TSTP Solution File: LAT274-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LAT274-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bC61pZycWf 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 Aug 31 06:46:27 EDT 2023
% Result : Unsatisfiable 106.22s 15.79s
% Output : Refutation 106.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT274-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bC61pZycWf true
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 07:16:20 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.69/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.69/0.77 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.69/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.38/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.38/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.38/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 106.22/15.79 % Solved by fo/fo6_bce.sh.
% 106.22/15.79 % BCE start: 2758
% 106.22/15.79 % BCE eliminated: 592
% 106.22/15.79 % PE start: 2166
% 106.22/15.79 logic: eq
% 106.22/15.79 % PE eliminated: -655
% 106.22/15.79 % done 7827 iterations in 15.039s
% 106.22/15.79 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 106.22/15.79 % SZS output start Refutation
% 106.22/15.79 thf(t_a_type, type, t_a: $i).
% 106.22/15.79 thf(v_b_type, type, v_b: $i).
% 106.22/15.79 thf(v_sko__4mi_type, type, v_sko__4mi: $i > $i > $i > $i).
% 106.22/15.79 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 106.22/15.79 thf(c_Tarski_OisLub_type, type, c_Tarski_OisLub: $i > $i > $i > $i > $o).
% 106.22/15.79 thf(tc_set_type, type, tc_set: $i > $i).
% 106.22/15.79 thf(c_Pair_type, type, c_Pair: $i > $i > $i > $i > $i).
% 106.22/15.79 thf(c_in_type, type, c_in: $i > $i > $i > $o).
% 106.22/15.79 thf(c_emptyset_type, type, c_emptyset: $i).
% 106.22/15.79 thf(v_S_type, type, v_S: $i).
% 106.22/15.79 thf(v_r_type, type, v_r: $i).
% 106.22/15.79 thf(v_cl_type, type, v_cl: $i).
% 106.22/15.79 thf(v_A_type, type, v_A: $i).
% 106.22/15.79 thf(v_sko__4mk_type, type, v_sko__4mk: $i > $i > $i > $i).
% 106.22/15.79 thf(tc_prod_type, type, tc_prod: $i > $i > $i).
% 106.22/15.79 thf(v_L_type, type, v_L: $i).
% 106.22/15.79 thf(c_Tarski_Ointerval_type, type, c_Tarski_Ointerval: $i > $i > $i > $i > $i).
% 106.22/15.79 thf(v_sko__4mj_type, type, v_sko__4mj: $i > $i > $i > $i).
% 106.22/15.79 thf(v_a_type, type, v_a: $i).
% 106.22/15.79 thf(cls_conjecture_4, conjecture,
% 106.22/15.79 (~( c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a ))).
% 106.22/15.79 thf(zf_stmt_0, negated_conjecture,
% 106.22/15.79 (c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a),
% 106.22/15.79 inference('cnf.neg', [status(esa)], [cls_conjecture_4])).
% 106.22/15.79 thf(zip_derived_cl2755, plain, ( (c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a)),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_0])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0, axiom,
% 106.22/15.79 (( ~( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a ) ) |
% 106.22/15.79 ( ~( c_in @ V_z @ v_A @ t_a ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) |
% 106.22/15.79 ( c_in @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_S @ t_a ))).
% 106.22/15.79 thf(zip_derived_cl9, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (~ (c_Tarski_OisLub @ X0 @ v_cl @ X1 @ t_a)
% 106.22/15.79 | ~ (c_in @ X2 @ v_A @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ X1 @ X2 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mi @ X0 @ v_r @ X2) @ X0 @ t_a))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0])).
% 106.22/15.79 thf(zip_derived_cl9265, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (((v_S) != (X1))
% 106.22/15.79 | ((v_cl) != (v_cl))
% 106.22/15.79 | ((v_L) != (X0))
% 106.22/15.79 | ((t_a) != (t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mi @ X1 @ v_r @ X2) @ X1 @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X2 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @ X2 @ v_A @ t_a))),
% 106.22/15.79 inference('dp-resolution', [status(thm)],
% 106.22/15.79 [zip_derived_cl2755, zip_derived_cl9])).
