sk_) @ X1)
% 0.55/0.93 | (unorthogonal_lines @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.55/0.93 X1))))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl487, zip_derived_cl23])).
% 0.55/0.93 thf(zip_derived_cl26, plain,
% 0.55/0.93 ( (distinct_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))),
% 0.55/0.93 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/0.93 thf(cup1, axiom,
% 0.55/0.93 (![X:$i,Y:$i,Z:$i]:
% 0.55/0.93 ( ( distinct_lines @ Y @ Z ) =>
% 0.55/0.93 ( ( apart_point_and_line @ X @ Y ) | ( apart_point_and_line @ X @ Z ) |
% 0.55/0.93 ( convergent_lines @ Y @ Z ) ) ))).
% 0.55/0.93 thf(zip_derived_cl16, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @ X1)
% 0.55/0.93 | ~ (distinct_lines @ X1 @ X2)
% 0.55/0.93 | (apart_point_and_line @ X0 @ X2)
% 0.55/0.93 | (convergent_lines @ X1 @ X2))),
% 0.55/0.93 inference('cnf', [status(esa)], [cup1])).
% 0.55/0.93 thf(zip_derived_cl64, plain,
% 0.55/0.93 (![X0 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (apart_point_and_line @ X0 @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))
% 0.55/0.93 | (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl16])).
% 0.55/0.93 thf(zip_derived_cl295, plain,
% 0.55/0.93 ((![X0 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (apart_point_and_line @ X0 @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))))
% 0.55/0.93 <= ((![X0 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @
% 0.55/0.93 (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (apart_point_and_line @ X0 @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))))),
% 0.55/0.93 inference('split', [status(esa)], [zip_derived_cl64])).
% 0.55/0.93 thf(ooc2, axiom,
% 0.55/0.93 (![A:$i,L:$i]:
% 0.55/0.93 ( ~( apart_point_and_line @ A @ ( orthogonal_through_point @ L @ A ) ) ))).
% 0.55/0.93 thf(zip_derived_cl24, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ~ (apart_point_and_line @ X0 @ (orthogonal_through_point @ X1 @ X0))),
% 0.55/0.93 inference('cnf', [status(esa)], [ooc2])).
% 0.55/0.93 thf(zip_derived_cl301, plain,
% 0.55/0.93 (( (apart_point_and_line @ sk_ @ (parallel_through_point @ sk__1 @ sk_)))
% 0.55/0.93 <= ((![X0 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @
% 0.55/0.93 (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (apart_point_and_line @ X0 @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_)))))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl295, zip_derived_cl24])).
% 0.55/0.93 thf(cp2, axiom,
% 0.55/0.93 (![X:$i,Y:$i]:
% 0.55/0.93 ( ~( apart_point_and_line @ X @ ( parallel_through_point @ Y @ X ) ) ))).
% 0.55/0.93 thf(zip_derived_cl15, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ~ (apart_point_and_line @ X0 @ (parallel_through_point @ X1 @ X0))),
% 0.55/0.93 inference('cnf', [status(esa)], [cp2])).
% 0.55/0.93 thf('0', plain,
% 0.55/0.93 (~
% 0.55/0.93 (![X0 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (apart_point_and_line @ X0 @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl15])).
% 0.55/0.93 thf('1', plain,
% 0.55/0.93 ((![X1 : $i]:
% 0.55/0.93 ( (unorthogonal_lines @ (parallel_through_point @ sk__1 @ sk_) @ X1)
% 0.55/0.93 | (unorthogonal_lines @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.55/0.93 X1))) |
% 0.55/0.93 (![X0 : $i]:
% 0.55/0.93 ( (apart_point_and_line @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (apart_point_and_line @ X0 @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_))))),
% 0.55/0.93 inference('split', [status(esa)], [zip_derived_cl69])).
% 0.55/0.93 thf('2', plain,
% 0.55/0.93 ((![X1 : $i]:
% 0.55/0.93 ( (unorthogonal_lines @ (parallel_through_point @ sk__1 @ sk_) @ X1)
% 0.55/0.93 | (unorthogonal_lines @
% 0.55/0.93 (orthogonal_through_point @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_) @ sk_) @
% 0.55/0.93 X1)))),
% 0.55/0.93 inference('sat_resolution*', [status(thm)], ['0', '1'])).
