TSTP Solution File: HEN011-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Jkll573A2l true
% Computer : n008.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 01:57:54 EDT 2023
% Result : Unsatisfiable 55.16s 8.47s
% Output : Refutation 55.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : HEN011-2 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Jkll573A2l true
% 0.13/0.34 % Computer : n008.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 : Thu Aug 24 13:39:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 55.16/8.47 % Solved by fo/fo5.sh.
% 55.16/8.47 % done 21055 iterations in 7.690s
% 55.16/8.47 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 55.16/8.47 % SZS output start Refutation
% 55.16/8.47 thf(divide_type, type, divide: $i > $i > $i).
% 55.16/8.47 thf(idQb_Q__idQ_idQa_type, type, idQb_Q__idQ_idQa: $i).
% 55.16/8.47 thf(idQ_idQb_type, type, idQ_idQb: $i).
% 55.16/8.47 thf(idQ_idQa_type, type, idQ_idQa: $i).
% 55.16/8.47 thf(idQa_Q__idQ_idQb_type, type, idQa_Q__idQ_idQb: $i).
% 55.16/8.47 thf(identity_type, type, identity: $i).
% 55.16/8.47 thf(b_type, type, b: $i).
% 55.16/8.47 thf(a_type, type, a: $i).
% 55.16/8.47 thf(idQb_type, type, idQb: $i).
% 55.16/8.47 thf(less_equal_type, type, less_equal: $i > $i > $o).
% 55.16/8.47 thf(idQa_type, type, idQa: $i).
% 55.16/8.47 thf(quotient_type, type, quotient: $i > $i > $i > $o).
% 55.16/8.47 thf(zero_type, type, zero: $i).
% 55.16/8.47 thf(closure, axiom, (quotient @ X @ Y @ ( divide @ X @ Y ))).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(identity_divide_idQa, axiom, (quotient @ identity @ idQa @ idQ_idQa)).
% 55.16/8.47 thf(zip_derived_cl23, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 55.16/8.47 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 55.16/8.47 thf(identity_divide_a, axiom, (quotient @ identity @ a @ idQa)).
% 55.16/8.47 thf(zip_derived_cl19, plain, ( (quotient @ identity @ a @ idQa)),
% 55.16/8.47 inference('cnf', [status(esa)], [identity_divide_a])).
% 55.16/8.47 thf(one_inversion_equals_three, axiom,
% 55.16/8.47 (( ~( quotient @ identity @ X @ Y1 ) ) |
% 55.16/8.47 ( ~( quotient @ identity @ Y1 @ Y2 ) ) |
% 55.16/8.47 ( ~( quotient @ identity @ Y2 @ Y3 ) ) | ( ( Y1 ) = ( Y3 ) ))).
% 55.16/8.47 thf(zip_derived_cl17, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 (~ (quotient @ identity @ X0 @ X1)
% 55.16/8.47 | ~ (quotient @ identity @ X1 @ X2)
% 55.16/8.47 | ~ (quotient @ identity @ X2 @ X3)
% 55.16/8.47 | ((X1) = (X3)))),
% 55.16/8.47 inference('cnf', [status(esa)], [one_inversion_equals_three])).
% 55.16/8.47 thf(zip_derived_cl99, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 (((idQa) = (X0))
% 55.16/8.47 | ~ (quotient @ identity @ X1 @ X0)
% 55.16/8.47 | ~ (quotient @ identity @ idQa @ X1))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl17])).
% 55.16/8.47 thf(zip_derived_cl968, plain,
% 55.16/8.47 (![X0 : $i]: (~ (quotient @ identity @ idQ_idQa @ X0) | ((idQa) = (X0)))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl99])).
% 55.16/8.47 thf(zip_derived_cl971, plain, (((idQa) = (divide @ identity @ idQ_idQa))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl968])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl975, plain, ( (quotient @ identity @ idQ_idQa @ idQa)),
% 55.16/8.47 inference('sup+', [status(thm)], [zip_derived_cl971, zip_derived_cl7])).
% 55.16/8.47 thf(idQb_divide_idQ_idQa, axiom,
% 55.16/8.47 (quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa)).
