%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET853-1 : 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.3Ljg3ghLto true
% Computer : n031.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 0.51s 0.94s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET853-1 : TPTP v9.2.0. Released v3.2.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3Ljg3ghLto true
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 1 13:19:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in FO mode
% 0.44/0.60 % Total configuration time : 435
% 0.44/0.60 % Estimated wc time : 1092
% 0.44/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.49/0.70 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.49/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.49/0.71 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.49/0.72 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.49/0.72 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.49/0.72 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.51/0.94 % Solved by fo/fo3_bce.sh.
% 0.51/0.94 % BCE start: 134
% 0.51/0.94 % BCE eliminated: 72
% 0.51/0.94 % PE start: 62
% 0.51/0.94 logic: eq
% 0.51/0.94 % PE eliminated: 0
% 0.51/0.94 % done 166 iterations in 0.216s
% 0.51/0.94 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.51/0.94 % SZS output start Refutation
% 0.51/0.94 thf(c_in_type, type, c_in: $i > $i > $i > $o).
% 0.51/0.94 thf(v_x_type, type, v_x: $i).
% 0.51/0.94 thf(v_xa_type, type, v_xa: $i).
% 0.51/0.94 thf(c_Zorn_Osucc_type, type, c_Zorn_Osucc: $i > $i > $i > $i).
% 0.51/0.94 thf(t_a_type, type, t_a: $i).
% 0.51/0.94 thf(c_Zorn_OTFin__linear__lemma1__1_type, type, c_Zorn_OTFin__linear__lemma1__1:
% 0.51/0.94 $i > $i > $i > $i).
% 0.51/0.94 thf(v_S_type, type, v_S: $i).
% 0.51/0.94 thf(tc_set_type, type, tc_set: $i > $i).
% 0.51/0.94 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 0.51/0.94 thf(c_Zorn_OTFin_type, type, c_Zorn_OTFin: $i > $i > $i).
% 0.51/0.94 thf(cls_conjecture_4, conjecture,
% 0.51/0.94 (c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ v_S @ v_xa @ t_a ) @
% 0.51/0.94 ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ))).
% 0.51/0.94 thf(zf_stmt_0, negated_conjecture,
% 0.51/0.94 (~( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ v_S @ v_xa @ t_a ) @
% 0.51/0.94 ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )),
% 0.51/0.94 inference('cnf.neg', [status(esa)], [cls_conjecture_4])).
% 0.51/0.94 thf(zip_derived_cl129, plain,
% 0.51/0.94 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_xa @ t_a) @
% 0.51/0.94 (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.51/0.94 thf(cls_conjecture_5, conjecture,
% 0.51/0.94 (~( ( ~( c_in @
% 0.51/0.94 V_U @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.51/0.94 ( ~( c_lessequals @ V_U @ v_x @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.51/0.94 ( ( V_U ) = ( v_x ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ v_S @ V_U @ t_a ) @ v_x @
% 0.51/0.94 ( tc_set @ ( tc_set @ t_a ) ) ) ))).
% 0.51/0.94 thf(zf_stmt_1, negated_conjecture,
% 0.51/0.94 (( ~( c_in @
% 0.51/0.94 V_U @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.51/0.94 ( ~( c_lessequals @ V_U @ v_x @ ( tc_set @ ( tc_set @ t_a ) ) ) ) |
% 0.51/0.94 ( ( V_U ) = ( v_x ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ v_S @ V_U @ t_a ) @ v_x @ ( tc_set @ ( tc_set @ t_a ) ) )),
% 0.51/0.94 inference('cnf.neg', [status(esa)], [cls_conjecture_5])).
% 0.51/0.94 thf(zip_derived_cl128, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ((X0) = (v_x))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ X0 @ t_a) @ v_x @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.51/0.94 thf(cls_Zorn_Osucc__trans_0, axiom,
% 0.51/0.94 (( ~( c_lessequals @ V_x @ V_y @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 V_x @ ( c_Zorn_Osucc @ V_S @ V_y @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.51/0.94 thf(zip_derived_cl127, plain,
% 0.51/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.51/0.94 (~ (c_lessequals @ X0 @ X1 @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ X0 @ (c_Zorn_Osucc @ X3 @ X1 @ X2) @
% 0.51/0.94 (tc_set @ (tc_set @ X2))))),
% 0.51/0.94 inference('cnf', [status(esa)], [cls_Zorn_Osucc__trans_0])).