% 0.55/0.93 thf(zip_derived_cl492, plain,
% 0.55/0.93 ( (unorthogonal_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_))),
% 0.55/0.93 inference('simpl_trail', [status(thm)], [zip_derived_cl490, '2'])).
% 0.55/0.93 thf(oac1, axiom,
% 0.55/0.93 (![L:$i,M:$i,N:$i]:
% 0.55/0.93 ( ( ( unorthogonal_lines @ L @ M ) & ( convergent_lines @ L @ M ) ) =>
% 0.55/0.93 ( ( ( unorthogonal_lines @ M @ N ) & ( convergent_lines @ M @ N ) ) |
% 0.55/0.93 ( ( unorthogonal_lines @ L @ N ) & ( convergent_lines @ L @ N ) ) ) ))).
% 0.55/0.93 thf(zf_stmt_1, type, zip_tseitin_1 : $i > $i > $o).
% 0.55/0.93 thf(zf_stmt_2, axiom,
% 0.55/0.93 (![N:$i,L:$i]:
% 0.55/0.93 ( ( zip_tseitin_1 @ N @ L ) =>
% 0.55/0.93 ( ( convergent_lines @ L @ N ) & ( unorthogonal_lines @ L @ N ) ) ))).
% 0.55/0.93 thf(zf_stmt_3, type, zip_tseitin_0 : $i > $i > $o).
% 0.55/0.93 thf(zf_stmt_4, axiom,
% 0.55/0.93 (![N:$i,M:$i]:
% 0.55/0.93 ( ( zip_tseitin_0 @ N @ M ) =>
% 0.55/0.93 ( ( convergent_lines @ M @ N ) & ( unorthogonal_lines @ M @ N ) ) ))).
% 0.55/0.93 thf(zf_stmt_5, axiom,
% 0.55/0.93 (![L:$i,M:$i,N:$i]:
% 0.55/0.93 ( ( ( convergent_lines @ L @ M ) & ( unorthogonal_lines @ L @ M ) ) =>
% 0.55/0.93 ( ( zip_tseitin_1 @ N @ L ) | ( zip_tseitin_0 @ N @ M ) ) ))).
% 0.55/0.93 thf(zip_derived_cl22, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.93 (~ (unorthogonal_lines @ X0 @ X1)
% 0.55/0.93 | ~ (convergent_lines @ X0 @ X1)
% 0.55/0.93 | (zip_tseitin_1 @ X2 @ X0)
% 0.55/0.93 | (zip_tseitin_0 @ X2 @ X1))),
% 0.55/0.93 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.55/0.93 thf(zip_derived_cl494, plain,
% 0.55/0.93 (![X0 : $i]:
% 0.55/0.93 (~ (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (zip_tseitin_1 @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_)))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl492, zip_derived_cl22])).
% 0.55/0.93 thf(zip_derived_cl520, plain,
% 0.55/0.93 ((![X0 : $i]:
% 0.55/0.93 ( (zip_tseitin_1 @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_))))
% 0.55/0.93 <= ((![X0 : $i]:
% 0.55/0.93 ( (zip_tseitin_1 @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (zip_tseitin_0 @ X0 @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_)))))),
% 0.55/0.93 inference('split', [status(esa)], [zip_derived_cl494])).
% 0.55/0.93 thf(zip_derived_cl20, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ( (convergent_lines @ X0 @ X1) | ~ (zip_tseitin_1 @ X1 @ X0))),
% 0.55/0.93 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.55/0.93 thf(zip_derived_cl522, plain,
% 0.55/0.93 ((![X0 : $i]:
% 0.55/0.93 ( (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0)))
% 0.55/0.93 <= ((![X0 : $i]:
% 0.55/0.93 ( (zip_tseitin_1 @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (zip_tseitin_0 @ X0 @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_)))))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl520, zip_derived_cl20])).
