TSTP Solution File: SET863-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.wn4pxI3Ulr true
% Computer : n002.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 Aug 31 16:16:31 EDT 2023
% Result : Unsatisfiable 1.17s 0.78s
% Output : Refutation 1.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.wn4pxI3Ulr true
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 16:12:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.64 % Total configuration time : 435
% 0.20/0.64 % Estimated wc time : 1092
% 0.20/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.17/0.78 % Solved by fo/fo6_bce.sh.
% 1.17/0.78 % BCE start: 14
% 1.17/0.78 % BCE eliminated: 0
% 1.17/0.78 % PE start: 14
% 1.17/0.78 logic: neq
% 1.17/0.78 % PE eliminated: 0
% 1.17/0.78 % done 56 iterations in 0.068s
% 1.17/0.78 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.17/0.78 % SZS output start Refutation
% 1.17/0.78 thf(c_Zorn_Ochain__extend__1_type, type, c_Zorn_Ochain__extend__1: $i > $i >
% 1.17/0.78 $i > $i).
% 1.17/0.78 thf(c_in_type, type, c_in: $i > $i > $i > $o).
% 1.17/0.78 thf(v_c_type, type, v_c: $i).
% 1.17/0.78 thf(v_x_type, type, v_x: $i).
% 1.17/0.78 thf(c_Zorn_Omaxchain_type, type, c_Zorn_Omaxchain: $i > $i > $i).
% 1.17/0.78 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 1.17/0.78 thf(v_S_type, type, v_S: $i).
% 1.17/0.78 thf(c_insert_type, type, c_insert: $i > $i > $i > $i).
% 1.17/0.78 thf(c_emptyset_type, type, c_emptyset: $i).
% 1.17/0.78 thf(v_y_type, type, v_y: $i).
% 1.17/0.78 thf(c_Zorn_Ochain_type, type, c_Zorn_Ochain: $i > $i > $i).
% 1.17/0.78 thf(c_union_type, type, c_union: $i > $i > $i > $i).
% 1.17/0.78 thf(v_xa_type, type, v_xa: $i).
% 1.17/0.78 thf(tc_set_type, type, tc_set: $i > $i).
% 1.17/0.78 thf(t_a_type, type, t_a: $i).
% 1.17/0.78 thf(c_Zorn_Omaxchain__super__lemma__1_type, type, c_Zorn_Omaxchain__super__lemma__1:
% 1.17/0.78 $i > $i > $i > $i).
% 1.17/0.78 thf(c_Main_OsubsetI__1_type, type, c_Main_OsubsetI__1: $i > $i > $i > $i).
% 1.17/0.78 thf(cls_conjecture_0, conjecture,
% 1.17/0.78 (~( c_in @
% 1.17/0.78 v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ))).
% 1.17/0.78 thf(zf_stmt_0, negated_conjecture,
% 1.17/0.78 (c_in @
% 1.17/0.78 v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 1.17/0.78 inference('cnf.neg', [status(esa)], [cls_conjecture_0])).
% 1.17/0.78 thf(zip_derived_cl7, plain,
% 1.17/0.78 ( (c_in @ v_c @ (c_Zorn_Omaxchain @ v_S @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.17/0.78 thf(cls_conjecture_1, conjecture,
% 1.17/0.78 (~( c_in @
% 1.17/0.78 v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ))).
% 1.17/0.78 thf(zf_stmt_1, negated_conjecture,
% 1.17/0.78 (c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) )),
% 1.17/0.78 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 1.17/0.78 thf(zip_derived_cl8, plain,
% 1.17/0.78 ( (c_in @ v_c @ (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.17/0.78 thf(cls_conjecture_3, conjecture, (~( c_in @ v_x @ v_S @ ( tc_set @ t_a ) ))).
% 1.17/0.78 thf(zf_stmt_2, negated_conjecture, (c_in @ v_x @ v_S @ ( tc_set @ t_a )),
% 1.17/0.78 inference('cnf.neg', [status(esa)], [cls_conjecture_3])).