% 0.51/0.94 thf(zip_derived_cl129, plain,
% 0.51/0.94 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_xa @ t_a) @
% 0.51/0.94 (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.51/0.94 thf(zip_derived_cl474, plain,
% 0.51/0.94 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_xa @ t_a) @ v_x @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl127, zip_derived_cl129])).
% 0.51/0.94 thf(zip_derived_cl481, plain,
% 0.51/0.94 ((((v_xa) = (v_x))
% 0.51/0.94 | ~ (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl474])).
% 0.51/0.94 thf(cls_conjecture_1, conjecture,
% 0.51/0.94 (~( c_in @
% 0.51/0.94 v_xa @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ))).
% 0.51/0.94 thf(zf_stmt_2, negated_conjecture,
% 0.51/0.94 (c_in @ v_xa @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 0.51/0.94 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 0.51/0.94 thf(zip_derived_cl132, plain,
% 0.51/0.94 ( (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.51/0.94 thf(zip_derived_cl482, plain,
% 0.51/0.94 ((((v_xa) = (v_x))
% 0.51/0.94 | ~ (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('demod', [status(thm)], [zip_derived_cl481, zip_derived_cl132])).
% 0.51/0.94 thf(zip_derived_cl132, plain,
% 0.51/0.94 ( (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.51/0.94 thf(zip_derived_cl132, plain,
% 0.51/0.94 ( (c_in @ v_xa @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.51/0.94 thf(zip_derived_cl128, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ((X0) = (v_x))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ X0 @ t_a) @ v_x @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.51/0.94 thf(cls_Zorn_OTFin__linear__lemma1_3, axiom,
% 0.51/0.94 (( ~( c_in @
% 0.51/0.94 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( ~( c_in @
% 0.51/0.94 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( ~( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @
% 0.51/0.94 V_S @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ T_a ) @
% 0.51/0.94 V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.51/0.94 thf(zip_derived_cl126, plain,
% 0.51/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | ~ (c_lessequals @
% 0.51/0.94 (c_Zorn_Osucc @ X1 @
% 0.51/0.94 (c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) @ X2) @
% 0.51/0.94 X0 @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.51/0.94 (tc_set @ (tc_set @ X2))))),
% 0.51/0.94 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_3])).
% 0.51/0.94 thf(zip_derived_cl526, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x))
% 0.51/0.94 | ~ (c_lessequals @
% 0.51/0.94 (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @ v_x @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.51/0.94 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl126])).
% 0.51/0.94 thf(cls_conjecture_0, conjecture,
% 0.51/0.94 (~( c_in @
% 0.51/0.94 v_x @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ))).
% 0.51/0.94 thf(zf_stmt_3, negated_conjecture,
% 0.51/0.94 (c_in @ v_x @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 0.51/0.94 inference('cnf.neg', [status(esa)], [cls_conjecture_0])).
% 0.51/0.94 thf(zip_derived_cl133, plain,
% 0.51/0.94 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.51/0.94 thf(zip_derived_cl528, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x))
% 0.51/0.94 | ~ (c_lessequals @
% 0.51/0.94 (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @ v_x @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.51/0.94 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('demod', [status(thm)], [zip_derived_cl526, zip_derived_cl133])).
% 0.51/0.94 thf(zip_derived_cl133, plain,
% 0.51/0.94 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.51/0.94 thf(cls_Zorn_OTFin__linear__lemma1_1, axiom,
% 0.51/0.94 (( ~( c_in @
% 0.51/0.94 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( ~( c_in @
% 0.51/0.94 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ V_m @
% 0.51/0.94 ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.51/0.94 thf(zip_derived_cl124, plain,
% 0.51/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @
% 0.51/0.94 (c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.51/0.94 (tc_set @ (tc_set @ X2))))),
% 0.51/0.94 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_1])).
