%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET837-2 : 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.7NClI4XwFW true
% Computer : n004.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 04:52:57 PM UTC 2025
% Result : Unsatisfiable 24.40s 4.12s
% Output : Refutation 24.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET837-2 : TPTP v9.2.0. Released v3.2.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7NClI4XwFW true
% 0.13/0.34 % Computer : n004.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 : Wed Oct 1 12:55:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % 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
% 0.13/0.35 % Running in FO mode
% 0.60/0.69 % Total configuration time : 435
% 0.60/0.69 % Estimated wc time : 1092
% 0.60/0.69 % Estimated cpu time (7 cpus) : 156.0
% 0.66/0.78 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.66/0.78 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.66/0.78 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.66/0.79 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.66/0.79 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.66/0.80 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.66/0.83 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 24.40/4.12 % Solved by fo/fo3_bce.sh.
% 24.40/4.12 % BCE start: 13
% 24.40/4.12 % BCE eliminated: 0
% 24.40/4.12 % PE start: 13
% 24.40/4.12 logic: eq
% 24.40/4.12 % PE eliminated: 0
% 24.40/4.12 % done 2002 iterations in 3.309s
% 24.40/4.12 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 24.40/4.12 % SZS output start Refutation
% 24.40/4.12 thf(c_in_type, type, c_in: $i > $i > $i > $o).
% 24.40/4.12 thf(v_Y_type, type, v_Y: $i).
% 24.40/4.12 thf(c_union_type, type, c_union: $i > $i > $i > $i).
% 24.40/4.12 thf(c_Main_OsubsetI__1_type, type, c_Main_OsubsetI__1: $i > $i > $i > $i).
% 24.40/4.12 thf(v_x_type, type, v_x: $i).
% 24.40/4.12 thf(v_Z_type, type, v_Z: $i).
% 24.40/4.12 thf(v_X_type, type, v_X: $i).
% 24.40/4.12 thf(tc_set_type, type, tc_set: $i > $i).
% 24.40/4.12 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 24.40/4.12 thf(t_a_type, type, t_a: $i).
% 24.40/4.12 thf(cls_Set_OsubsetI_1, axiom,
% 24.40/4.12 (( ~( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a ) ) |
% 24.40/4.12 ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ))).
% 24.40/4.12 thf(zip_derived_cl11, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 24.40/4.12 thf(cls_Set_OsubsetI_0, axiom,
% 24.40/4.12 (( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a ) |
% 24.40/4.12 ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ))).
% 24.40/4.12 thf(zip_derived_cl10, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X0 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_0])).
% 24.40/4.12 thf(cls_Set_OUnE_0, axiom,
% 24.40/4.12 (( ~( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) |
% 24.40/4.12 ( c_in @ V_c @ V_B @ T_a ) | ( c_in @ V_c @ V_A @ T_a ))).
% 24.40/4.12 thf(zip_derived_cl8, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ (c_union @ X1 @ X2 @ X3) @ X3)
% 24.40/4.12 | (c_in @ X0 @ X2 @ X3)
% 24.40/4.12 | (c_in @ X0 @ X1 @ X3))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OUnE_0])).
% 24.40/4.12 thf(zip_derived_cl154, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X3 @ (tc_set @ X0))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X1 @
% 24.40/4.12 X0))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl8])).
% 24.40/4.12 thf(zip_derived_cl305, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X1 @ (tc_set @ X0))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X1 @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X1 @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl154])).
% 24.40/4.12 thf(zip_derived_cl315, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_in @ (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X1 @ X0) @
% 24.40/4.12 X2 @ X0)
% 24.40/4.12 | (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X1 @ (tc_set @ X0)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl305])).
% 24.40/4.12 thf(cls_conjecture_2, conjecture,
% 24.40/4.12 (~( ( ( v_X ) != ( c_union @ v_Y @ v_Z @ t_a ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( c_lessequals @ v_Y @ v_x @ ( tc_set @ t_a ) ) ))).
% 24.40/4.12 thf(zf_stmt_0, negated_conjecture,
% 24.40/4.12 (( ( v_X ) != ( c_union @ v_Y @ v_Z @ t_a ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( c_lessequals @ v_Y @ v_x @ ( tc_set @ t_a ) )),
% 24.40/4.12 inference('cnf.neg', [status(esa)], [cls_conjecture_2])).