% 1.17/0.78 thf(zip_derived_cl9, plain, ( (c_in @ v_x @ v_S @ (tc_set @ t_a))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.17/0.78 thf(cls_Zorn_Ochain__extend_0, axiom,
% 1.17/0.78 (( ~( c_in @ V_z @ V_S @ ( tc_set @ T_a ) ) ) |
% 1.17/0.78 ( ~( c_in @
% 1.17/0.78 V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 1.17/0.78 ( c_in @
% 1.17/0.78 ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_c @ ( tc_set @ T_a ) ) |
% 1.17/0.78 ( c_in @
% 1.17/0.78 ( c_union @
% 1.17/0.78 ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @
% 1.17/0.78 ( tc_set @ T_a ) ) @
% 1.17/0.78 ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 1.17/0.78 thf(zip_derived_cl3, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ X1 @ (tc_set @ X2))
% 1.17/0.78 | ~ (c_in @ X3 @ (c_Zorn_Ochain @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 1.17/0.78 | (c_in @ (c_Zorn_Ochain__extend__1 @ X3 @ X0 @ X2) @ X3 @
% 1.17/0.78 (tc_set @ X2))
% 1.17/0.78 | (c_in @
% 1.17/0.78 (c_union @ (c_insert @ X0 @ c_emptyset @ (tc_set @ X2)) @ X3 @
% 1.17/0.78 (tc_set @ X2)) @
% 1.17/0.78 (c_Zorn_Ochain @ X1 @ X2) @ (tc_set @ (tc_set @ X2))))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Zorn_Ochain__extend_0])).
% 1.17/0.78 thf(zip_derived_cl34, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ (c_Zorn_Ochain @ v_S @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | (c_in @ (c_Zorn_Ochain__extend__1 @ X0 @ v_x @ t_a) @ X0 @
% 1.17/0.78 (tc_set @ t_a))
% 1.17/0.78 | (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ X0 @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 1.17/0.78 thf(zip_derived_cl82, plain,
% 1.17/0.78 (( (c_in @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @ v_c @
% 1.17/0.78 (tc_set @ t_a))
% 1.17/0.78 | (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ v_c @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 1.17/0.78 thf(cls_conjecture_5, conjecture, (~( c_in @ v_xa @ v_x @ t_a ))).
% 1.17/0.78 thf(zf_stmt_3, negated_conjecture, (c_in @ v_xa @ v_x @ t_a),
% 1.17/0.78 inference('cnf.neg', [status(esa)], [cls_conjecture_5])).
% 1.17/0.78 thf(zip_derived_cl11, plain, ( (c_in @ v_xa @ v_x @ t_a)),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.17/0.78 thf(zip_derived_cl7, plain,
% 1.17/0.78 ( (c_in @ v_c @ (c_Zorn_Omaxchain @ v_S @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.17/0.78 thf(cls_Zorn_Omaxchain__super__lemma_0, axiom,
% 1.17/0.78 (( ~( c_in @ V_z @ V_x @ T_a ) ) |
% 1.17/0.78 ( ~( c_in @
% 1.17/0.78 V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @
% 1.17/0.78 ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 1.17/0.78 ( ~( c_in @
% 1.17/0.78 ( c_union @
% 1.17/0.78 ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @
% 1.17/0.78 ( tc_set @ T_a ) ) @
% 1.17/0.78 ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 1.17/0.78 ( c_in @ V_z @ V_y @ T_a ) |
% 1.17/0.78 ( c_in @
% 1.17/0.78 ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_c @
% 1.17/0.78 ( tc_set @ T_a ) ))).
% 1.17/0.78 thf(zip_derived_cl5, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ X1 @ X2)
% 1.17/0.78 | ~ (c_in @ X3 @ (c_Zorn_Omaxchain @ X4 @ X2) @
% 1.17/0.78 (tc_set @ (tc_set @ X2)))
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ X1 @ c_emptyset @ (tc_set @ X2)) @ X3 @
% 1.17/0.78 (tc_set @ X2)) @
% 1.17/0.78 (c_Zorn_Ochain @ X4 @ X2) @ (tc_set @ (tc_set @ X2)))
% 1.17/0.78 | (c_in @ X0 @ X5 @ X2)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ X3 @ X5 @ X2) @ X3 @
% 1.17/0.78 (tc_set @ X2)))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Zorn_Omaxchain__super__lemma_0])).
