%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET853-2 : TPTP v9.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.aTPe9ssKGZ true
% Computer : n009.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 04:53:01 PM UTC 2025
% Result : Unsatisfiable 0.58s 0.81s
% Output : Refutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET853-2 : TPTP v9.2.0. Released v3.2.0.
% 0.08/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.aTPe9ssKGZ true
% 0.13/0.35 % Computer : n009.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 13:08:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.56/0.64 % Total configuration time : 435
% 0.56/0.64 % Estimated wc time : 1092
% 0.56/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.71 % /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
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.58/0.81 % Solved by fo/fo3_bce.sh.
% 0.58/0.81 % BCE start: 13
% 0.58/0.81 % BCE eliminated: 0
% 0.58/0.81 % PE start: 13
% 0.58/0.81 logic: eq
% 0.58/0.81 % PE eliminated: 0
% 0.58/0.81 % done 53 iterations in 0.053s
% 0.58/0.81 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/0.81 % SZS output start Refutation
% 0.58/0.81 thf(c_Zorn_Osucc_type, type, c_Zorn_Osucc: $i > $i > $i > $i).
% 0.58/0.81 thf(c_Zorn_OTFin__linear__lemma1__1_type, type, c_Zorn_OTFin__linear__lemma1__1:
% 0.58/0.81 $i > $i > $i > $i).
% 0.58/0.81 thf(c_in_type, type, c_in: $i > $i > $i > $o).
% 0.58/0.81 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 0.58/0.81 thf(v_x_type, type, v_x: $i).
% 0.58/0.81 thf(v_xa_type, type, v_xa: $i).
% 0.58/0.81 thf(c_Zorn_OTFin_type, type, c_Zorn_OTFin: $i > $i > $i).
% 0.58/0.81 thf(tc_set_type, type, tc_set: $i > $i).
% 0.58/0.81 thf(v_S_type, type, v_S: $i).
% 0.58/0.81 thf(t_a_type, type, t_a: $i).
% 0.58/0.81 thf(cls_conjecture_4, conjecture,
% 0.58/0.81 (c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ v_S @ v_xa @ t_a ) @
% 0.58/0.81 ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ))).
% 0.58/0.81 thf(zf_stmt_0, negated_conjecture,
% 0.58/0.81 (~( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ v_S @ v_xa @ t_a ) @
% 0.58/0.81 ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )),
% 0.58/0.81 inference('cnf.neg', [status(esa)], [cls_conjecture_4])).
% 0.58/0.81 thf(zip_derived_cl4, plain,
% 0.58/0.81 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_xa @ t_a) @
% 0.58/0.81 (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.58/0.81 thf(cls_conjecture_5, conjecture,
% 0.58/0.81 (~( ( ~( c_in @
% 0.58/0.81 V_U @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.58/0.81 ( ~( c_lessequals @ V_U @ v_x @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.58/0.81 ( ( V_U ) = ( v_x ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ v_S @ V_U @ t_a ) @ v_x @
% 0.58/0.81 ( tc_set @ ( tc_set @ t_a ) ) ) ))).
% 0.58/0.81 thf(zf_stmt_1, negated_conjecture,
% 0.58/0.81 (( ~( c_in @
% 0.58/0.81 V_U @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.58/0.81 ( ~( c_lessequals @ V_U @ v_x @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.58/0.81 ( ( V_U ) = ( v_x ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ v_S @ V_U @ t_a ) @ v_x @ ( tc_set @ ( tc_set @ t_a ) ) )),
% 0.58/0.81 inference('cnf.neg', [status(esa)], [cls_conjecture_5])).
% 0.58/0.81 thf(zip_derived_cl5, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ((X0) = (v_x))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ X0 @ t_a) @ v_x @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.58/0.81 thf(cls_Zorn_Osucc__trans_0, axiom,
% 0.58/0.81 (( ~( c_lessequals @ V_x @ V_y @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 V_x @ ( c_Zorn_Osucc @ V_S @ V_y @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.58/0.81 thf(zip_derived_cl12, plain,
% 0.58/0.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.81 (~ (c_lessequals @ X0 @ X1 @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ X0 @ (c_Zorn_Osucc @ X3 @ X1 @ X2) @
% 0.58/0.81 (tc_set @ (tc_set @ X2))))),
% 0.58/0.81 inference('cnf', [status(esa)], [cls_Zorn_Osucc__trans_0])).
% 0.58/0.81 thf(zip_derived_cl4, plain,
% 0.58/0.81 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_xa @ t_a) @
% 0.58/0.81 (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.58/0.81 thf(zip_derived_cl86, plain,
% 0.58/0.81 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_xa @ t_a) @ v_x @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 0.58/0.81 thf(zip_derived_cl89, plain,
% 0.58/0.81 ((((v_xa) = (v_x))
% 0.58/0.81 | ~ (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl86])).
% 0.58/0.81 thf(cls_conjecture_1, conjecture,
% 0.58/0.81 (~( c_in @
% 0.58/0.81 v_xa @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ))).