% 55.16/8.47 thf(zip_derived_cl24, plain,
% 55.16/8.47 ( (quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa)),
% 55.16/8.47 inference('cnf', [status(esa)], [idQb_divide_idQ_idQa])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(identity_divide_idQb, axiom, (quotient @ identity @ idQb @ idQ_idQb)).
% 55.16/8.47 thf(zip_derived_cl21, plain, ( (quotient @ identity @ idQb @ idQ_idQb)),
% 55.16/8.47 inference('cnf', [status(esa)], [identity_divide_idQb])).
% 55.16/8.47 thf(quotient_property, axiom,
% 55.16/8.47 (( ~( quotient @ X @ Y @ V1 ) ) | ( ~( quotient @ Y @ Z @ V2 ) ) |
% 55.16/8.47 ( ~( quotient @ X @ Z @ V3 ) ) | ( ~( quotient @ V3 @ V2 @ V4 ) ) |
% 55.16/8.47 ( ~( quotient @ V1 @ Z @ V5 ) ) | ( less_equal @ V4 @ V5 ))).
% 55.16/8.47 thf(zip_derived_cl3, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 55.16/8.47 (~ (quotient @ X0 @ X1 @ X2)
% 55.16/8.47 | ~ (quotient @ X1 @ X3 @ X4)
% 55.16/8.47 | ~ (quotient @ X0 @ X3 @ X5)
% 55.16/8.47 | ~ (quotient @ X5 @ X4 @ X6)
% 55.16/8.47 | ~ (quotient @ X2 @ X3 @ X7)
% 55.16/8.47 | (less_equal @ X6 @ X7))),
% 55.16/8.47 inference('cnf', [status(esa)], [quotient_property])).
% 55.16/8.47 thf(zip_derived_cl78, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 55.16/8.47 ( (less_equal @ X1 @ X0)
% 55.16/8.47 | ~ (quotient @ idQ_idQb @ X2 @ X0)
% 55.16/8.47 | ~ (quotient @ X4 @ X3 @ X1)
% 55.16/8.47 | ~ (quotient @ identity @ X2 @ X4)
% 55.16/8.47 | ~ (quotient @ idQb @ X2 @ X3))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl3])).
% 55.16/8.47 thf(zip_derived_cl520, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 (~ (quotient @ idQb @ X0 @ X1)
% 55.16/8.47 | ~ (quotient @ identity @ X0 @ X2)
% 55.16/8.47 | ~ (quotient @ X2 @ X1 @ X3)
% 55.16/8.47 | (less_equal @ X3 @ (divide @ idQ_idQb @ X0)))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl78])).
% 55.16/8.47 thf(zip_derived_cl5758, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 ( (less_equal @ X0 @ (divide @ idQ_idQb @ idQ_idQa))
% 55.16/8.47 | ~ (quotient @ X1 @ idQb_Q__idQ_idQa @ X0)
% 55.16/8.47 | ~ (quotient @ identity @ idQ_idQa @ X1))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl520])).
% 55.16/8.47 thf(zip_derived_cl59251, plain,
% 55.16/8.47 (![X0 : $i]:
% 55.16/8.47 (~ (quotient @ idQa @ idQb_Q__idQ_idQa @ X0)
% 55.16/8.47 | (less_equal @ X0 @ (divide @ idQ_idQb @ idQ_idQa)))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl975, zip_derived_cl5758])).
% 55.16/8.47 thf(zip_derived_cl59253, plain,
% 55.16/8.47 ( (less_equal @ (divide @ idQa @ idQb_Q__idQ_idQa) @
% 55.16/8.47 (divide @ idQ_idQb @ idQ_idQa))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl59251])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(divisor_existence, axiom,
% 55.16/8.47 (( ~( quotient @ X @ Y @ Z ) ) | ( less_equal @ Z @ X ))).
% 55.16/8.47 thf(zip_derived_cl2, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.16/8.47 (~ (quotient @ X0 @ X1 @ X2) | (less_equal @ X2 @ X0))),
% 55.16/8.47 inference('cnf', [status(esa)], [divisor_existence])).