% 24.40/4.12 thf(zip_derived_cl2, plain,
% 24.40/4.12 ((((v_X) != (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ v_Y @ v_x @ (tc_set @ t_a)))),
% 24.40/4.12 inference('cnf', [status(esa)], [zf_stmt_0])).
% 24.40/4.12 thf(zip_derived_cl10, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X0 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_0])).
% 24.40/4.12 thf(cls_conjecture_1, conjecture,
% 24.40/4.12 (~( ( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) |
% 24.40/4.12 ( ( v_X ) = ( c_union @ v_Y @ v_Z @ t_a ) ) ))).
% 24.40/4.12 thf(zf_stmt_1, negated_conjecture,
% 24.40/4.12 (( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) |
% 24.40/4.12 ( ( v_X ) = ( c_union @ v_Y @ v_Z @ t_a ) )),
% 24.40/4.12 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 24.40/4.12 thf(zip_derived_cl1, plain,
% 24.40/4.12 (( (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('cnf', [status(esa)], [zf_stmt_1])).
% 24.40/4.12 thf(cls_Set_OsubsetD_0, axiom,
% 24.40/4.12 (( ~( c_in @ V_c @ V_A @ T_a ) ) |
% 24.40/4.12 ( ~( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) |
% 24.40/4.12 ( c_in @ V_c @ V_B @ T_a ))).
% 24.40/4.12 thf(zip_derived_cl9, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 24.40/4.12 | (c_in @ X0 @ X3 @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 24.40/4.12 thf(zip_derived_cl143, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_in @ X0 @ v_X @ t_a)
% 24.40/4.12 | ~ (c_in @ X0 @ v_Z @ t_a))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 24.40/4.12 thf(zip_derived_cl156, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 ( (c_lessequals @ v_Z @ X0 @ (tc_set @ t_a))
% 24.40/4.12 | (c_in @ (c_Main_OsubsetI__1 @ v_Z @ X0 @ t_a) @ v_X @ t_a)
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl143])).
% 24.40/4.12 thf(cls_Set_OUnCI_1, axiom,
% 24.40/4.12 (( ~( c_in @ V_c @ V_A @ T_a ) ) |
% 24.40/4.12 ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ))).
% 24.40/4.12 thf(zip_derived_cl7, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | (c_in @ X0 @ (c_union @ X1 @ X3 @ X2) @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OUnCI_1])).
% 24.40/4.12 thf(zip_derived_cl11, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 24.40/4.12 thf(zip_derived_cl148, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X3 @ (c_union @ X2 @ X1 @ X0) @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_lessequals @ X3 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl234, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ v_Z @ (c_union @ v_X @ X0 @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ v_Z @ (c_union @ v_X @ X0 @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl148])).
% 24.40/4.12 thf(zip_derived_cl237, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 ( (c_lessequals @ v_Z @ (c_union @ v_X @ X0 @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl234])).
% 24.40/4.12 thf(zip_derived_cl9, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 24.40/4.12 | (c_in @ X0 @ X3 @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 24.40/4.12 thf(zip_derived_cl253, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_in @ X1 @ (c_union @ v_X @ X0 @ t_a) @ t_a)
% 24.40/4.12 | ~ (c_in @ X1 @ v_Z @ t_a))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl237, zip_derived_cl9])).
% 24.40/4.12 thf(zip_derived_cl11, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 24.40/4.12 thf(zip_derived_cl328, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X1 @ (c_union @ v_X @ X0 @ t_a) @ t_a) @
% 24.40/4.12 v_Z @ t_a)
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ X1 @ (c_union @ v_X @ X0 @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl253, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl154, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X3 @ (tc_set @ X0))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X1 @
% 24.40/4.12 X0))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl8])).
% 24.40/4.12 thf(cls_Set_OUnCI_0, axiom,
% 24.40/4.12 (( ~( c_in @ V_c @ V_B @ T_a ) ) |
% 24.40/4.12 ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ))).
% 24.40/4.12 thf(zip_derived_cl6, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | (c_in @ X0 @ (c_union @ X3 @ X1 @ X2) @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OUnCI_0])).
% 24.40/4.12 thf(zip_derived_cl11, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 24.40/4.12 thf(zip_derived_cl145, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X3 @ (c_union @ X2 @ X1 @ X0) @ X0) @ X1 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_lessequals @ X3 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl10, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X0 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_0])).
% 24.40/4.12 thf(cls_conjecture_0, conjecture,
% 24.40/4.12 (~( ( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) |
% 24.40/4.12 ( ( v_X ) = ( c_union @ v_Y @ v_Z @ t_a ) ) ))).