% 106.22/15.79 thf(zip_derived_cl55845, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (~ (c_in @ X2 @ v_A @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X2 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mi @ X1 @ v_r @ X2) @ X1 @ t_a)
% 106.22/15.79 | ((v_L) != (X0))
% 106.22/15.79 | ((v_S) != (X1)))),
% 106.22/15.79 inference('simplify', [status(thm)], [zip_derived_cl9265])).
% 106.22/15.79 thf(zip_derived_cl55846, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (((v_S) != (X0))
% 106.22/15.79 | (c_in @ (v_sko__4mi @ X0 @ v_r @ X1) @ X0 @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ X1 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @ X1 @ v_A @ t_a))),
% 106.22/15.79 inference('eq_res', [status(thm)], [zip_derived_cl55845])).
% 106.22/15.79 thf(cls_conjecture_2, conjecture,
% 106.22/15.79 (~( c_lessequals @
% 106.22/15.79 v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) ))).
% 106.22/15.79 thf(zf_stmt_1, negated_conjecture,
% 106.22/15.79 (c_lessequals @
% 106.22/15.79 v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a )),
% 106.22/15.79 inference('cnf.neg', [status(esa)], [cls_conjecture_2])).
% 106.22/15.79 thf(zip_derived_cl2753, plain,
% 106.22/15.79 ( (c_lessequals @ v_S @ (c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a) @
% 106.22/15.79 (tc_set @ t_a))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0, axiom,
% 106.22/15.79 (( ~( c_in @ V_x @ V_S @ T_a ) ) |
% 106.22/15.79 ( ~( c_lessequals @
% 106.22/15.79 V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @
% 106.22/15.79 ( tc_set @ T_a ) ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ))).
% 106.22/15.79 thf(zip_derived_cl5, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.22/15.79 (~ (c_in @ X0 @ X1 @ X2)
% 106.22/15.79 | ~ (c_lessequals @ X1 @ (c_Tarski_Ointerval @ X3 @ X4 @ X5 @ X2) @
% 106.22/15.79 (tc_set @ X2))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X5 @ X2 @ X2) @ X3 @ (tc_prod @ X2 @ X2)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0])).
% 106.22/15.79 thf(zip_derived_cl34264, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ X0 @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ v_b @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl2753, zip_derived_cl5])).
% 106.22/15.79 thf(cls_conjecture_1, conjecture, (~( c_in @ v_b @ v_A @ t_a ))).
% 106.22/15.79 thf(zf_stmt_2, negated_conjecture, (c_in @ v_b @ v_A @ t_a),
% 106.22/15.79 inference('cnf.neg', [status(esa)], [cls_conjecture_1])).
% 106.22/15.79 thf(zip_derived_cl2752, plain, ( (c_in @ v_b @ v_A @ t_a)),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_2])).
% 106.22/15.79 thf(zip_derived_cl2755, plain, ( (c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a)),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_0])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1, axiom,
% 106.22/15.79 (( ~( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a ) ) |
% 106.22/15.79 ( ~( c_in @ V_z @ v_A @ t_a ) ) |
% 106.22/15.79 ( ~( c_in @
% 106.22/15.79 ( c_Pair @ ( v_sko__4mi @ V_S @ v_r @ V_z ) @ V_z @ t_a @ t_a ) @
% 106.22/15.79 v_r @ ( tc_prod @ t_a @ t_a ) ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_L @ V_z @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ))).
% 106.22/15.79 thf(zip_derived_cl10, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (~ (c_Tarski_OisLub @ X0 @ v_cl @ X1 @ t_a)
% 106.22/15.79 | ~ (c_in @ X2 @ v_A @ t_a)
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mi @ X0 @ v_r @ X2) @ X2 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X1 @ X2 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1])).
% 106.22/15.79 thf(zip_derived_cl9268, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (((v_S) != (X1))
% 106.22/15.79 | ((v_cl) != (v_cl))
% 106.22/15.79 | ((v_L) != (X0))
% 106.22/15.79 | ((t_a) != (t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X2 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mi @ X1 @ v_r @ X2) @ X2 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @ X2 @ v_A @ t_a))),
% 106.22/15.79 inference('dp-resolution', [status(thm)],
% 106.22/15.79 [zip_derived_cl2755, zip_derived_cl10])).
