TSTP Solution File: HEN010-10 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : HEN010-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.AIvujS1U3i true
% Computer : n026.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 01:57:52 EDT 2023
% Result : Unsatisfiable 18.19s 3.23s
% Output : Refutation 18.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN010-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.AIvujS1U3i true
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 13:49:47 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 18.19/3.23 % Solved by fo/fo6_bce.sh.
% 18.19/3.23 % BCE start: 23
% 18.19/3.23 % BCE eliminated: 0
% 18.19/3.23 % PE start: 23
% 18.19/3.23 logic: eq
% 18.19/3.23 % PE eliminated: 0
% 18.19/3.23 % done 1572 iterations in 2.490s
% 18.19/3.23 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 18.19/3.23 % SZS output start Refutation
% 18.19/3.23 thf(idQa_Q__idQ_idQa_type, type, idQa_Q__idQ_idQa: $i).
% 18.19/3.23 thf(idQ_idQa_type, type, idQ_idQa: $i).
% 18.19/3.23 thf(true_type, type, true: $i).
% 18.19/3.23 thf(idQa_type, type, idQa: $i).
% 18.19/3.23 thf(a_type, type, a: $i).
% 18.19/3.23 thf(ifeq2_type, type, ifeq2: $i > $i > $i > $i > $i).
% 18.19/3.23 thf(zero_type, type, zero: $i).
% 18.19/3.23 thf(divide_type, type, divide: $i > $i > $i).
% 18.19/3.23 thf(quotient_type, type, quotient: $i > $i > $i > $i).
% 18.19/3.23 thf(identity_type, type, identity: $i).
% 18.19/3.23 thf(less_equal_type, type, less_equal: $i > $i > $i).
% 18.19/3.23 thf(ifeq_type, type, ifeq: $i > $i > $i > $i > $i).
% 18.19/3.23 thf(closure, axiom, (( quotient @ X @ Y @ ( divide @ X @ Y ) ) = ( true ))).
% 18.19/3.23 thf(zip_derived_cl9, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((quotient @ X0 @ X1 @ (divide @ X0 @ X1)) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [closure])).
% 18.19/3.23 thf(identity_divide_a, axiom,
% 18.19/3.23 (( quotient @ identity @ a @ idQa ) = ( true ))).
% 18.19/3.23 thf(zip_derived_cl19, plain, (((quotient @ identity @ a @ idQa) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_divide_a])).
% 18.19/3.23 thf(identity_divide_idQa, axiom,
% 18.19/3.23 (( quotient @ identity @ idQa @ idQ_idQa ) = ( true ))).
% 18.19/3.23 thf(zip_derived_cl20, plain,
% 18.19/3.23 (((quotient @ identity @ idQa @ idQ_idQa) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_divide_idQa])).
% 18.19/3.23 thf(xQyLEz_implies_xQzLEy, axiom,
% 18.19/3.23 (( ifeq @
% 18.19/3.23 ( quotient @ X @ Z @ W2 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( quotient @ X @ Y @ W1 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( less_equal @ W1 @ Z ) @ true @ ( less_equal @ W2 @ Y ) @ true ) @
% 18.19/3.23 true ) @
% 18.19/3.23 true ) =
% 18.19/3.23 ( true ))).
% 18.19/3.23 thf(zip_derived_cl16, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X0 @ X1 @ X2) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X0 @ X3 @ X4) @ true @
% 18.19/3.23 (ifeq @ (less_equal @ X4 @ X1) @ true @ (less_equal @ X2 @ X3) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [xQyLEz_implies_xQzLEy])).
% 18.19/3.23 thf(zip_derived_cl259, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((ifeq @ true @ true @
% 18.19/3.23 (ifeq @ (quotient @ identity @ X0 @ X1) @ true @
% 18.19/3.23 (ifeq @ (less_equal @ X1 @ idQa) @ true @
% 18.19/3.23 (less_equal @ idQ_idQa @ X0) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 18.19/3.23 thf(zip_derived_cl4408, plain,
% 18.19/3.23 (((ifeq @ true @ true @
% 18.19/3.23 (ifeq @ true @ true @
% 18.19/3.23 (ifeq @ (less_equal @ idQa @ idQa) @ true @
% 18.19/3.23 (less_equal @ idQ_idQa @ a) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl259])).
% 18.19/3.23 thf(x_divide_x_is_zero, axiom, (( quotient @ X @ X @ zero ) = ( true ))).
% 18.19/3.23 thf(zip_derived_cl13, plain,
% 18.19/3.23 (![X0 : $i]: ((quotient @ X0 @ X0 @ zero) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [x_divide_x_is_zero])).
% 18.19/3.23 thf(less_equal_quotient, axiom,
% 18.19/3.23 (( ifeq @
% 18.19/3.23 ( quotient @ X @ Y @ zero ) @ true @ ( less_equal @ X @ Y ) @ true ) =
% 18.19/3.23 ( true ))).