% 24.40/4.12 thf(zf_stmt_2, negated_conjecture,
% 24.40/4.12 (( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) |
% 24.40/4.12 ( ( v_X ) = ( c_union @ v_Y @ v_Z @ t_a ) )),
% 24.40/4.12 inference('cnf.neg', [status(esa)], [cls_conjecture_0])).
% 24.40/4.12 thf(zip_derived_cl0, plain,
% 24.40/4.12 (( (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('cnf', [status(esa)], [zf_stmt_2])).
% 24.40/4.12 thf(zip_derived_cl9, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 24.40/4.12 | (c_in @ X0 @ X3 @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 24.40/4.12 thf(zip_derived_cl142, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_in @ X0 @ v_X @ t_a)
% 24.40/4.12 | ~ (c_in @ X0 @ v_Y @ t_a))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 24.40/4.12 thf(zip_derived_cl155, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 ( (c_lessequals @ v_Y @ X0 @ (tc_set @ t_a))
% 24.40/4.12 | (c_in @ (c_Main_OsubsetI__1 @ v_Y @ X0 @ t_a) @ v_X @ t_a)
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl142])).
% 24.40/4.12 thf(zip_derived_cl188, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 ( (c_lessequals @ v_Y @ (c_union @ X0 @ v_X @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ v_Y @ (c_union @ X0 @ v_X @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl145, zip_derived_cl155])).
% 24.40/4.12 thf(zip_derived_cl190, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ v_Y @ (c_union @ X0 @ v_X @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl188])).
% 24.40/4.12 thf(zip_derived_cl9, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 24.40/4.12 | (c_in @ X0 @ X3 @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 24.40/4.12 thf(zip_derived_cl193, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_in @ X1 @ (c_union @ X0 @ v_X @ t_a) @ t_a)
% 24.40/4.12 | ~ (c_in @ X1 @ v_Y @ t_a))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl190, zip_derived_cl9])).
% 24.40/4.12 thf(zip_derived_cl11, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 24.40/4.12 thf(zip_derived_cl196, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X1 @ (c_union @ X0 @ v_X @ t_a) @ t_a) @
% 24.40/4.12 v_Y @ t_a)
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ X1 @ (c_union @ X0 @ v_X @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl193, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl486, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 ( (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ v_Y @ X1 @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_X @ t_a) @ t_a) @
% 24.40/4.12 X1 @ t_a)
% 24.40/4.12 | (c_lessequals @ (c_union @ v_Y @ X1 @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_X @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ v_Y @ X1 @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_X @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl196])).
% 24.40/4.12 thf(zip_derived_cl489, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ v_Y @ X1 @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_X @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ v_Y @ X1 @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_X @ t_a) @ t_a) @
% 24.40/4.12 X1 @ t_a))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl486])).
% 24.40/4.12 thf(zip_derived_cl17175, plain,
% 24.40/4.12 (( (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ v_X @ v_X @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ v_X @ v_X @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl328, zip_derived_cl489])).
% 24.40/4.12 thf(zip_derived_cl11, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 24.40/4.12 thf(zip_derived_cl154, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X3 @ (tc_set @ X0))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X1 @
% 24.40/4.12 X0))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl8])).
% 24.40/4.12 thf(zip_derived_cl309, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_in @ (c_Main_OsubsetI__1 @ (c_union @ X1 @ X1 @ X0) @ X2 @ X0) @
% 24.40/4.12 X1 @ X0)
% 24.40/4.12 | (c_lessequals @ (c_union @ X1 @ X1 @ X0) @ X2 @ (tc_set @ X0)))),
% 24.40/4.12 inference('eq_fact', [status(thm)], [zip_derived_cl154])).
% 24.40/4.12 thf(zip_derived_cl3247, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X1 @ X1 @ X0) @ X1 @ (tc_set @ X0))
% 24.40/4.12 | (c_lessequals @ (c_union @ X1 @ X1 @ X0) @ X1 @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl309])).
% 24.40/4.12 thf(zip_derived_cl3270, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 (c_lessequals @ (c_union @ X1 @ X1 @ X0) @ X1 @ (tc_set @ X0))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl3247])).
% 24.40/4.12 thf(zip_derived_cl10, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X0 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_0])).