% 0.58/0.81 thf(zf_stmt_2, negated_conjecture,
% 0.58/0.81 (c_in @ v_xa @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 0.58/0.81 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 0.58/0.81 thf(zip_derived_cl1, plain,
% 0.58/0.81 ( (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.58/0.81 thf(zip_derived_cl90, plain,
% 0.58/0.81 ((((v_xa) = (v_x))
% 0.58/0.81 | ~ (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl1])).
% 0.58/0.81 thf(zip_derived_cl1, plain,
% 0.58/0.81 ( (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.58/0.81 thf(zip_derived_cl1, plain,
% 0.58/0.81 ( (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.58/0.81 thf(zip_derived_cl5, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ((X0) = (v_x))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ X0 @ t_a) @ v_x @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.58/0.81 thf(cls_Zorn_OTFin__linear__lemma1_3, axiom,
% 0.58/0.81 (( ~( c_in @
% 0.58/0.81 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( ~( c_in @
% 0.58/0.81 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( ~( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @
% 0.58/0.81 V_S @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ T_a ) @
% 0.58/0.81 V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.58/0.81 thf(zip_derived_cl11, plain,
% 0.58/0.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | ~ (c_lessequals @
% 0.58/0.81 (c_Zorn_Osucc @ X1 @
% 0.58/0.81 (c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) @ X2) @
% 0.58/0.81 X0 @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.58/0.81 (tc_set @ (tc_set @ X2))))),
% 0.58/0.81 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_3])).
% 0.58/0.81 thf(zip_derived_cl101, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x))
% 0.58/0.81 | ~ (c_lessequals @
% 0.58/0.81 (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @ v_x @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.58/0.81 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl11])).
% 0.58/0.81 thf(cls_conjecture_0, conjecture,
% 0.58/0.81 (~( c_in @
% 0.58/0.81 v_x @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ))).
% 0.58/0.81 thf(zf_stmt_3, negated_conjecture,
% 0.58/0.81 (c_in @ v_x @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 0.58/0.81 inference('cnf.neg', [status(esa)], [cls_conjecture_0])).
% 0.58/0.81 thf(zip_derived_cl0, plain,
% 0.58/0.81 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.58/0.81 thf(zip_derived_cl103, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x))
% 0.58/0.81 | ~ (c_lessequals @
% 0.58/0.81 (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @ v_x @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.58/0.81 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 0.58/0.81 thf(zip_derived_cl0, plain,
% 0.58/0.81 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.58/0.81 thf(cls_Zorn_OTFin__linear__lemma1_1, axiom,
% 0.58/0.81 (( ~( c_in @
% 0.58/0.81 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( ~( c_in @
% 0.58/0.81 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ V_m @
% 0.58/0.81 ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.58/0.81 thf(zip_derived_cl9, plain,
% 0.58/0.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @
% 0.58/0.81 (c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.58/0.81 (tc_set @ (tc_set @ X2))))),
% 0.58/0.81 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_1])).
% 0.58/0.81 thf(zip_derived_cl104, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 ( (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @
% 0.58/0.81 (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @ v_x @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.58/0.81 thf(zip_derived_cl190, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.58/0.81 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x)))),
% 0.58/0.81 inference('clc', [status(thm)], [zip_derived_cl103, zip_derived_cl104])).
% 0.58/0.81 thf(zip_derived_cl0, plain,
% 0.58/0.81 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.58/0.81 thf(cls_Zorn_OTFin__linear__lemma1_0, axiom,
% 0.58/0.81 (( ~( c_in @
% 0.58/0.81 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( ~( c_in @
% 0.58/0.81 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( c_in @
% 0.58/0.81 ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @
% 0.58/0.81 ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.58/0.81 thf(zip_derived_cl8, plain,
% 0.58/0.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) @
% 0.58/0.81 (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.58/0.81 (tc_set @ (tc_set @ X2))))),
% 0.58/0.81 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_0])).
% 0.58/0.81 thf(zip_derived_cl96, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 ( (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.58/0.81 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl8])).
% 0.58/0.81 thf(zip_derived_cl191, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('clc', [status(thm)], [zip_derived_cl190, zip_derived_cl96])).
% 0.58/0.81 thf(zip_derived_cl193, plain,
% 0.58/0.81 (( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x)))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl191])).
% 0.58/0.81 thf(cls_conjecture_2, conjecture,
% 0.58/0.81 (~( c_lessequals @
% 0.58/0.81 v_xa @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @
% 0.58/0.81 ( tc_set @ ( tc_set @ t_a ) ) ))).
% 0.58/0.81 thf(zf_stmt_4, negated_conjecture,
% 0.58/0.81 (c_lessequals @
% 0.58/0.81 v_xa @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 0.58/0.81 inference('cnf.neg', [status(esa)], [cls_conjecture_2])).
% 0.58/0.81 thf(zip_derived_cl2, plain,
% 0.58/0.81 ( (c_lessequals @ v_xa @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.58/0.81 thf(cls_Set_Osubset__antisym_0, axiom,
% 0.58/0.81 (( ~( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( ~( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( ( V_A ) = ( V_B ) ))).