% 55.16/8.47 thf(zip_derived_cl51, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (less_equal @ (divide @ X1 @ X0) @ X1)),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 55.16/8.47 thf(quotient_less_equal, axiom,
% 55.16/8.47 (( ~( less_equal @ X @ Y ) ) | ( quotient @ X @ Y @ zero ))).
% 55.16/8.47 thf(zip_derived_cl0, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 (~ (less_equal @ X0 @ X1) | (quotient @ X0 @ X1 @ zero))),
% 55.16/8.47 inference('cnf', [status(esa)], [quotient_less_equal])).
% 55.16/8.47 thf(zip_derived_cl215, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ (divide @ X0 @ X1) @ X0 @ zero)),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl0])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(xLEy_implies_xQzLEyQz, axiom,
% 55.16/8.47 (( ~( less_equal @ X @ Y ) ) | ( ~( quotient @ X @ Z @ W1 ) ) |
% 55.16/8.47 ( ~( quotient @ Y @ Z @ W2 ) ) | ( less_equal @ W1 @ W2 ))).
% 55.16/8.47 thf(zip_derived_cl16, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 55.16/8.47 (~ (less_equal @ X0 @ X1)
% 55.16/8.47 | ~ (quotient @ X0 @ X2 @ X3)
% 55.16/8.47 | ~ (quotient @ X1 @ X2 @ X4)
% 55.16/8.47 | (less_equal @ X3 @ X4))),
% 55.16/8.47 inference('cnf', [status(esa)], [xLEy_implies_xQzLEyQz])).
% 55.16/8.47 thf(zip_derived_cl146, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 ( (less_equal @ (divide @ X1 @ X0) @ X2)
% 55.16/8.47 | ~ (quotient @ X3 @ X0 @ X2)
% 55.16/8.47 | ~ (less_equal @ X1 @ X3))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl16])).
% 55.16/8.47 thf(zip_derived_cl1993, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.16/8.47 (~ (less_equal @ X2 @ (divide @ X0 @ X1))
% 55.16/8.47 | (less_equal @ (divide @ X2 @ X0) @ zero))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl215, zip_derived_cl146])).
% 55.16/8.47 thf(zip_derived_cl60067, plain,
% 55.16/8.47 ( (less_equal @
% 55.16/8.47 (divide @ (divide @ idQa @ idQb_Q__idQ_idQa) @ idQ_idQb) @ zero)),
% 55.16/8.47 inference('sup-', [status(thm)],
% 55.16/8.47 [zip_derived_cl59253, zip_derived_cl1993])).
% 55.16/8.47 thf(zero_is_smallest, axiom, (less_equal @ zero @ X)).
% 55.16/8.47 thf(zip_derived_cl4, plain, (![X0 : $i]: (less_equal @ zero @ X0)),
% 55.16/8.47 inference('cnf', [status(esa)], [zero_is_smallest])).
% 55.16/8.47 thf(less_equal_and_equal, axiom,
% 55.16/8.47 (( ~( less_equal @ X @ Y ) ) | ( ~( less_equal @ Y @ X ) ) |
% 55.16/8.47 ( ( X ) = ( Y ) ))).
% 55.16/8.47 thf(zip_derived_cl5, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 55.16/8.47 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 55.16/8.47 thf(zip_derived_cl29, plain,
% 55.16/8.47 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 55.16/8.47 thf(zip_derived_cl60565, plain,
% 55.16/8.47 (((zero) = (divide @ (divide @ idQa @ idQb_Q__idQ_idQa) @ idQ_idQb))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl60067, zip_derived_cl29])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(x_divde_zero_is_x, axiom, (quotient @ X @ zero @ X)).
% 55.16/8.47 thf(zip_derived_cl12, plain, (![X0 : $i]: (quotient @ X0 @ zero @ X0)),
% 55.16/8.47 inference('cnf', [status(esa)], [x_divde_zero_is_x])).
% 55.16/8.47 thf(zip_derived_cl2, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.16/8.47 (~ (quotient @ X0 @ X1 @ X2) | (less_equal @ X2 @ X0))),
% 55.16/8.47 inference('cnf', [status(esa)], [divisor_existence])).