% 24.40/4.12 thf(zip_derived_cl145, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X3 @ (c_union @ X2 @ X1 @ X0) @ X0) @ X1 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_lessequals @ X3 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl182, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_lessequals @ X1 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0))
% 24.40/4.12 | (c_lessequals @ X1 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl145])).
% 24.40/4.12 thf(zip_derived_cl183, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (c_lessequals @ X1 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl182])).
% 24.40/4.12 thf(cls_Set_Osubset__antisym_0, axiom,
% 24.40/4.12 (( ~( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) |
% 24.40/4.12 ( ( V_A ) = ( V_B ) ))).
% 24.40/4.12 thf(zip_derived_cl12, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_lessequals @ X0 @ X1 @ (tc_set @ X2))
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X0 @ (tc_set @ X2))
% 24.40/4.12 | ((X1) = (X0)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_Osubset__antisym_0])).
% 24.40/4.12 thf(zip_derived_cl263, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (((c_union @ X2 @ X1 @ X0) = (X1))
% 24.40/4.12 | ~ (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X1 @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl183, zip_derived_cl12])).
% 24.40/4.12 thf(zip_derived_cl3362, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]: ((c_union @ X1 @ X1 @ X0) = (X1))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl3270, zip_derived_cl263])).
% 24.40/4.12 thf(zip_derived_cl3362, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]: ((c_union @ X1 @ X1 @ X0) = (X1))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl3270, zip_derived_cl263])).
% 24.40/4.12 thf(zip_derived_cl17239, plain,
% 24.40/4.12 (( (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('demod', [status(thm)],
% 24.40/4.12 [zip_derived_cl17175, zip_derived_cl3362, zip_derived_cl3362])).
% 24.40/4.12 thf(zip_derived_cl17240, plain,
% 24.40/4.12 ((((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @ v_X @ (tc_set @ t_a)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl17239])).
% 24.40/4.12 thf(zip_derived_cl10, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X0 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_0])).
% 24.40/4.12 thf(zip_derived_cl148, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X3 @ (c_union @ X2 @ X1 @ X0) @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_lessequals @ X3 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl232, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 ( (c_lessequals @ X1 @ (c_union @ X1 @ X2 @ X0) @ (tc_set @ X0))
% 24.40/4.12 | (c_lessequals @ X1 @ (c_union @ X1 @ X2 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl148])).
% 24.40/4.12 thf(zip_derived_cl235, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (c_lessequals @ X1 @ (c_union @ X1 @ X2 @ X0) @ (tc_set @ X0))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl232])).
% 24.40/4.12 thf(zip_derived_cl183, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (c_lessequals @ X1 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl182])).
% 24.40/4.12 thf(cls_conjecture_5, conjecture,
% 24.40/4.12 (~( ( ~( c_lessequals @ v_Y @ V_U @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ V_U @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( c_lessequals @ v_X @ V_U @ ( tc_set @ t_a ) ) |
% 24.40/4.12 ( ( v_X ) = ( c_union @ v_Y @ v_Z @ t_a ) ) ))).
% 24.40/4.12 thf(zf_stmt_3, negated_conjecture,
% 24.40/4.12 (( ~( c_lessequals @ v_Y @ V_U @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ V_U @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( c_lessequals @ v_X @ V_U @ ( tc_set @ t_a ) ) |
% 24.40/4.12 ( ( v_X ) = ( c_union @ v_Y @ v_Z @ t_a ) )),
% 24.40/4.12 inference('cnf.neg', [status(esa)], [cls_conjecture_5])).
% 24.40/4.12 thf(zip_derived_cl5, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (~ (c_lessequals @ v_Y @ X0 @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ X0 @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ v_X @ X0 @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('cnf', [status(esa)], [zf_stmt_3])).
% 24.40/4.12 thf(zip_derived_cl264, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ v_X @ (c_union @ X0 @ v_Z @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ (c_union @ X0 @ v_Z @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl183, zip_derived_cl5])).
% 24.40/4.12 thf(zip_derived_cl340, plain,
% 24.40/4.12 (( (c_lessequals @ v_X @ (c_union @ v_Y @ v_Z @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl235, zip_derived_cl264])).
% 24.40/4.12 thf(zip_derived_cl12, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_lessequals @ X0 @ X1 @ (tc_set @ X2))
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X0 @ (tc_set @ X2))
% 24.40/4.12 | ((X1) = (X0)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_Osubset__antisym_0])).