% 1.17/0.78 thf(zip_derived_cl53, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.17/0.78 (~ (c_in @ X1 @ X0 @ t_a)
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ X0 @ c_emptyset @ (tc_set @ t_a)) @
% 1.17/0.78 v_c @ (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | (c_in @ X1 @ X2 @ t_a)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X2 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl5])).
% 1.17/0.78 thf(zip_derived_cl92, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ v_c @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | (c_in @ v_xa @ X0 @ t_a)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X0 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl53])).
% 1.17/0.78 thf(zip_derived_cl109, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 ( (c_in @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @ v_c @
% 1.17/0.78 (tc_set @ t_a))
% 1.17/0.78 | (c_in @ v_xa @ X0 @ t_a)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X0 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl92])).
% 1.17/0.78 thf(cls_Set_OsubsetI_0, axiom,
% 1.17/0.78 (( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a ) |
% 1.17/0.78 ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ))).
% 1.17/0.78 thf(zip_derived_cl1, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.17/0.78 ( (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X0 @ X2)
% 1.17/0.78 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Set_OsubsetI_0])).
% 1.17/0.78 thf(cls_conjecture_7, conjecture,
% 1.17/0.78 (~( ( ~( c_in @ V_U @ v_c @ ( tc_set @ t_a ) ) ) |
% 1.17/0.78 ( c_lessequals @ V_U @ v_y @ ( tc_set @ t_a ) ) ))).
% 1.17/0.78 thf(zf_stmt_4, negated_conjecture,
% 1.17/0.78 (( ~( c_in @ V_U @ v_c @ ( tc_set @ t_a ) ) ) |
% 1.17/0.78 ( c_lessequals @ V_U @ v_y @ ( tc_set @ t_a ) )),
% 1.17/0.78 inference('cnf.neg', [status(esa)], [cls_conjecture_7])).
% 1.17/0.78 thf(zip_derived_cl13, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_lessequals @ X0 @ v_y @ (tc_set @ t_a)))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.17/0.78 thf(cls_Set_OsubsetD_0, axiom,
% 1.17/0.78 (( ~( c_in @ V_c @ V_A @ T_a ) ) |
% 1.17/0.78 ( ~( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) |
% 1.17/0.78 ( c_in @ V_c @ V_B @ T_a ))).
% 1.17/0.78 thf(zip_derived_cl0, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ X1 @ X2)
% 1.17/0.78 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 1.17/0.78 | (c_in @ X0 @ X3 @ X2))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 1.17/0.78 thf(zip_derived_cl35, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ X1 @ X0 @ t_a)
% 1.17/0.78 | (c_in @ X1 @ v_y @ t_a))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl0])).
% 1.17/0.78 thf(zip_derived_cl36, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i]:
% 1.17/0.78 ( (c_lessequals @ X0 @ X1 @ (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ X0 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ t_a) @ v_y @ t_a))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl35])).
% 1.17/0.78 thf(cls_conjecture_4, conjecture,
% 1.17/0.78 (~( c_lessequals @ v_y @ v_x @ ( tc_set @ t_a ) ))).
% 1.17/0.78 thf(zf_stmt_5, negated_conjecture,
% 1.17/0.78 (c_lessequals @ v_y @ v_x @ ( tc_set @ t_a )),
% 1.17/0.78 inference('cnf.neg', [status(esa)], [cls_conjecture_4])).
% 1.17/0.78 thf(zip_derived_cl10, plain, ( (c_lessequals @ v_y @ v_x @ (tc_set @ t_a))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.17/0.78 thf(zip_derived_cl0, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ X1 @ X2)
% 1.17/0.78 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 1.17/0.78 | (c_in @ X0 @ X3 @ X2))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 1.17/0.78 thf(zip_derived_cl24, plain,
% 1.17/0.78 (![X0 : $i]: (~ (c_in @ X0 @ v_y @ t_a) | (c_in @ X0 @ v_x @ t_a))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl0])).