% 55.16/8.47 thf(zip_derived_cl34, plain, (![X0 : $i]: (less_equal @ X0 @ X0)),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl2])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(xQyLEz_implies_xQzLEy, axiom,
% 55.16/8.47 (( ~( quotient @ X @ Y @ W1 ) ) | ( ~( less_equal @ W1 @ Z ) ) |
% 55.16/8.47 ( ~( quotient @ X @ Z @ W2 ) ) | ( less_equal @ W2 @ Y ))).
% 55.16/8.47 thf(zip_derived_cl14, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 55.16/8.47 (~ (quotient @ X0 @ X1 @ X2)
% 55.16/8.47 | ~ (less_equal @ X2 @ X3)
% 55.16/8.47 | ~ (quotient @ X0 @ X3 @ X4)
% 55.16/8.47 | (less_equal @ X4 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [xQyLEz_implies_xQzLEy])).
% 55.16/8.47 thf(zip_derived_cl116, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 ( (less_equal @ X2 @ X0)
% 55.16/8.47 | ~ (quotient @ X1 @ X3 @ X2)
% 55.16/8.47 | ~ (less_equal @ (divide @ X1 @ X0) @ X3))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl14])).
% 55.16/8.47 thf(zip_derived_cl1339, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.16/8.47 (~ (quotient @ X1 @ (divide @ X1 @ X0) @ X2) | (less_equal @ X2 @ X0))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl34, zip_derived_cl116])).
% 55.16/8.47 thf(zip_derived_cl4314, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 (less_equal @ (divide @ X1 @ (divide @ X1 @ X0)) @ X0)),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1339])).
% 55.16/8.47 thf(zip_derived_cl60607, plain,
% 55.16/8.47 ( (less_equal @ (divide @ (divide @ idQa @ idQb_Q__idQ_idQa) @ zero) @
% 55.16/8.47 idQ_idQb)),
% 55.16/8.47 inference('sup+', [status(thm)],
% 55.16/8.47 [zip_derived_cl60565, zip_derived_cl4314])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl12, plain, (![X0 : $i]: (quotient @ X0 @ zero @ X0)),
% 55.16/8.47 inference('cnf', [status(esa)], [x_divde_zero_is_x])).
% 55.16/8.47 thf(well_defined, axiom,
% 55.16/8.47 (( ~( quotient @ X @ Y @ Z ) ) | ( ~( quotient @ X @ Y @ W ) ) |
% 55.16/8.47 ( ( Z ) = ( W ) ))).
% 55.16/8.47 thf(zip_derived_cl8, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 (~ (quotient @ X0 @ X1 @ X2)
% 55.16/8.47 | ~ (quotient @ X0 @ X1 @ X3)
% 55.16/8.47 | ((X2) = (X3)))),
% 55.16/8.47 inference('cnf', [status(esa)], [well_defined])).
% 55.16/8.47 thf(zip_derived_cl54, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (quotient @ X0 @ zero @ X1))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl8])).
% 55.16/8.47 thf(zip_derived_cl166, plain, (![X0 : $i]: ((X0) = (divide @ X0 @ zero))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl54])).
% 55.16/8.47 thf(zip_derived_cl60665, plain,
% 55.16/8.47 ( (less_equal @ (divide @ idQa @ idQb_Q__idQ_idQa) @ idQ_idQb)),
% 55.16/8.47 inference('demod', [status(thm)],
% 55.16/8.47 [zip_derived_cl60607, zip_derived_cl166])).
% 55.16/8.47 thf(zip_derived_cl116, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 ( (less_equal @ X2 @ X0)
% 55.16/8.47 | ~ (quotient @ X1 @ X3 @ X2)
% 55.16/8.47 | ~ (less_equal @ (divide @ X1 @ X0) @ X3))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl14])).
% 55.16/8.47 thf(zip_derived_cl60699, plain,
% 55.16/8.47 (![X0 : $i]:
% 55.16/8.47 (~ (quotient @ idQa @ idQ_idQb @ X0)
% 55.16/8.47 | (less_equal @ X0 @ idQb_Q__idQ_idQa))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl60665, zip_derived_cl116])).