% 24.40/4.12 thf(zip_derived_cl345, plain,
% 24.40/4.12 ((((v_X) = (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | ((c_union @ v_Y @ v_Z @ t_a) = (v_X))
% 24.40/4.12 | ~ (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @ v_X @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl340, zip_derived_cl12])).
% 24.40/4.12 thf(zip_derived_cl346, plain,
% 24.40/4.12 ((~ (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) = (c_union @ v_Y @ v_Z @ t_a)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl345])).
% 24.40/4.12 thf(zip_derived_cl17745, plain, (((v_X) = (c_union @ v_Y @ v_Z @ t_a))),
% 24.40/4.12 inference('clc', [status(thm)], [zip_derived_cl17240, zip_derived_cl346])).
% 24.40/4.12 thf(zip_derived_cl17746, plain,
% 24.40/4.12 ((((v_X) != (v_X))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ v_Y @ v_x @ (tc_set @ t_a)))),
% 24.40/4.12 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl17745])).
% 24.40/4.12 thf(zip_derived_cl17747, plain,
% 24.40/4.12 (( (c_lessequals @ v_Y @ v_x @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl17746])).
% 24.40/4.12 thf(zip_derived_cl17745, plain, (((v_X) = (c_union @ v_Y @ v_Z @ t_a))),
% 24.40/4.12 inference('clc', [status(thm)], [zip_derived_cl17240, zip_derived_cl346])).
% 24.40/4.12 thf(zip_derived_cl183, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (c_lessequals @ X1 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl182])).
% 24.40/4.12 thf(zip_derived_cl17797, plain,
% 24.40/4.12 ( (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl17745, zip_derived_cl183])).
% 24.40/4.12 thf(zip_derived_cl17745, plain, (((v_X) = (c_union @ v_Y @ v_Z @ t_a))),
% 24.40/4.12 inference('clc', [status(thm)], [zip_derived_cl17240, zip_derived_cl346])).
% 24.40/4.12 thf(zip_derived_cl235, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (c_lessequals @ X1 @ (c_union @ X1 @ X2 @ X0) @ (tc_set @ X0))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl232])).
% 24.40/4.12 thf(zip_derived_cl17816, plain,
% 24.40/4.12 ( (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl17745, zip_derived_cl235])).
% 24.40/4.12 thf(zip_derived_cl18781, plain,
% 24.40/4.12 ( (c_lessequals @ v_Y @ v_x @ (tc_set @ t_a))),
% 24.40/4.12 inference('demod', [status(thm)],
% 24.40/4.12 [zip_derived_cl17747, zip_derived_cl17797, zip_derived_cl17816])).
% 24.40/4.12 thf(zip_derived_cl9, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 24.40/4.12 | (c_in @ X0 @ X3 @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 24.40/4.12 thf(zip_derived_cl18782, plain,
% 24.40/4.12 (![X0 : $i]: ( (c_in @ X0 @ v_x @ t_a) | ~ (c_in @ X0 @ v_Y @ t_a))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl18781, zip_derived_cl9])).
% 24.40/4.12 thf(zip_derived_cl11, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ X1 @ X2) @ X1 @ X2)
% 24.40/4.12 | (c_lessequals @ X0 @ X1 @ (tc_set @ X2)))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetI_1])).
% 24.40/4.12 thf(zip_derived_cl18798, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (~ (c_in @ (c_Main_OsubsetI__1 @ X0 @ v_x @ t_a) @ v_Y @ t_a)
% 24.40/4.12 | (c_lessequals @ X0 @ v_x @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl18782, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl18841, plain,
% 24.40/4.12 (( (c_lessequals @ (c_union @ v_Y @ v_x @ t_a) @ v_x @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ v_Y @ v_x @ t_a) @ v_x @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl315, zip_derived_cl18798])).
% 24.40/4.12 thf(zip_derived_cl18852, plain,
% 24.40/4.12 ( (c_lessequals @ (c_union @ v_Y @ v_x @ t_a) @ v_x @ (tc_set @ t_a))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl18841])).
% 24.40/4.12 thf(zip_derived_cl263, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.40/4.12 (((c_union @ X2 @ X1 @ X0) = (X1))
% 24.40/4.12 | ~ (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X1 @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl183, zip_derived_cl12])).
% 24.40/4.12 thf(zip_derived_cl18956, plain, (((c_union @ v_Y @ v_x @ t_a) = (v_x))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl18852, zip_derived_cl263])).