% 106.22/15.79 thf(zip_derived_cl55859, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (~ (c_in @ X2 @ v_A @ t_a)
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mi @ X1 @ v_r @ X2) @ X2 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X2 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ((v_L) != (X0))
% 106.22/15.79 | ((v_S) != (X1)))),
% 106.22/15.79 inference('simplify', [status(thm)], [zip_derived_cl9268])).
% 106.22/15.79 thf(zip_derived_cl55860, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (((v_S) != (X0))
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ X1 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mi @ X0 @ v_r @ X1) @ X1 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @ X1 @ v_A @ t_a))),
% 106.22/15.79 inference('eq_res', [status(thm)], [zip_derived_cl55859])).
% 106.22/15.79 thf(zip_derived_cl55939, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ X0 @ v_A @ t_a)
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mi @ v_S @ v_r @ X0) @ X0 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('eq_res', [status(thm)], [zip_derived_cl55860])).
% 106.22/15.79 thf(zip_derived_cl56027, plain,
% 106.22/15.79 ((~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mi @ v_S @ v_r @ v_b) @ v_b @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ v_b @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl2752, zip_derived_cl55939])).
% 106.22/15.79 thf(zip_derived_cl69731, plain,
% 106.22/15.79 ((~ (c_in @ (v_sko__4mi @ v_S @ v_r @ v_b) @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ v_b @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl34264, zip_derived_cl56027])).
% 106.22/15.79 thf(zip_derived_cl69772, plain,
% 106.22/15.79 ((~ (c_in @ v_b @ v_A @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ v_b @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ((v_S) != (v_S))
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ v_b @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl55846, zip_derived_cl69731])).
% 106.22/15.79 thf(zip_derived_cl2752, plain, ( (c_in @ v_b @ v_A @ t_a)),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_2])).
% 106.22/15.79 thf(zip_derived_cl69773, plain,
% 106.22/15.79 (( (c_in @ (c_Pair @ v_L @ v_b @ t_a @ t_a) @ v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ((v_S) != (v_S))
% 106.22/15.79 | (c_in @ (c_Pair @ v_L @ v_b @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('demod', [status(thm)],
% 106.22/15.79 [zip_derived_cl69772, zip_derived_cl2752])).
% 106.22/15.79 thf(zip_derived_cl69774, plain,
% 106.22/15.79 ( (c_in @ (c_Pair @ v_L @ v_b @ t_a @ t_a) @ v_r @ (tc_prod @ t_a @ t_a))),
% 106.22/15.79 inference('simplify', [status(thm)], [zip_derived_cl69773])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0, axiom,
% 106.22/15.79 (( ~( c_in @
% 106.22/15.79 ( c_Pair @ V_x @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) |
% 106.22/15.79 ( ~( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) |
% 106.22/15.79 ( c_in @ V_x @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ T_a ))).
% 106.22/15.79 thf(zip_derived_cl6, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.22/15.79 (~ (c_in @ (c_Pair @ X0 @ X1 @ X2 @ X2) @ X3 @ (tc_prod @ X2 @ X2))
% 106.22/15.79 | ~ (c_in @ (c_Pair @ X4 @ X0 @ X2 @ X2) @ X3 @ (tc_prod @ X2 @ X2))
% 106.22/15.79 | (c_in @ X0 @ (c_Tarski_Ointerval @ X3 @ X4 @ X1 @ X2) @ X2))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0])).
% 106.22/15.79 thf(zip_derived_cl69798, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ (c_Pair @ X0 @ v_L @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ v_L @ (c_Tarski_Ointerval @ v_r @ X0 @ v_b @ t_a) @ t_a))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl69774, zip_derived_cl6])).
% 106.22/15.79 thf(cls_conjecture_6, conjecture,
% 106.22/15.79 (c_in @ v_L @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ t_a)).