% 1.17/0.78 thf(zip_derived_cl55, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i]:
% 1.17/0.78 (~ (c_in @ X1 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_lessequals @ X1 @ X0 @ (tc_set @ t_a))
% 1.17/0.78 | (c_in @ (c_Main_OsubsetI__1 @ X1 @ X0 @ t_a) @ v_x @ t_a))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl24])).
% 1.17/0.78 thf(cls_Set_OsubsetI_1, axiom,
% 1.17/0.78 (( ~( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a ) ) |
% 1.17/0.78 ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ))).
% 1.17/0.78 thf(zip_derived_cl2, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.17/0.78 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 1.17/0.78 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 1.17/0.78 thf(zip_derived_cl59, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 ( (c_lessequals @ X0 @ v_x @ (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ X0 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_lessequals @ X0 @ v_x @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl2])).
% 1.17/0.78 thf(zip_derived_cl61, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_lessequals @ X0 @ v_x @ (tc_set @ t_a)))),
% 1.17/0.78 inference('simplify', [status(thm)], [zip_derived_cl59])).
% 1.17/0.78 thf(zip_derived_cl9, plain, ( (c_in @ v_x @ v_S @ (tc_set @ t_a))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.17/0.78 thf(cls_Zorn_Ochain__extend_1, axiom,
% 1.17/0.78 (( ~( c_in @ V_z @ V_S @ ( tc_set @ T_a ) ) ) |
% 1.17/0.78 ( ~( c_in @
% 1.17/0.78 V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 1.17/0.78 ( ~( c_lessequals @
% 1.17/0.78 ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_z @
% 1.17/0.78 ( tc_set @ T_a ) ) ) |
% 1.17/0.78 ( c_in @
% 1.17/0.78 ( c_union @
% 1.17/0.78 ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @
% 1.17/0.78 ( tc_set @ T_a ) ) @
% 1.17/0.78 ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ))).
% 1.17/0.78 thf(zip_derived_cl4, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ X1 @ (tc_set @ X2))
% 1.17/0.78 | ~ (c_in @ X3 @ (c_Zorn_Ochain @ X1 @ X2) @ (tc_set @ (tc_set @ X2)))
% 1.17/0.78 | ~ (c_lessequals @ (c_Zorn_Ochain__extend__1 @ X3 @ X0 @ X2) @ X0 @
% 1.17/0.78 (tc_set @ X2))
% 1.17/0.78 | (c_in @
% 1.17/0.78 (c_union @ (c_insert @ X0 @ c_emptyset @ (tc_set @ X2)) @ X3 @
% 1.17/0.78 (tc_set @ X2)) @
% 1.17/0.78 (c_Zorn_Ochain @ X1 @ X2) @ (tc_set @ (tc_set @ X2))))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Zorn_Ochain__extend_1])).
% 1.17/0.78 thf(zip_derived_cl44, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ (c_Zorn_Ochain @ v_S @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | ~ (c_lessequals @ (c_Zorn_Ochain__extend__1 @ X0 @ v_x @ t_a) @
% 1.17/0.78 v_x @ (tc_set @ t_a))
% 1.17/0.78 | (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ X0 @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl4])).
% 1.17/0.78 thf(zip_derived_cl92, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ v_c @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | (c_in @ v_xa @ X0 @ t_a)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X0 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl53])).
% 1.17/0.78 thf(zip_derived_cl108, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_lessequals @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @
% 1.17/0.78 v_x @ (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ v_c @ (c_Zorn_Ochain @ v_S @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | (c_in @ v_xa @ X0 @ t_a)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X0 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl92])).
% 1.17/0.78 thf(zip_derived_cl8, plain,
% 1.17/0.78 ( (c_in @ v_c @ (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.17/0.78 thf(zip_derived_cl110, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_lessequals @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @
% 1.17/0.78 v_x @ (tc_set @ t_a))
% 1.17/0.78 | (c_in @ v_xa @ X0 @ t_a)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X0 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a)))),
% 1.17/0.78 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl8])).
% 1.17/0.78 thf(zip_derived_cl111, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @ v_c @
% 1.17/0.78 (tc_set @ t_a))
% 1.17/0.78 | (c_in @ v_xa @ X0 @ t_a)
% 1.17/0.78 | (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X0 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl110])).