% 0.55/0.93 thf(zip_derived_cl521, plain,
% 0.55/0.93 ((~ (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_)))
% 0.55/0.93 <= (~
% 0.55/0.93 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_))))),
% 0.55/0.93 inference('split', [status(esa)], [zip_derived_cl494])).
% 0.55/0.93 thf(occu1, axiom,
% 0.55/0.93 (![L:$i,M:$i]:
% 0.55/0.93 ( ( unorthogonal_lines @ L @ M ) | ( convergent_lines @ L @ M ) ))).
% 0.55/0.93 thf(zip_derived_cl17, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ( (unorthogonal_lines @ X0 @ X1) | (convergent_lines @ X0 @ X1))),
% 0.55/0.93 inference('cnf', [status(esa)], [occu1])).
% 0.55/0.93 thf(zip_derived_cl23, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.55/0.93 inference('cnf', [status(esa)], [ooc1])).
% 0.55/0.93 thf(zip_derived_cl39, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl23])).
% 0.55/0.93 thf(apart6, axiom,
% 0.55/0.93 (![X:$i,Y:$i,Z:$i]:
% 0.55/0.93 ( ( convergent_lines @ X @ Y ) =>
% 0.55/0.93 ( ( convergent_lines @ X @ Z ) | ( convergent_lines @ Y @ Z ) ) ))).
% 0.55/0.93 thf(zip_derived_cl5, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.93 (~ (convergent_lines @ X0 @ X1)
% 0.55/0.93 | (convergent_lines @ X0 @ X2)
% 0.55/0.93 | (convergent_lines @ X1 @ X2))),
% 0.55/0.93 inference('cnf', [status(esa)], [apart6])).
% 0.55/0.93 thf(zip_derived_cl41, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.93 ( (convergent_lines @ (orthogonal_through_point @ X0 @ X1) @ X2)
% 0.55/0.93 | (convergent_lines @ X0 @ X2))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl5])).
% 0.55/0.93 thf(zip_derived_cl5, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.93 (~ (convergent_lines @ X0 @ X1)
% 0.55/0.93 | (convergent_lines @ X0 @ X2)
% 0.55/0.93 | (convergent_lines @ X1 @ X2))),
% 0.55/0.93 inference('cnf', [status(esa)], [apart6])).
% 0.55/0.93 thf(zip_derived_cl56, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/0.93 ( (convergent_lines @ X2 @ X0)
% 0.55/0.93 | (convergent_lines @ (orthogonal_through_point @ X2 @ X1) @ X3)
% 0.55/0.93 | (convergent_lines @ X0 @ X3))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl5])).
% 0.55/0.93 thf(apart3, axiom, (![X:$i]: ( ~( convergent_lines @ X @ X ) ))).
% 0.55/0.93 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 0.55/0.93 inference('cnf', [status(esa)], [apart3])).
% 0.55/0.93 thf(zip_derived_cl134, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.93 ( (convergent_lines @ X2 @ (orthogonal_through_point @ X1 @ X0))
% 0.55/0.93 | (convergent_lines @ X1 @ X2))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl2])).
% 0.55/0.93 thf(zip_derived_cl525, plain,
% 0.55/0.93 (( (convergent_lines @ sk__1 @ (parallel_through_point @ sk__1 @ sk_)))
% 0.55/0.93 <= (~
% 0.55/0.93 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_))))),
% 0.55/0.93 inference('s_sup+', [status(thm)], [zip_derived_cl521, zip_derived_cl134])).
% 0.55/0.93 thf(zip_derived_cl5, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/0.93 (~ (convergent_lines @ X0 @ X1)
% 0.55/0.93 | (convergent_lines @ X0 @ X2)
% 0.55/0.93 | (convergent_lines @ X1 @ X2))),
% 0.55/0.93 inference('cnf', [status(esa)], [apart6])).
% 0.55/0.93 thf(zip_derived_cl528, plain,
% 0.55/0.93 ((![X0 : $i]:
% 0.55/0.93 ( (convergent_lines @ sk__1 @ X0)
% 0.55/0.93 | (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0)))
% 0.55/0.93 <= (~
% 0.55/0.93 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_))))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl525, zip_derived_cl5])).