% 106.22/15.79 thf(zf_stmt_3, negated_conjecture,
% 106.22/15.79 (~( c_in @ v_L @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ t_a )),
% 106.22/15.79 inference('cnf.neg', [status(esa)], [cls_conjecture_6])).
% 106.22/15.79 thf(zip_derived_cl2757, plain,
% 106.22/15.79 (~ (c_in @ v_L @ (c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a) @ t_a)),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_3])).
% 106.22/15.79 thf(zip_derived_cl69851, plain,
% 106.22/15.79 (~ (c_in @ (c_Pair @ v_a @ v_L @ t_a @ t_a) @ v_r @ (tc_prod @ t_a @ t_a))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl69798, zip_derived_cl2757])).
% 106.22/15.79 thf(zip_derived_cl2753, plain,
% 106.22/15.79 ( (c_lessequals @ v_S @ (c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a) @
% 106.22/15.79 (tc_set @ t_a))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0, axiom,
% 106.22/15.79 (( ~( c_in @ V_x @ V_S @ T_a ) ) |
% 106.22/15.79 ( ~( c_lessequals @
% 106.22/15.79 V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @
% 106.22/15.79 ( tc_set @ T_a ) ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ))).
% 106.22/15.79 thf(zip_derived_cl4, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.22/15.79 (~ (c_in @ X0 @ X1 @ X2)
% 106.22/15.79 | ~ (c_lessequals @ X1 @ (c_Tarski_Ointerval @ X3 @ X4 @ X5 @ X2) @
% 106.22/15.79 (tc_set @ X2))
% 106.22/15.79 | (c_in @ (c_Pair @ X4 @ X0 @ X2 @ X2) @ X3 @ (tc_prod @ X2 @ X2)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0])).
% 106.22/15.79 thf(zip_derived_cl34259, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ X0 @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_a @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl2753, zip_derived_cl4])).
% 106.22/15.79 thf(zip_derived_cl2753, plain,
% 106.22/15.79 ( (c_lessequals @ v_S @ (c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a) @
% 106.22/15.79 (tc_set @ t_a))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2, axiom,
% 106.22/15.79 (( ~( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @
% 106.22/15.79 v_r @ ( tc_prod @ t_a @ t_a ) ) ) |
% 106.22/15.79 ( ~( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) |
% 106.22/15.79 ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a ) |
% 106.22/15.79 ( ( V_S ) = ( c_emptyset ) ))).
% 106.22/15.79 thf(zip_derived_cl2, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.22/15.79 (~ (c_in @ (c_Pair @ X0 @ (v_sko__4mj @ X1 @ X0 @ v_r) @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_lessequals @ X1 @ X2 @ (tc_set @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X3 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mk @ X3 @ X1 @ v_r) @ X1 @ t_a)
% 106.22/15.79 | ((X1) = (c_emptyset)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2])).
% 106.22/15.79 thf(zip_derived_cl34253, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (~ (c_in @
% 106.22/15.79 (c_Pair @ X0 @ (v_sko__4mj @ v_S @ X0 @ v_r) @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X1 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mk @ X1 @ v_S @ v_r) @ v_S @ t_a)
% 106.22/15.79 | ((v_S) = (c_emptyset)))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl2753, zip_derived_cl2])).
% 106.22/15.79 thf(cls_conjecture_3, conjecture, (( v_S ) = ( c_emptyset ))).
% 106.22/15.79 thf(zf_stmt_4, negated_conjecture, (( v_S ) != ( c_emptyset )),
% 106.22/15.79 inference('cnf.neg', [status(esa)], [cls_conjecture_3])).
% 106.22/15.79 thf(zip_derived_cl2754, plain, (((v_S) != (c_emptyset))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_4])).
% 106.22/15.79 thf(zip_derived_cl34256, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (~ (c_in @
% 106.22/15.79 (c_Pair @ X0 @ (v_sko__4mj @ v_S @ X0 @ v_r) @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X1 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mk @ X1 @ v_S @ v_r) @ v_S @ t_a))),
% 106.22/15.79 inference('simplify_reflect-', [status(thm)],
% 106.22/15.79 [zip_derived_cl34253, zip_derived_cl2754])).