% 55.16/8.47 thf(zip_derived_cl60737, plain,
% 55.16/8.47 ( (less_equal @ (divide @ idQa @ idQ_idQb) @ idQb_Q__idQ_idQa)),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl60699])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(idQa_divide_idQ_idQb, axiom,
% 55.16/8.47 (quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb)).
% 55.16/8.47 thf(zip_derived_cl22, plain,
% 55.16/8.47 ( (quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb)),
% 55.16/8.47 inference('cnf', [status(esa)], [idQa_divide_idQ_idQb])).
% 55.16/8.47 thf(zip_derived_cl8, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 (~ (quotient @ X0 @ X1 @ X2)
% 55.16/8.47 | ~ (quotient @ X0 @ X1 @ X3)
% 55.16/8.47 | ((X2) = (X3)))),
% 55.16/8.47 inference('cnf', [status(esa)], [well_defined])).
% 55.16/8.47 thf(zip_derived_cl61, plain,
% 55.16/8.47 (![X0 : $i]:
% 55.16/8.47 (((idQa_Q__idQ_idQb) = (X0)) | ~ (quotient @ idQa @ idQ_idQb @ X0))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl8])).
% 55.16/8.47 thf(zip_derived_cl91, plain,
% 55.16/8.47 (((idQa_Q__idQ_idQb) = (divide @ idQa @ idQ_idQb))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl61])).
% 55.16/8.47 thf(zip_derived_cl24, plain,
% 55.16/8.47 ( (quotient @ idQb @ idQ_idQa @ idQb_Q__idQ_idQa)),
% 55.16/8.47 inference('cnf', [status(esa)], [idQb_divide_idQ_idQa])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl21, plain, ( (quotient @ identity @ idQb @ idQ_idQb)),
% 55.16/8.47 inference('cnf', [status(esa)], [identity_divide_idQb])).
% 55.16/8.47 thf(identity_divide_b, axiom, (quotient @ identity @ b @ idQb)).
% 55.16/8.47 thf(zip_derived_cl20, plain, ( (quotient @ identity @ b @ idQb)),
% 55.16/8.47 inference('cnf', [status(esa)], [identity_divide_b])).
% 55.16/8.47 thf(zip_derived_cl17, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 (~ (quotient @ identity @ X0 @ X1)
% 55.16/8.47 | ~ (quotient @ identity @ X1 @ X2)
% 55.16/8.47 | ~ (quotient @ identity @ X2 @ X3)
% 55.16/8.47 | ((X1) = (X3)))),
% 55.16/8.47 inference('cnf', [status(esa)], [one_inversion_equals_three])).
% 55.16/8.47 thf(zip_derived_cl101, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 (((idQb) = (X0))
% 55.16/8.47 | ~ (quotient @ identity @ X1 @ X0)
% 55.16/8.47 | ~ (quotient @ identity @ idQb @ X1))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl17])).
% 55.16/8.47 thf(zip_derived_cl1030, plain,
% 55.16/8.47 (![X0 : $i]: (~ (quotient @ identity @ idQ_idQb @ X0) | ((idQb) = (X0)))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl101])).
% 55.16/8.47 thf(zip_derived_cl1033, plain, (((idQb) = (divide @ identity @ idQ_idQb))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1030])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl1053, plain, ( (quotient @ identity @ idQ_idQb @ idQb)),
% 55.16/8.47 inference('sup+', [status(thm)], [zip_derived_cl1033, zip_derived_cl7])).
% 55.16/8.47 thf(zip_derived_cl22, plain,
% 55.16/8.47 ( (quotient @ idQa @ idQ_idQb @ idQa_Q__idQ_idQb)),
% 55.16/8.47 inference('cnf', [status(esa)], [idQa_divide_idQ_idQb])).
% 55.16/8.47 thf(zip_derived_cl7, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]: (quotient @ X0 @ X1 @ (divide @ X0 @ X1))),
% 55.16/8.47 inference('cnf', [status(esa)], [closure])).