% 1.17/0.78 thf(zip_derived_cl112, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 ( (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ v_c @ X0 @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_in @ v_xa @ X0 @ t_a))),
% 1.17/0.78 inference('clc', [status(thm)], [zip_derived_cl109, zip_derived_cl111])).
% 1.17/0.78 thf(zip_derived_cl11, plain, ( (c_in @ v_xa @ v_x @ t_a)),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.17/0.78 thf(zip_derived_cl13, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_lessequals @ X0 @ v_y @ (tc_set @ t_a)))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.17/0.78 thf(cls_Zorn_Omaxchain__super__lemma_1, axiom,
% 1.17/0.78 (( ~( c_in @ V_z @ V_x @ T_a ) ) |
% 1.17/0.78 ( ~( c_in @
% 1.17/0.78 V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @
% 1.17/0.78 ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 1.17/0.78 ( ~( c_in @
% 1.17/0.78 ( c_union @
% 1.17/0.78 ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @
% 1.17/0.78 ( tc_set @ T_a ) ) @
% 1.17/0.78 ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) |
% 1.17/0.78 ( ~( c_lessequals @
% 1.17/0.78 ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_y @
% 1.17/0.78 ( tc_set @ T_a ) ) ) |
% 1.17/0.78 ( c_in @ V_z @ V_y @ T_a ))).
% 1.17/0.78 thf(zip_derived_cl6, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ X1 @ X2)
% 1.17/0.78 | ~ (c_in @ X3 @ (c_Zorn_Omaxchain @ X4 @ X2) @
% 1.17/0.78 (tc_set @ (tc_set @ X2)))
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ X1 @ c_emptyset @ (tc_set @ X2)) @ X3 @
% 1.17/0.78 (tc_set @ X2)) @
% 1.17/0.78 (c_Zorn_Ochain @ X4 @ X2) @ (tc_set @ (tc_set @ X2)))
% 1.17/0.78 | ~ (c_lessequals @
% 1.17/0.78 (c_Zorn_Omaxchain__super__lemma__1 @ X3 @ X5 @ X2) @ X5 @
% 1.17/0.78 (tc_set @ X2))
% 1.17/0.78 | (c_in @ X0 @ X5 @ X2))),
% 1.17/0.78 inference('cnf', [status(esa)], [cls_Zorn_Omaxchain__super__lemma_1])).
% 1.17/0.78 thf(zip_derived_cl64, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.17/0.78 (~ (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ X0 @ v_y @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ X2 @ X1 @ t_a)
% 1.17/0.78 | ~ (c_in @ X0 @ (c_Zorn_Omaxchain @ X3 @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ X1 @ c_emptyset @ (tc_set @ t_a)) @ X0 @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ X3 @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | (c_in @ X2 @ v_y @ t_a))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl6])).
% 1.17/0.78 thf(zip_derived_cl124, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i]:
% 1.17/0.78 (~ (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ X0 @ v_y @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ X0 @ (c_Zorn_Omaxchain @ X1 @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @
% 1.17/0.78 X0 @ (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ X1 @ t_a) @ (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | (c_in @ v_xa @ v_y @ t_a))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl64])).
% 1.17/0.78 thf(cls_conjecture_6, conjecture, (c_in @ v_xa @ v_y @ t_a)).
% 1.17/0.78 thf(zf_stmt_6, negated_conjecture, (~( c_in @ v_xa @ v_y @ t_a )),
% 1.17/0.78 inference('cnf.neg', [status(esa)], [cls_conjecture_6])).
% 1.17/0.78 thf(zip_derived_cl12, plain, (~ (c_in @ v_xa @ v_y @ t_a)),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.17/0.78 thf(zip_derived_cl126, plain,
% 1.17/0.78 (![X0 : $i, X1 : $i]:
% 1.17/0.78 (~ (c_in @ (c_Zorn_Omaxchain__super__lemma__1 @ X0 @ v_y @ t_a) @
% 1.17/0.78 v_c @ (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ X0 @ (c_Zorn_Omaxchain @ X1 @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @
% 1.17/0.78 X0 @ (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ X1 @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl12])).