% 106.22/15.79 thf(zip_derived_cl63551, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ (v_sko__4mj @ v_S @ v_a @ v_r) @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_a @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mk @ X0 @ v_S @ v_r) @ v_S @ t_a))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl34259, zip_derived_cl34256])).
% 106.22/15.79 thf(zip_derived_cl2753, plain,
% 106.22/15.79 ( (c_lessequals @ v_S @ (c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a) @
% 106.22/15.79 (tc_set @ t_a))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0, axiom,
% 106.22/15.79 (( ~( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) |
% 106.22/15.79 ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a ) |
% 106.22/15.79 ( c_in @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_S @ t_a ) |
% 106.22/15.79 ( ( V_S ) = ( c_emptyset ) ))).
% 106.22/15.79 thf(zip_derived_cl0, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.22/15.79 (~ (c_lessequals @ X0 @ X1 @ (tc_set @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X2 @ X3 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mj @ X0 @ X2 @ v_r) @ X0 @ t_a)
% 106.22/15.79 | (c_in @ (v_sko__4mk @ X3 @ X0 @ v_r) @ X0 @ t_a)
% 106.22/15.79 | ((X0) = (c_emptyset)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0])).
% 106.22/15.79 thf(zip_derived_cl34251, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 ( (c_in @ (c_Pair @ X1 @ X0 @ t_a @ t_a) @ v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mj @ v_S @ X1 @ v_r) @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (v_sko__4mk @ X0 @ v_S @ v_r) @ v_S @ t_a)
% 106.22/15.79 | ((v_S) = (c_emptyset)))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl2753, zip_derived_cl0])).
% 106.22/15.79 thf(zip_derived_cl2754, plain, (((v_S) != (c_emptyset))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_4])).
% 106.22/15.79 thf(zip_derived_cl34254, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 ( (c_in @ (c_Pair @ X1 @ X0 @ t_a @ t_a) @ v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mj @ v_S @ X1 @ v_r) @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (v_sko__4mk @ X0 @ v_S @ v_r) @ v_S @ t_a))),
% 106.22/15.79 inference('simplify_reflect-', [status(thm)],
% 106.22/15.79 [zip_derived_cl34251, zip_derived_cl2754])).
% 106.22/15.79 thf(zip_derived_cl74820, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 ( (c_in @ (v_sko__4mk @ X0 @ v_S @ v_r) @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_a @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('clc', [status(thm)],
% 106.22/15.79 [zip_derived_cl63551, zip_derived_cl34254])).
% 106.22/15.79 thf(zip_derived_cl2755, plain, ( (c_Tarski_OisLub @ v_S @ v_cl @ v_L @ t_a)),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_0])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0, axiom,
% 106.22/15.79 (( ~( c_Tarski_OisLub @ V_S @ v_cl @ V_L @ t_a ) ) |
% 106.22/15.79 ( ~( c_in @ V_y @ V_S @ t_a ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_y @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ))).
% 106.22/15.79 thf(zip_derived_cl8, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (~ (c_Tarski_OisLub @ X0 @ v_cl @ X1 @ t_a)
% 106.22/15.79 | ~ (c_in @ X2 @ X0 @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ X2 @ X1 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0])).
% 106.22/15.79 thf(zip_derived_cl9262, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (((v_S) != (X1))
% 106.22/15.79 | ((v_cl) != (v_cl))
% 106.22/15.79 | ((v_L) != (X0))
% 106.22/15.79 | ((t_a) != (t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X2 @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @ X2 @ X1 @ t_a))),
% 106.22/15.79 inference('dp-resolution', [status(thm)],
% 106.22/15.79 [zip_derived_cl2755, zip_derived_cl8])).
% 106.22/15.79 thf(zip_derived_cl55835, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.22/15.79 (~ (c_in @ X2 @ X1 @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ X2 @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ((v_L) != (X0))
% 106.22/15.79 | ((v_S) != (X1)))),
% 106.22/15.79 inference('simplify', [status(thm)], [zip_derived_cl9262])).