% 55.16/8.47 thf(zip_derived_cl23, plain, ( (quotient @ identity @ idQa @ idQ_idQa)),
% 55.16/8.47 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 55.16/8.47 thf(zip_derived_cl3, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 55.16/8.47 (~ (quotient @ X0 @ X1 @ X2)
% 55.16/8.47 | ~ (quotient @ X1 @ X3 @ X4)
% 55.16/8.47 | ~ (quotient @ X0 @ X3 @ X5)
% 55.16/8.47 | ~ (quotient @ X5 @ X4 @ X6)
% 55.16/8.47 | ~ (quotient @ X2 @ X3 @ X7)
% 55.16/8.47 | (less_equal @ X6 @ X7))),
% 55.16/8.47 inference('cnf', [status(esa)], [quotient_property])).
% 55.16/8.47 thf(zip_derived_cl76, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 55.16/8.47 ( (less_equal @ X1 @ X0)
% 55.16/8.47 | ~ (quotient @ idQ_idQa @ X2 @ X0)
% 55.16/8.47 | ~ (quotient @ X4 @ X3 @ X1)
% 55.16/8.47 | ~ (quotient @ identity @ X2 @ X4)
% 55.16/8.47 | ~ (quotient @ idQa @ X2 @ X3))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl3])).
% 55.16/8.47 thf(zip_derived_cl452, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 (~ (quotient @ idQa @ X0 @ X1)
% 55.16/8.47 | ~ (quotient @ identity @ X0 @ X2)
% 55.16/8.47 | ~ (quotient @ X2 @ X1 @ X3)
% 55.16/8.47 | (less_equal @ X3 @ (divide @ idQ_idQa @ X0)))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl76])).
% 55.16/8.47 thf(zip_derived_cl4945, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 ( (less_equal @ X0 @ (divide @ idQ_idQa @ idQ_idQb))
% 55.16/8.47 | ~ (quotient @ X1 @ idQa_Q__idQ_idQb @ X0)
% 55.16/8.47 | ~ (quotient @ identity @ idQ_idQb @ X1))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl452])).
% 55.16/8.47 thf(zip_derived_cl47731, plain,
% 55.16/8.47 (![X0 : $i]:
% 55.16/8.47 (~ (quotient @ idQb @ idQa_Q__idQ_idQb @ X0)
% 55.16/8.47 | (less_equal @ X0 @ (divide @ idQ_idQa @ idQ_idQb)))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl1053, zip_derived_cl4945])).
% 55.16/8.47 thf(zip_derived_cl47809, plain,
% 55.16/8.47 ( (less_equal @ (divide @ idQb @ idQa_Q__idQ_idQb) @
% 55.16/8.47 (divide @ idQ_idQa @ idQ_idQb))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl47731])).
% 55.16/8.47 thf(zip_derived_cl1993, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 55.16/8.47 (~ (less_equal @ X2 @ (divide @ X0 @ X1))
% 55.16/8.47 | (less_equal @ (divide @ X2 @ X0) @ zero))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl215, zip_derived_cl146])).
% 55.16/8.47 thf(zip_derived_cl48677, plain,
% 55.16/8.47 ( (less_equal @
% 55.16/8.47 (divide @ (divide @ idQb @ idQa_Q__idQ_idQb) @ idQ_idQa) @ zero)),
% 55.16/8.47 inference('sup-', [status(thm)],
% 55.16/8.47 [zip_derived_cl47809, zip_derived_cl1993])).
% 55.16/8.47 thf(zip_derived_cl29, plain,
% 55.16/8.47 (![X0 : $i]: (((zero) = (X0)) | ~ (less_equal @ X0 @ zero))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 55.16/8.47 thf(zip_derived_cl48920, plain,
% 55.16/8.47 (((zero) = (divide @ (divide @ idQb @ idQa_Q__idQ_idQb) @ idQ_idQa))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl48677, zip_derived_cl29])).
% 55.16/8.47 thf(zip_derived_cl4314, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 (less_equal @ (divide @ X1 @ (divide @ X1 @ X0)) @ X0)),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1339])).