% 1.17/0.78 thf(zip_derived_cl133, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 ( (c_in @ v_xa @ v_y @ t_a)
% 1.17/0.78 | ~ (c_in @ v_c @ (c_Zorn_Omaxchain @ X0 @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @
% 1.17/0.78 v_c @ (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ X0 @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl126])).
% 1.17/0.78 thf(zip_derived_cl12, plain, (~ (c_in @ v_xa @ v_y @ t_a)),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.17/0.78 thf(zip_derived_cl134, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ v_c @ (c_Zorn_Omaxchain @ X0 @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | ~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @
% 1.17/0.78 v_c @ (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ X0 @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('demod', [status(thm)], [zip_derived_cl133, zip_derived_cl12])).
% 1.17/0.78 thf(zip_derived_cl135, plain,
% 1.17/0.78 (~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ v_c @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl134])).
% 1.17/0.78 thf(zip_derived_cl82, plain,
% 1.17/0.78 (( (c_in @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @ v_c @
% 1.17/0.78 (tc_set @ t_a))
% 1.17/0.78 | (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ v_c @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl34])).
% 1.17/0.78 thf(zip_derived_cl61, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ v_c @ (tc_set @ t_a))
% 1.17/0.78 | (c_lessequals @ X0 @ v_x @ (tc_set @ t_a)))),
% 1.17/0.78 inference('simplify', [status(thm)], [zip_derived_cl59])).
% 1.17/0.78 thf(zip_derived_cl44, plain,
% 1.17/0.78 (![X0 : $i]:
% 1.17/0.78 (~ (c_in @ X0 @ (c_Zorn_Ochain @ v_S @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a)))
% 1.17/0.78 | ~ (c_lessequals @ (c_Zorn_Ochain__extend__1 @ X0 @ v_x @ t_a) @
% 1.17/0.78 v_x @ (tc_set @ t_a))
% 1.17/0.78 | (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ X0 @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl4])).
% 1.17/0.78 thf(zip_derived_cl135, plain,
% 1.17/0.78 (~ (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ v_c @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl134])).
% 1.17/0.78 thf(zip_derived_cl136, plain,
% 1.17/0.78 ((~ (c_lessequals @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @ v_x @
% 1.17/0.78 (tc_set @ t_a))
% 1.17/0.78 | ~ (c_in @ v_c @ (c_Zorn_Ochain @ v_S @ t_a) @
% 1.17/0.78 (tc_set @ (tc_set @ t_a))))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl135])).
% 1.17/0.78 thf(zip_derived_cl8, plain,
% 1.17/0.78 ( (c_in @ v_c @ (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.17/0.78 thf(zip_derived_cl138, plain,
% 1.17/0.78 (~ (c_lessequals @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @ v_x @
% 1.17/0.78 (tc_set @ t_a))),
% 1.17/0.78 inference('demod', [status(thm)], [zip_derived_cl136, zip_derived_cl8])).
% 1.17/0.78 thf(zip_derived_cl139, plain,
% 1.17/0.78 (~ (c_in @ (c_Zorn_Ochain__extend__1 @ v_c @ v_x @ t_a) @ v_c @
% 1.17/0.78 (tc_set @ t_a))),
% 1.17/0.78 inference('s_sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl138])).
% 1.17/0.78 thf(zip_derived_cl141, plain,
% 1.17/0.78 ( (c_in @
% 1.17/0.78 (c_union @ (c_insert @ v_x @ c_emptyset @ (tc_set @ t_a)) @ v_c @
% 1.17/0.78 (tc_set @ t_a)) @
% 1.17/0.78 (c_Zorn_Ochain @ v_S @ t_a) @ (tc_set @ (tc_set @ t_a)))),
% 1.17/0.78 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl139])).
% 1.17/0.78 thf(zip_derived_cl145, plain, ($false),
% 1.17/0.78 inference('demod', [status(thm)], [zip_derived_cl135, zip_derived_cl141])).
% 1.17/0.78
% 1.17/0.78 % SZS output end Refutation
% 1.17/0.78
% 1.17/0.78
% 1.17/0.78 % Terminating...
% 1.39/0.84 % Runner terminated.
% 1.39/0.85 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------