% 106.22/15.79 thf(zip_derived_cl55836, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (((v_S) != (X0))
% 106.22/15.79 | (c_in @ (c_Pair @ X1 @ v_L @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @ X1 @ X0 @ t_a))),
% 106.22/15.79 inference('eq_res', [status(thm)], [zip_derived_cl55835])).
% 106.22/15.79 thf(zip_derived_cl55861, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ X0 @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ v_L @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('eq_res', [status(thm)], [zip_derived_cl55836])).
% 106.22/15.79 thf(zip_derived_cl34259, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ X0 @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_a @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl2753, zip_derived_cl4])).
% 106.22/15.79 thf(zip_derived_cl2753, plain,
% 106.22/15.79 ( (c_lessequals @ v_S @ (c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a) @
% 106.22/15.79 (tc_set @ t_a))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3, axiom,
% 106.22/15.79 (( ~( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ t_a @ t_a ) @
% 106.22/15.79 v_r @ ( tc_prod @ t_a @ t_a ) ) ) |
% 106.22/15.79 ( ~( c_in @
% 106.22/15.79 ( c_Pair @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @
% 106.22/15.79 v_r @ ( tc_prod @ t_a @ t_a ) ) ) |
% 106.22/15.79 ( ~( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) |
% 106.22/15.79 ( ( V_S ) = ( c_emptyset ) ))).
% 106.22/15.79 thf(zip_derived_cl3, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.22/15.79 (~ (c_in @ (c_Pair @ X0 @ (v_sko__4mj @ X1 @ X0 @ v_r) @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mk @ X2 @ X1 @ v_r) @ X2 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_lessequals @ X1 @ X3 @ (tc_set @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X2 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ((X1) = (c_emptyset)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3])).
% 106.22/15.79 thf(zip_derived_cl34257, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (~ (c_in @
% 106.22/15.79 (c_Pair @ X0 @ (v_sko__4mj @ v_S @ X0 @ v_r) @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mk @ X1 @ v_S @ v_r) @ X1 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X1 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ((v_S) = (c_emptyset)))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl2753, zip_derived_cl3])).
% 106.22/15.79 thf(zip_derived_cl2754, plain, (((v_S) != (c_emptyset))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_4])).
% 106.22/15.79 thf(zip_derived_cl34258, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (~ (c_in @
% 106.22/15.79 (c_Pair @ X0 @ (v_sko__4mj @ v_S @ X0 @ v_r) @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mk @ X1 @ v_S @ v_r) @ X1 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X0 @ X1 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('simplify_reflect-', [status(thm)],
% 106.22/15.79 [zip_derived_cl34257, zip_derived_cl2754])).
% 106.22/15.79 thf(zip_derived_cl63557, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 (~ (c_in @ (v_sko__4mj @ v_S @ v_a @ v_r) @ v_S @ t_a)
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mk @ X0 @ v_S @ v_r) @ X0 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ v_a @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl34259, zip_derived_cl34258])).
% 106.22/15.79 thf(zip_derived_cl2753, plain,
% 106.22/15.79 ( (c_lessequals @ v_S @ (c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a) @
% 106.22/15.79 (tc_set @ t_a))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 106.22/15.79 thf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1, axiom,
% 106.22/15.79 (( ~( c_in @
% 106.22/15.79 ( c_Pair @ ( v_sko__4mk @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @
% 106.22/15.79 v_r @ ( tc_prod @ t_a @ t_a ) ) ) |
% 106.22/15.79 ( ~( c_lessequals @ V_S @ V_A @ ( tc_set @ t_a ) ) ) |
% 106.22/15.79 ( c_in @
% 106.22/15.79 ( c_Pair @ V_a @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) |
% 106.22/15.79 ( c_in @ ( v_sko__4mj @ V_S @ V_a @ v_r ) @ V_S @ t_a ) |
% 106.22/15.79 ( ( V_S ) = ( c_emptyset ) ))).