% 18.19/3.23 thf(zip_derived_cl3, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X0 @ X1 @ zero) @ true @
% 18.19/3.23 (less_equal @ X0 @ X1) @ true) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [less_equal_quotient])).
% 18.19/3.23 thf(zip_derived_cl30, plain,
% 18.19/3.23 (![X0 : $i]:
% 18.19/3.23 ((ifeq @ true @ true @ (less_equal @ X0 @ X0) @ true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl3])).
% 18.19/3.23 thf(ifeq_axiom_001, axiom, (( ifeq @ A @ A @ B @ C ) = ( B ))).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl58, plain, (![X0 : $i]: ((true) = (less_equal @ X0 @ X0))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl4424, plain, (((less_equal @ idQ_idQa @ a) = (true))),
% 18.19/3.23 inference('demod', [status(thm)],
% 18.19/3.23 [zip_derived_cl4408, zip_derived_cl58, zip_derived_cl1,
% 18.19/3.23 zip_derived_cl1, zip_derived_cl1])).
% 18.19/3.23 thf(identity_divide_idQ_idQa, axiom,
% 18.19/3.23 (( quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa ) = ( true ))).
% 18.19/3.23 thf(zip_derived_cl21, plain,
% 18.19/3.23 (((quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_divide_idQ_idQa])).
% 18.19/3.23 thf(xLEy_implies_zQyLEzQx, axiom,
% 18.19/3.23 (( ifeq @
% 18.19/3.23 ( quotient @ Z @ Y @ W1 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( quotient @ Z @ X @ W2 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( less_equal @ X @ Y ) @ true @ ( less_equal @ W1 @ W2 ) @ true ) @
% 18.19/3.23 true ) @
% 18.19/3.23 true ) =
% 18.19/3.23 ( true ))).
% 18.19/3.23 thf(zip_derived_cl17, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X0 @ X1 @ X2) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X0 @ X3 @ X4) @ true @
% 18.19/3.23 (ifeq @ (less_equal @ X3 @ X1) @ true @ (less_equal @ X2 @ X4) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [xLEy_implies_zQyLEzQx])).
% 18.19/3.23 thf(zip_derived_cl301, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ idQa @ X1 @ X0) @ true @
% 18.19/3.23 (ifeq @ true @ true @
% 18.19/3.23 (ifeq @ (less_equal @ idQ_idQa @ X1) @ true @
% 18.19/3.23 (less_equal @ X0 @ idQa_Q__idQ_idQa) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl17])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl323, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ idQa @ X1 @ X0) @ true @
% 18.19/3.23 (ifeq @ (less_equal @ idQ_idQa @ X1) @ true @
% 18.19/3.23 (less_equal @ X0 @ idQa_Q__idQ_idQa) @ true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('demod', [status(thm)], [zip_derived_cl301, zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl6421, plain,
% 18.19/3.23 (![X0 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ idQa @ a @ X0) @ true @
% 18.19/3.23 (ifeq @ true @ true @ (less_equal @ X0 @ idQa_Q__idQ_idQa) @ true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)],
% 18.19/3.23 [zip_derived_cl4424, zip_derived_cl323])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl6433, plain,
% 18.19/3.23 (![X0 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ idQa @ a @ X0) @ true @
% 18.19/3.23 (less_equal @ X0 @ idQa_Q__idQ_idQa) @ true) = (true))),
% 18.19/3.23 inference('demod', [status(thm)], [zip_derived_cl6421, zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl10957, plain,
% 18.19/3.23 (((ifeq @ true @ true @
% 18.19/3.23 (less_equal @ (divide @ idQa @ a) @ idQa_Q__idQ_idQa) @ true) = (
% 18.19/3.23 true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl6433])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl11089, plain,
% 18.19/3.23 (((true) = (less_equal @ (divide @ idQa @ a) @ idQa_Q__idQ_idQa))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl10957, zip_derived_cl1])).
% 18.19/3.23 thf(less_equal_and_equal, axiom,
% 18.19/3.23 (( ifeq2 @
% 18.19/3.23 ( less_equal @ Y @ X ) @ true @
% 18.19/3.23 ( ifeq2 @ ( less_equal @ X @ Y ) @ true @ X @ Y ) @ Y ) =
% 18.19/3.23 ( Y ))).
% 18.19/3.23 thf(zip_derived_cl7, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((ifeq2 @ (less_equal @ X0 @ X1) @ true @
% 18.19/3.23 (ifeq2 @ (less_equal @ X1 @ X0) @ true @ X1 @ X0) @ X0) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 18.19/3.23 thf(zip_derived_cl11101, plain,
% 18.19/3.23 (((ifeq2 @ (less_equal @ idQa_Q__idQ_idQa @ (divide @ idQa @ a)) @
% 18.19/3.23 true @
% 18.19/3.23 (ifeq2 @ true @ true @ (divide @ idQa @ a) @ idQa_Q__idQ_idQa) @
% 18.19/3.23 idQa_Q__idQ_idQa) = (idQa_Q__idQ_idQa))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl11089, zip_derived_cl7])).