% 0.55/0.93 thf(cp1, axiom,
% 0.55/0.93 (![X:$i,Y:$i]:
% 0.55/0.93 ( ~( convergent_lines @ ( parallel_through_point @ Y @ X ) @ Y ) ))).
% 0.55/0.93 thf(zip_derived_cl14, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ~ (convergent_lines @ (parallel_through_point @ X0 @ X1) @ X0)),
% 0.55/0.93 inference('cnf', [status(esa)], [cp1])).
% 0.55/0.93 thf(zip_derived_cl581, plain,
% 0.55/0.93 (( (convergent_lines @ sk__1 @ sk__1))
% 0.55/0.93 <= (~
% 0.55/0.93 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_))))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl528, zip_derived_cl14])).
% 0.55/0.93 thf(zip_derived_cl2, plain, (![X0 : $i]: ~ (convergent_lines @ X0 @ X0)),
% 0.55/0.93 inference('cnf', [status(esa)], [apart3])).
% 0.55/0.93 thf('3', plain,
% 0.55/0.93 (( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_)))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl581, zip_derived_cl2])).
% 0.55/0.93 thf('4', plain,
% 0.55/0.93 ((![X0 : $i]:
% 0.55/0.93 ( (zip_tseitin_1 @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_)))) |
% 0.55/0.93 ~
% 0.55/0.93 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @
% 0.55/0.93 (orthogonal_through_point @ sk__1 @ sk_)))),
% 0.55/0.93 inference('split', [status(esa)], [zip_derived_cl494])).
% 0.55/0.93 thf('5', plain,
% 0.55/0.93 ((![X0 : $i]:
% 0.55/0.93 ( (zip_tseitin_1 @ X0 @ (parallel_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_))))),
% 0.55/0.93 inference('sat_resolution*', [status(thm)], ['3', '4'])).
% 0.55/0.93 thf(zip_derived_cl591, plain,
% 0.55/0.93 (![X0 : $i]:
% 0.55/0.93 ( (zip_tseitin_0 @ X0 @ (orthogonal_through_point @ sk__1 @ sk_))
% 0.55/0.93 | (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0))),
% 0.55/0.93 inference('simpl_trail', [status(thm)], [zip_derived_cl522, '5'])).
% 0.55/0.93 thf(zip_derived_cl19, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ( (unorthogonal_lines @ X0 @ X1) | ~ (zip_tseitin_0 @ X1 @ X0))),
% 0.55/0.93 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.55/0.93 thf(zip_derived_cl594, plain,
% 0.55/0.93 (![X0 : $i]:
% 0.55/0.93 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ X0)
% 0.55/0.93 | (unorthogonal_lines @ (orthogonal_through_point @ sk__1 @ sk_) @
% 0.55/0.93 X0))),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl591, zip_derived_cl19])).
% 0.55/0.93 thf(zip_derived_cl23, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ~ (unorthogonal_lines @ (orthogonal_through_point @ X0 @ X1) @ X0)),
% 0.55/0.93 inference('cnf', [status(esa)], [ooc1])).
% 0.55/0.93 thf(zip_derived_cl641, plain,
% 0.55/0.93 ( (convergent_lines @ (parallel_through_point @ sk__1 @ sk_) @ sk__1)),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl594, zip_derived_cl23])).
% 0.55/0.93 thf(zip_derived_cl14, plain,
% 0.55/0.93 (![X0 : $i, X1 : $i]:
% 0.55/0.93 ~ (convergent_lines @ (parallel_through_point @ X0 @ X1) @ X0)),
% 0.55/0.93 inference('cnf', [status(esa)], [cp1])).
% 0.55/0.93 thf(zip_derived_cl645, plain, ($false),
% 0.55/0.93 inference('s_sup-', [status(thm)], [zip_derived_cl641, zip_derived_cl14])).
% 0.55/0.93
% 0.55/0.93 % SZS output end Refutation
% 0.55/0.93
% 0.55/0.93
% 0.55/0.93 % Terminating...
% 1.65/1.05 % Runner terminated.
% 1.65/1.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------