% 24.40/4.12 thf(zip_derived_cl148, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X3 @ (c_union @ X2 @ X1 @ X0) @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_lessequals @ X3 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl11])).
% 24.40/4.12 thf(zip_derived_cl145, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X3 @ (c_union @ X2 @ X1 @ X0) @ X0) @ X1 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_lessequals @ X3 @ (c_union @ X2 @ X1 @ X0) @ (tc_set @ X0)))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl11])).
% 24.40/4.12 thf(cls_conjecture_3, conjecture,
% 24.40/4.12 (~( ( ( v_X ) != ( c_union @ v_Y @ v_Z @ t_a ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( c_lessequals @ v_Z @ v_x @ ( tc_set @ t_a ) ) ))).
% 24.40/4.12 thf(zf_stmt_4, negated_conjecture,
% 24.40/4.12 (( ( v_X ) != ( c_union @ v_Y @ v_Z @ t_a ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( c_lessequals @ v_Z @ v_x @ ( tc_set @ t_a ) )),
% 24.40/4.12 inference('cnf.neg', [status(esa)], [cls_conjecture_3])).
% 24.40/4.12 thf(zip_derived_cl3, plain,
% 24.40/4.12 ((((v_X) != (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ v_Z @ v_x @ (tc_set @ t_a)))),
% 24.40/4.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 24.40/4.12 thf(zip_derived_cl9, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 (~ (c_in @ X0 @ X1 @ X2)
% 24.40/4.12 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ X2))
% 24.40/4.12 | (c_in @ X0 @ X3 @ X2))),
% 24.40/4.12 inference('cnf', [status(esa)], [cls_Set_OsubsetD_0])).
% 24.40/4.12 thf(zip_derived_cl144, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) != (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_in @ X0 @ v_x @ t_a)
% 24.40/4.12 | ~ (c_in @ X0 @ v_Z @ t_a))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl9])).
% 24.40/4.12 thf(zip_derived_cl177, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 ( (c_lessequals @ X1 @ (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ X1 @ (c_union @ X0 @ v_x @ t_a) @ t_a) @
% 24.40/4.12 v_Z @ t_a)
% 24.40/4.12 | ((v_X) != (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl145, zip_derived_cl144])).
% 24.40/4.12 thf(zip_derived_cl154, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X2 @ X1 @ X0) @ X3 @ (tc_set @ X0))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X2 @
% 24.40/4.12 X0)
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X2 @ X1 @ X0) @ X3 @ X0) @ X1 @
% 24.40/4.12 X0))),
% 24.40/4.12 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl8])).
% 24.40/4.12 thf(zip_derived_cl503, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 (~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) != (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ t_a) @
% 24.40/4.12 X1 @ t_a)
% 24.40/4.12 | (c_lessequals @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl154])).
% 24.40/4.12 thf(zip_derived_cl515, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 ( (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ t_a) @
% 24.40/4.12 X1 @ t_a)
% 24.40/4.12 | (c_lessequals @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) != (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl503])).
% 24.40/4.12 thf(zip_derived_cl17745, plain, (((v_X) = (c_union @ v_Y @ v_Z @ t_a))),
% 24.40/4.12 inference('clc', [status(thm)], [zip_derived_cl17240, zip_derived_cl346])).
% 24.40/4.12 thf(zip_derived_cl17816, plain,
% 24.40/4.12 ( (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl17745, zip_derived_cl235])).
% 24.40/4.12 thf(zip_derived_cl17797, plain,
% 24.40/4.12 ( (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl17745, zip_derived_cl183])).
% 24.40/4.12 thf(zip_derived_cl18124, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 ( (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ t_a) @
% 24.40/4.12 X1 @ t_a)
% 24.40/4.12 | (c_lessequals @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | ((v_X) != (v_X)))),
% 24.40/4.12 inference('demod', [status(thm)],
% 24.40/4.12 [zip_derived_cl515, zip_derived_cl17745, zip_derived_cl17816,
% 24.40/4.12 zip_derived_cl17797])).
% 24.40/4.12 thf(zip_derived_cl18125, plain,
% 24.40/4.12 (![X0 : $i, X1 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | (c_in @
% 24.40/4.12 (c_Main_OsubsetI__1 @ (c_union @ X1 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ t_a) @
% 24.40/4.12 X1 @ t_a))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl18124])).