% 18.19/3.23 thf(ifeq_axiom, axiom, (( ifeq2 @ A @ A @ B @ C ) = ( B ))).
% 18.19/3.23 thf(zip_derived_cl0, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom])).
% 18.19/3.23 thf(zip_derived_cl11192, plain,
% 18.19/3.23 (((ifeq2 @ (less_equal @ idQa_Q__idQ_idQa @ (divide @ idQa @ a)) @
% 18.19/3.23 true @ (divide @ idQa @ a) @ idQa_Q__idQ_idQa) = (idQa_Q__idQ_idQa))),
% 18.19/3.23 inference('demod', [status(thm)], [zip_derived_cl11101, zip_derived_cl0])).
% 18.19/3.23 thf(zip_derived_cl9, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((quotient @ X0 @ X1 @ (divide @ X0 @ X1)) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [closure])).
% 18.19/3.23 thf(zip_derived_cl19, plain, (((quotient @ identity @ a @ idQa) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_divide_a])).
% 18.19/3.23 thf(zip_derived_cl19, plain, (((quotient @ identity @ a @ idQa) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_divide_a])).
% 18.19/3.23 thf(x_divde_zero_is_x, axiom, (( quotient @ X @ zero @ X ) = ( true ))).
% 18.19/3.23 thf(zip_derived_cl14, plain,
% 18.19/3.23 (![X0 : $i]: ((quotient @ X0 @ zero @ X0) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [x_divde_zero_is_x])).
% 18.19/3.23 thf(quotient_property, axiom,
% 18.19/3.23 (( ifeq @
% 18.19/3.23 ( quotient @ V3 @ V2 @ V4 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( quotient @ V1 @ Z @ V5 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( quotient @ Y @ Z @ V2 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( quotient @ X @ Z @ V3 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( quotient @ X @ Y @ V1 ) @ true @ ( less_equal @ V4 @ V5 ) @
% 18.19/3.23 true ) @
% 18.19/3.23 true ) @
% 18.19/3.23 true ) @
% 18.19/3.23 true ) @
% 18.19/3.23 true ) =
% 18.19/3.23 ( true ))).
% 18.19/3.23 thf(zip_derived_cl5, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X0 @ X1 @ X2) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X3 @ X4 @ X5) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X6 @ X4 @ X1) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X7 @ X4 @ X0) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X7 @ X6 @ X3) @ true @
% 18.19/3.23 (less_equal @ X2 @ X5) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [quotient_property])).
% 18.19/3.23 thf(zip_derived_cl99, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 18.19/3.23 ((ifeq @ true @ true @
% 18.19/3.23 (ifeq @ (quotient @ X2 @ X5 @ X0) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X3 @ X5 @ zero) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X4 @ X5 @ X1) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X4 @ X3 @ X2) @ true @
% 18.19/3.23 (less_equal @ X1 @ X0) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl5])).
% 18.19/3.23 thf(zip_derived_cl829, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.19/3.23 ((ifeq @ true @ true @
% 18.19/3.23 (ifeq @ (quotient @ idQa @ X2 @ X0) @ true @
% 18.19/3.23 (ifeq @ (quotient @ a @ X2 @ zero) @ true @
% 18.19/3.23 (ifeq @ (quotient @ identity @ X2 @ X1) @ true @
% 18.19/3.23 (ifeq @ true @ true @ (less_equal @ X1 @ X0) @ true) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl99])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl861, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ idQa @ X2 @ X0) @ true @
% 18.19/3.23 (ifeq @ (quotient @ a @ X2 @ zero) @ true @
% 18.19/3.23 (ifeq @ (quotient @ identity @ X2 @ X1) @ true @
% 18.19/3.23 (less_equal @ X1 @ X0) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('demod', [status(thm)],
% 18.19/3.23 [zip_derived_cl829, zip_derived_cl1, zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl19436, plain,
% 18.19/3.23 (![X0 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ idQa @ a @ X0) @ true @
% 18.19/3.23 (ifeq @ (quotient @ a @ a @ zero) @ true @
% 18.19/3.23 (ifeq @ true @ true @ (less_equal @ idQa @ X0) @ true) @ true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl861])).