% 106.22/15.79 thf(zip_derived_cl1, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.22/15.79 (~ (c_in @ (c_Pair @ (v_sko__4mk @ X0 @ X1 @ v_r) @ X0 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_lessequals @ X1 @ X2 @ (tc_set @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X3 @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mj @ X1 @ X3 @ v_r) @ X1 @ t_a)
% 106.22/15.79 | ((X1) = (c_emptyset)))),
% 106.22/15.79 inference('cnf', [status(esa)],
% 106.22/15.79 [cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1])).
% 106.22/15.79 thf(zip_derived_cl34252, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mk @ X0 @ v_S @ v_r) @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X1 @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mj @ v_S @ X1 @ v_r) @ v_S @ t_a)
% 106.22/15.79 | ((v_S) = (c_emptyset)))),
% 106.22/15.79 inference('s_sup-', [status(thm)], [zip_derived_cl2753, zip_derived_cl1])).
% 106.22/15.79 thf(zip_derived_cl2754, plain, (((v_S) != (c_emptyset))),
% 106.22/15.79 inference('cnf', [status(esa)], [zf_stmt_4])).
% 106.22/15.79 thf(zip_derived_cl34255, plain,
% 106.22/15.79 (![X0 : $i, X1 : $i]:
% 106.22/15.79 (~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mk @ X0 @ v_S @ v_r) @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (c_Pair @ X1 @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | (c_in @ (v_sko__4mj @ v_S @ X1 @ v_r) @ v_S @ t_a))),
% 106.22/15.79 inference('simplify_reflect-', [status(thm)],
% 106.22/15.79 [zip_derived_cl34252, zip_derived_cl2754])).
% 106.22/15.79 thf(zip_derived_cl74857, plain,
% 106.22/15.79 (![X0 : $i]:
% 106.22/15.79 ( (c_in @ (c_Pair @ v_a @ X0 @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a))
% 106.22/15.79 | ~ (c_in @
% 106.22/15.79 (c_Pair @ (v_sko__4mk @ X0 @ v_S @ v_r) @ X0 @ t_a @ t_a) @
% 106.22/15.79 v_r @ (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('clc', [status(thm)],
% 106.22/15.79 [zip_derived_cl63557, zip_derived_cl34255])).
% 106.22/15.79 thf(zip_derived_cl74879, plain,
% 106.22/15.79 ((~ (c_in @ (v_sko__4mk @ v_L @ v_S @ v_r) @ v_S @ t_a)
% 106.22/15.79 | (c_in @ (c_Pair @ v_a @ v_L @ t_a @ t_a) @ v_r @
% 106.22/15.79 (tc_prod @ t_a @ t_a)))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl55861, zip_derived_cl74857])).
% 106.22/15.79 thf(zip_derived_cl69851, plain,
% 106.22/15.79 (~ (c_in @ (c_Pair @ v_a @ v_L @ t_a @ t_a) @ v_r @ (tc_prod @ t_a @ t_a))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl69798, zip_derived_cl2757])).
% 106.22/15.79 thf(zip_derived_cl74880, plain,
% 106.22/15.79 (~ (c_in @ (v_sko__4mk @ v_L @ v_S @ v_r) @ v_S @ t_a)),
% 106.22/15.79 inference('demod', [status(thm)],
% 106.22/15.79 [zip_derived_cl74879, zip_derived_cl69851])).
% 106.22/15.79 thf(zip_derived_cl74886, plain,
% 106.22/15.79 ( (c_in @ (c_Pair @ v_a @ v_L @ t_a @ t_a) @ v_r @ (tc_prod @ t_a @ t_a))),
% 106.22/15.79 inference('s_sup-', [status(thm)],
% 106.22/15.79 [zip_derived_cl74820, zip_derived_cl74880])).
% 106.22/15.79 thf(zip_derived_cl74912, plain, ($false),
% 106.22/15.79 inference('demod', [status(thm)],
% 106.22/15.79 [zip_derived_cl69851, zip_derived_cl74886])).
% 106.22/15.79
% 106.22/15.79 % SZS output end Refutation
% 106.22/15.79
% 106.22/15.79
% 106.22/15.79 % Terminating...
% 106.81/15.92 % Runner terminated.
% 106.81/15.94 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------