% 0.58/0.81 thf(zip_derived_cl6, plain,
% 0.58/0.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.81 (~ (c_lessequals @ X0 @ X1 @ (tc_set @ X2))
% 0.58/0.81 | ~ (c_lessequals @ X1 @ X0 @ (tc_set @ X2))
% 0.58/0.81 | ((X1) = (X0)))),
% 0.58/0.81 inference('cnf', [status(esa)], [cls_Set_Osubset__antisym_0])).
% 0.58/0.81 thf(zip_derived_cl80, plain,
% 0.58/0.81 ((((c_Zorn_Osucc @ v_S @ v_x @ t_a) = (v_xa))
% 0.58/0.81 | ~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl6])).
% 0.58/0.81 thf(cls_conjecture_3, conjecture,
% 0.58/0.81 (( v_xa ) = ( c_Zorn_Osucc @ v_S @ v_x @ t_a ))).
% 0.58/0.81 thf(zf_stmt_5, negated_conjecture,
% 0.58/0.81 (( v_xa ) != ( c_Zorn_Osucc @ v_S @ v_x @ t_a )),
% 0.58/0.81 inference('cnf.neg', [status(esa)], [cls_conjecture_3])).
% 0.58/0.81 thf(zip_derived_cl3, plain, (((v_xa) != (c_Zorn_Osucc @ v_S @ v_x @ t_a))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.58/0.81 thf(zip_derived_cl84, plain,
% 0.58/0.81 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('simplify_reflect-', [status(thm)],
% 0.58/0.81 [zip_derived_cl80, zip_derived_cl3])).
% 0.58/0.81 thf(zip_derived_cl198, plain,
% 0.58/0.81 (( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x)))),
% 0.58/0.81 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl84])).
% 0.58/0.81 thf(cls_Zorn_OTFin__linear__lemma1_2, axiom,
% 0.58/0.81 (( ~( c_in @
% 0.58/0.81 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( ~( c_in @
% 0.58/0.81 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.58/0.81 ( ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) != ( V_m ) ) |
% 0.58/0.81 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.58/0.81 ( c_lessequals @
% 0.58/0.81 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.58/0.81 thf(zip_derived_cl10, plain,
% 0.58/0.81 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | ((c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) != (X0))
% 0.58/0.81 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.58/0.81 (tc_set @ (tc_set @ X2))))),
% 0.58/0.81 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_2])).
% 0.58/0.81 thf(zip_derived_cl199, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (((v_x) != (v_x))
% 0.58/0.81 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl10])).
% 0.58/0.81 thf(zip_derived_cl0, plain,
% 0.58/0.81 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.58/0.81 thf(zip_derived_cl203, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (((v_x) != (v_x))
% 0.58/0.81 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.58/0.81 (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('demod', [status(thm)], [zip_derived_cl199, zip_derived_cl0])).
% 0.58/0.81 thf(zip_derived_cl204, plain,
% 0.58/0.81 (![X0 : $i]:
% 0.58/0.81 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('simplify', [status(thm)], [zip_derived_cl203])).
% 0.58/0.81 thf(zip_derived_cl211, plain,
% 0.58/0.81 (( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl204])).
% 0.58/0.81 thf(zip_derived_cl216, plain,
% 0.58/0.81 (( (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))
% 0.58/0.81 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.58/0.81 inference('simplify', [status(thm)], [zip_derived_cl211])).
% 0.58/0.81 thf(zip_derived_cl84, plain,
% 0.58/0.81 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.58/0.81 (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('simplify_reflect-', [status(thm)],
% 0.58/0.81 [zip_derived_cl80, zip_derived_cl3])).
% 0.58/0.81 thf(zip_derived_cl219, plain,
% 0.58/0.81 ( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))),
% 0.58/0.81 inference('clc', [status(thm)], [zip_derived_cl216, zip_derived_cl84])).
% 0.58/0.81 thf(zip_derived_cl220, plain, (((v_xa) = (v_x))),
% 0.58/0.81 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl219])).
% 0.58/0.81 thf(cls_Set_Osubset__refl_0, axiom,
% 0.58/0.81 (c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ))).
% 0.58/0.81 thf(zip_derived_cl7, plain,
% 0.58/0.81 (![X0 : $i, X1 : $i]: (c_lessequals @ X0 @ X0 @ (tc_set @ X1))),
% 0.58/0.81 inference('cnf', [status(esa)], [cls_Set_Osubset__refl_0])).
% 0.58/0.81 thf(zip_derived_cl225, plain, ($false),
% 0.58/0.81 inference('demod', [status(thm)],
% 0.58/0.81 [zip_derived_cl4, zip_derived_cl220, zip_derived_cl7])).
% 0.58/0.81
% 0.58/0.81 % SZS output end Refutation
% 0.58/0.81
% 0.58/0.81
% 0.58/0.81 % Terminating...
% 1.51/0.86 % Runner terminated.
% 1.51/0.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------