% 55.16/8.47 thf(zip_derived_cl48961, plain,
% 55.16/8.47 ( (less_equal @ (divide @ (divide @ idQb @ idQa_Q__idQ_idQb) @ zero) @
% 55.16/8.47 idQ_idQa)),
% 55.16/8.47 inference('sup+', [status(thm)],
% 55.16/8.47 [zip_derived_cl48920, zip_derived_cl4314])).
% 55.16/8.47 thf(zip_derived_cl166, plain, (![X0 : $i]: ((X0) = (divide @ X0 @ zero))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl54])).
% 55.16/8.47 thf(zip_derived_cl49008, plain,
% 55.16/8.47 ( (less_equal @ (divide @ idQb @ idQa_Q__idQ_idQb) @ idQ_idQa)),
% 55.16/8.47 inference('demod', [status(thm)],
% 55.16/8.47 [zip_derived_cl48961, zip_derived_cl166])).
% 55.16/8.47 thf(zip_derived_cl116, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 55.16/8.47 ( (less_equal @ X2 @ X0)
% 55.16/8.47 | ~ (quotient @ X1 @ X3 @ X2)
% 55.16/8.47 | ~ (less_equal @ (divide @ X1 @ X0) @ X3))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl14])).
% 55.16/8.47 thf(zip_derived_cl49171, plain,
% 55.16/8.47 (![X0 : $i]:
% 55.16/8.47 (~ (quotient @ idQb @ idQ_idQa @ X0)
% 55.16/8.47 | (less_equal @ X0 @ idQa_Q__idQ_idQb))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl49008, zip_derived_cl116])).
% 55.16/8.47 thf(zip_derived_cl49186, plain,
% 55.16/8.47 ( (less_equal @ idQb_Q__idQ_idQa @ idQa_Q__idQ_idQb)),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl49171])).
% 55.16/8.47 thf(zip_derived_cl5, plain,
% 55.16/8.47 (![X0 : $i, X1 : $i]:
% 55.16/8.47 (~ (less_equal @ X0 @ X1) | ~ (less_equal @ X1 @ X0) | ((X0) = (X1)))),
% 55.16/8.47 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 55.16/8.47 thf(zip_derived_cl49189, plain,
% 55.16/8.47 ((((idQb_Q__idQ_idQa) = (idQa_Q__idQ_idQb))
% 55.16/8.47 | ~ (less_equal @ idQa_Q__idQ_idQb @ idQb_Q__idQ_idQa))),
% 55.16/8.47 inference('sup-', [status(thm)], [zip_derived_cl49186, zip_derived_cl5])).
% 55.16/8.47 thf(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa, conjecture,
% 55.16/8.47 (( idQa_Q__idQ_idQb ) = ( idQb_Q__idQ_idQa ))).
% 55.16/8.47 thf(zf_stmt_0, negated_conjecture,
% 55.16/8.47 (( idQa_Q__idQ_idQb ) != ( idQb_Q__idQ_idQa )),
% 55.16/8.47 inference('cnf.neg', [status(esa)],
% 55.16/8.47 [prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa])).
% 55.16/8.47 thf(zip_derived_cl25, plain, (((idQa_Q__idQ_idQb) != (idQb_Q__idQ_idQa))),
% 55.16/8.47 inference('cnf', [status(esa)], [zf_stmt_0])).
% 55.16/8.47 thf(zip_derived_cl49220, plain,
% 55.16/8.47 (~ (less_equal @ idQa_Q__idQ_idQb @ idQb_Q__idQ_idQa)),
% 55.16/8.47 inference('simplify_reflect-', [status(thm)],
% 55.16/8.47 [zip_derived_cl49189, zip_derived_cl25])).
% 55.16/8.47 thf(zip_derived_cl60739, plain, ($false),
% 55.16/8.47 inference('demod', [status(thm)],
% 55.16/8.47 [zip_derived_cl60737, zip_derived_cl91, zip_derived_cl49220])).
% 55.16/8.47
% 55.16/8.47 % SZS output end Refutation
% 55.16/8.47
% 55.16/8.47
% 55.16/8.47 % Terminating...
% 55.16/8.56 % Runner terminated.
% 55.16/8.58 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------