% 0.51/0.94 thf(zip_derived_cl508, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 ( (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @
% 0.51/0.94 (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @ v_x @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl124])).
% 0.51/0.94 thf(zip_derived_cl621, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.51/0.94 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x)))),
% 0.51/0.94 inference('clc', [status(thm)], [zip_derived_cl528, zip_derived_cl508])).
% 0.51/0.94 thf(zip_derived_cl133, plain,
% 0.51/0.94 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.51/0.94 thf(cls_Zorn_OTFin__linear__lemma1_0, axiom,
% 0.51/0.94 (( ~( c_in @
% 0.51/0.94 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( ~( c_in @
% 0.51/0.94 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( c_in @
% 0.51/0.94 ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @
% 0.51/0.94 ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.51/0.94 thf(zip_derived_cl123, plain,
% 0.51/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) @
% 0.51/0.94 (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.51/0.94 (tc_set @ (tc_set @ X2))))),
% 0.51/0.94 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_0])).
% 0.51/0.94 thf(zip_derived_cl486, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 ( (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_in @ (c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) @
% 0.51/0.94 (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl123])).
% 0.51/0.94 thf(zip_derived_cl622, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('clc', [status(thm)], [zip_derived_cl621, zip_derived_cl486])).
% 0.51/0.94 thf(zip_derived_cl626, plain,
% 0.51/0.94 (( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x)))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl622])).
% 0.51/0.94 thf(cls_conjecture_2, conjecture,
% 0.51/0.94 (~( c_lessequals @
% 0.51/0.94 v_xa @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @
% 0.51/0.94 ( tc_set @ ( tc_set @ t_a ) ) ))).
% 0.51/0.94 thf(zf_stmt_4, negated_conjecture,
% 0.51/0.94 (c_lessequals @
% 0.51/0.94 v_xa @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 0.51/0.94 inference('cnf.neg', [status(esa)], [cls_conjecture_2])).
% 0.51/0.94 thf(zip_derived_cl131, plain,
% 0.51/0.94 ( (c_lessequals @ v_xa @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.51/0.94 thf(cls_Set_Osubset__antisym_0, axiom,
% 0.51/0.94 (( ~( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( ~( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( ( V_A ) = ( V_B ) ))).
% 0.51/0.94 thf(zip_derived_cl46, plain,
% 0.51/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.51/0.94 (~ (c_lessequals @ X0 @ X1 @ (tc_set @ X2))
% 0.51/0.94 | ~ (c_lessequals @ X1 @ X0 @ (tc_set @ X2))
% 0.51/0.94 | ((X1) = (X0)))),
% 0.51/0.94 inference('cnf', [status(esa)], [cls_Set_Osubset__antisym_0])).
% 0.51/0.94 thf(zip_derived_cl405, plain,
% 0.51/0.94 ((((c_Zorn_Osucc @ v_S @ v_x @ t_a) = (v_xa))
% 0.51/0.94 | ~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl46])).
% 0.51/0.94 thf(cls_conjecture_3, conjecture,
% 0.51/0.94 (( v_xa ) = ( c_Zorn_Osucc @ v_S @ v_x @ t_a ))).
% 0.51/0.94 thf(zf_stmt_5, negated_conjecture,
% 0.51/0.94 (( v_xa ) != ( c_Zorn_Osucc @ v_S @ v_x @ t_a )),
% 0.51/0.94 inference('cnf.neg', [status(esa)], [cls_conjecture_3])).
% 0.51/0.94 thf(zip_derived_cl130, plain, (((v_xa) != (c_Zorn_Osucc @ v_S @ v_x @ t_a))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.51/0.94 thf(zip_derived_cl408, plain,
% 0.51/0.94 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('simplify_reflect-', [status(thm)],
% 0.51/0.94 [zip_derived_cl405, zip_derived_cl130])).
% 0.51/0.94 thf(zip_derived_cl628, plain,
% 0.51/0.94 (( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ((c_Zorn_OTFin__linear__lemma1__1 @ v_S @ v_x @ t_a) = (v_x)))),
% 0.51/0.94 inference('demod', [status(thm)], [zip_derived_cl626, zip_derived_cl408])).