% 24.40/4.12 thf(zip_derived_cl18143, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 ( (c_lessequals @ (c_union @ X0 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a))
% 24.40/4.12 | (c_lessequals @ (c_union @ X0 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a)))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl148, zip_derived_cl18125])).
% 24.40/4.12 thf(zip_derived_cl18154, plain,
% 24.40/4.12 (![X0 : $i]:
% 24.40/4.12 (c_lessequals @ (c_union @ X0 @ v_Z @ t_a) @
% 24.40/4.12 (c_union @ X0 @ v_x @ t_a) @ (tc_set @ t_a))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl18143])).
% 24.40/4.12 thf(zip_derived_cl20843, plain,
% 24.40/4.12 ( (c_lessequals @ (c_union @ v_Y @ v_Z @ t_a) @ v_x @ (tc_set @ t_a))),
% 24.40/4.12 inference('sup+', [status(thm)],
% 24.40/4.12 [zip_derived_cl18956, zip_derived_cl18154])).
% 24.40/4.12 thf(zip_derived_cl17745, plain, (((v_X) = (c_union @ v_Y @ v_Z @ t_a))),
% 24.40/4.12 inference('clc', [status(thm)], [zip_derived_cl17240, zip_derived_cl346])).
% 24.40/4.12 thf(cls_conjecture_4, conjecture,
% 24.40/4.12 (~( ( ( v_X ) != ( c_union @ v_Y @ v_Z @ t_a ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_X @ v_x @ ( tc_set @ t_a ) ) ) ))).
% 24.40/4.12 thf(zf_stmt_5, negated_conjecture,
% 24.40/4.12 (( ( v_X ) != ( c_union @ v_Y @ v_Z @ t_a ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Y @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_Z @ v_X @ ( tc_set @ t_a ) ) ) |
% 24.40/4.12 ( ~( c_lessequals @ v_X @ v_x @ ( tc_set @ t_a ) ) )),
% 24.40/4.12 inference('cnf.neg', [status(esa)], [cls_conjecture_4])).
% 24.40/4.12 thf(zip_derived_cl4, plain,
% 24.40/4.12 ((((v_X) != (c_union @ v_Y @ v_Z @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_X @ v_x @ (tc_set @ t_a)))),
% 24.40/4.12 inference('cnf', [status(esa)], [zf_stmt_5])).
% 24.40/4.12 thf(zip_derived_cl17745, plain, (((v_X) = (c_union @ v_Y @ v_Z @ t_a))),
% 24.40/4.12 inference('clc', [status(thm)], [zip_derived_cl17240, zip_derived_cl346])).
% 24.40/4.12 thf(zip_derived_cl17750, plain,
% 24.40/4.12 ((((v_X) != (v_X))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_X @ v_x @ (tc_set @ t_a)))),
% 24.40/4.12 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl17745])).
% 24.40/4.12 thf(zip_derived_cl17751, plain,
% 24.40/4.12 ((~ (c_lessequals @ v_X @ v_x @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))
% 24.40/4.12 | ~ (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a)))),
% 24.40/4.12 inference('simplify', [status(thm)], [zip_derived_cl17750])).
% 24.40/4.12 thf(zip_derived_cl17797, plain,
% 24.40/4.12 ( (c_lessequals @ v_Z @ v_X @ (tc_set @ t_a))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl17745, zip_derived_cl183])).
% 24.40/4.12 thf(zip_derived_cl17816, plain,
% 24.40/4.12 ( (c_lessequals @ v_Y @ v_X @ (tc_set @ t_a))),
% 24.40/4.12 inference('sup+', [status(thm)], [zip_derived_cl17745, zip_derived_cl235])).
% 24.40/4.12 thf(zip_derived_cl18070, plain,
% 24.40/4.12 (~ (c_lessequals @ v_X @ v_x @ (tc_set @ t_a))),
% 24.40/4.12 inference('demod', [status(thm)],
% 24.40/4.12 [zip_derived_cl17751, zip_derived_cl17797, zip_derived_cl17816])).
% 24.40/4.12 thf(zip_derived_cl20850, plain, ($false),
% 24.40/4.12 inference('demod', [status(thm)],
% 24.40/4.12 [zip_derived_cl20843, zip_derived_cl17745, zip_derived_cl18070])).
% 24.40/4.12
% 24.40/4.12 % SZS output end Refutation
% 24.40/4.12
% 24.40/4.12
% 24.40/4.12 % Terminating...
% 24.78/4.22 % Runner terminated.
% 24.78/4.23 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------