% 0.51/0.94 thf(cls_Zorn_OTFin__linear__lemma1_2, axiom,
% 0.51/0.94 (( ~( c_in @
% 0.51/0.94 V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( ~( c_in @
% 0.51/0.94 V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 0.51/0.94 ( ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) != ( V_m ) ) |
% 0.51/0.94 ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) ) |
% 0.51/0.94 ( c_lessequals @
% 0.51/0.94 ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 0.51/0.94 thf(zip_derived_cl125, plain,
% 0.51/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | ~ (c_in @ X3 @ (c_Zorn_OTFin @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | ((c_Zorn_OTFin__linear__lemma1__1 @ X1 @ X0 @ X2) != (X0))
% 0.51/0.94 | (c_lessequals @ X3 @ X0 @ (tc_set @ (tc_set @ X2)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ X1 @ X0 @ X2) @ X3 @
% 0.51/0.94 (tc_set @ (tc_set @ X2))))),
% 0.51/0.94 inference('cnf', [status(esa)], [cls_Zorn_OTFin__linear__lemma1_2])).
% 0.51/0.94 thf(zip_derived_cl629, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (((v_x) != (v_x))
% 0.51/0.94 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl628, zip_derived_cl125])).
% 0.51/0.94 thf(zip_derived_cl133, plain,
% 0.51/0.94 ( (c_in @ v_x @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.51/0.94 thf(zip_derived_cl635, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (((v_x) != (v_x))
% 0.51/0.94 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | ~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @
% 0.51/0.94 (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('demod', [status(thm)], [zip_derived_cl629, zip_derived_cl133])).
% 0.51/0.94 thf(zip_derived_cl636, plain,
% 0.51/0.94 (![X0 : $i]:
% 0.51/0.94 (~ (c_in @ X0 @ (c_Zorn_OTFin @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ X0 @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ X0 @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('simplify', [status(thm)], [zip_derived_cl635])).
% 0.51/0.94 thf(zip_derived_cl648, plain,
% 0.51/0.94 (( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl636])).
% 0.51/0.94 thf(zip_derived_cl651, plain,
% 0.51/0.94 (( (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))
% 0.51/0.94 | (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a))))),
% 0.51/0.94 inference('simplify', [status(thm)], [zip_derived_cl648])).
% 0.51/0.94 thf(zip_derived_cl408, plain,
% 0.51/0.94 (~ (c_lessequals @ (c_Zorn_Osucc @ v_S @ v_x @ t_a) @ v_xa @
% 0.51/0.94 (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('simplify_reflect-', [status(thm)],
% 0.51/0.94 [zip_derived_cl405, zip_derived_cl130])).
% 0.51/0.94 thf(zip_derived_cl652, plain,
% 0.51/0.94 ( (c_lessequals @ v_xa @ v_x @ (tc_set @ (tc_set @ t_a)))),
% 0.51/0.94 inference('clc', [status(thm)], [zip_derived_cl651, zip_derived_cl408])).
% 0.51/0.94 thf(zip_derived_cl653, plain, (((v_xa) = (v_x))),
% 0.51/0.94 inference('demod', [status(thm)], [zip_derived_cl482, zip_derived_cl652])).
% 0.51/0.94 thf(cls_Set_Osubset__refl_0, axiom,
% 0.51/0.94 (c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ))).
% 0.51/0.94 thf(zip_derived_cl47, plain,
% 0.51/0.94 (![X0 : $i, X1 : $i]: (c_lessequals @ X0 @ X0 @ (tc_set @ X1))),
% 0.51/0.94 inference('cnf', [status(esa)], [cls_Set_Osubset__refl_0])).
% 0.51/0.94 thf(zip_derived_cl660, plain, ($false),
% 0.51/0.94 inference('demod', [status(thm)],
% 0.51/0.94 [zip_derived_cl129, zip_derived_cl653, zip_derived_cl47])).
% 0.51/0.94
% 0.51/0.94 % SZS output end Refutation
% 0.51/0.94
% 0.51/0.94
% 0.51/0.94 % Terminating...
% 0.53/1.03 % Runner terminated.
% 1.64/1.05 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------