% 18.19/3.23 thf(zip_derived_cl13, plain,
% 18.19/3.23 (![X0 : $i]: ((quotient @ X0 @ X0 @ zero) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [x_divide_x_is_zero])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl19478, plain,
% 18.19/3.23 (![X0 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ idQa @ a @ X0) @ true @
% 18.19/3.23 (less_equal @ idQa @ X0) @ true) = (true))),
% 18.19/3.23 inference('demod', [status(thm)],
% 18.19/3.23 [zip_derived_cl19436, zip_derived_cl13, zip_derived_cl1,
% 18.19/3.23 zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl20428, plain,
% 18.19/3.23 (((ifeq @ true @ true @ (less_equal @ idQa @ (divide @ idQa @ a)) @ true)
% 18.19/3.23 = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl19478])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl20458, plain,
% 18.19/3.23 (((true) = (less_equal @ idQa @ (divide @ idQa @ a)))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl20428, zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl7, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((ifeq2 @ (less_equal @ X0 @ X1) @ true @
% 18.19/3.23 (ifeq2 @ (less_equal @ X1 @ X0) @ true @ X1 @ X0) @ X0) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [less_equal_and_equal])).
% 18.19/3.23 thf(zip_derived_cl20462, plain,
% 18.19/3.23 (((ifeq2 @ true @ true @
% 18.19/3.23 (ifeq2 @ (less_equal @ (divide @ idQa @ a) @ idQa) @ true @
% 18.19/3.23 (divide @ idQa @ a) @ idQa) @
% 18.19/3.23 idQa) = (idQa))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl20458, zip_derived_cl7])).
% 18.19/3.23 thf(zip_derived_cl19, plain, (((quotient @ identity @ a @ idQa) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_divide_a])).
% 18.19/3.23 thf(zip_derived_cl9, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i]:
% 18.19/3.23 ((quotient @ X0 @ X1 @ (divide @ X0 @ X1)) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [closure])).
% 18.19/3.23 thf(xLEy_implies_xQzLEyQz, axiom,
% 18.19/3.23 (( ifeq @
% 18.19/3.23 ( quotient @ Y @ Z @ W2 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( quotient @ X @ Z @ W1 ) @ true @
% 18.19/3.23 ( ifeq @
% 18.19/3.23 ( less_equal @ X @ Y ) @ true @ ( less_equal @ W1 @ W2 ) @ true ) @
% 18.19/3.23 true ) @
% 18.19/3.23 true ) =
% 18.19/3.23 ( true ))).
% 18.19/3.23 thf(zip_derived_cl18, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X0 @ X1 @ X2) @ true @
% 18.19/3.23 (ifeq @ (quotient @ X3 @ X1 @ X4) @ true @
% 18.19/3.23 (ifeq @ (less_equal @ X3 @ X0) @ true @ (less_equal @ X4 @ X2) @
% 18.19/3.23 true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [xLEy_implies_xQzLEyQz])).
% 18.19/3.23 thf(zip_derived_cl339, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X3 @ X1 @ X0) @ true @
% 18.19/3.23 (ifeq @ true @ true @
% 18.19/3.23 (ifeq @ (less_equal @ X2 @ X3) @ true @
% 18.19/3.23 (less_equal @ (divide @ X2 @ X1) @ X0) @ true) @
% 18.19/3.23 true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl18])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl361, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X3 @ X1 @ X0) @ true @
% 18.19/3.23 (ifeq @ (less_equal @ X2 @ X3) @ true @
% 18.19/3.23 (less_equal @ (divide @ X2 @ X1) @ X0) @ true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('demod', [status(thm)], [zip_derived_cl339, zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl7268, plain,
% 18.19/3.23 (![X0 : $i]:
% 18.19/3.23 ((ifeq @ true @ true @
% 18.19/3.23 (ifeq @ (less_equal @ X0 @ identity) @ true @
% 18.19/3.23 (less_equal @ (divide @ X0 @ a) @ idQa) @ true) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl361])).
% 18.19/3.23 thf(identity_is_largest, axiom, (( less_equal @ X @ identity ) = ( true ))).
% 18.19/3.23 thf(zip_derived_cl8, plain,
% 18.19/3.23 (![X0 : $i]: ((less_equal @ X0 @ identity) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_is_largest])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl7297, plain,
% 18.19/3.23 (![X0 : $i]: ((less_equal @ (divide @ X0 @ a) @ idQa) = (true))),
% 18.19/3.23 inference('demod', [status(thm)],
% 18.19/3.23 [zip_derived_cl7268, zip_derived_cl8, zip_derived_cl1,
% 18.19/3.23 zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl0, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom])).
% 18.19/3.23 thf(zip_derived_cl0, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom])).
% 18.19/3.23 thf(zip_derived_cl20574, plain, (((divide @ idQa @ a) = (idQa))),
% 18.19/3.23 inference('demod', [status(thm)],
% 18.19/3.23 [zip_derived_cl20462, zip_derived_cl7297, zip_derived_cl0,
% 18.19/3.23 zip_derived_cl0])).
% 18.19/3.23 thf(zip_derived_cl21, plain,
% 18.19/3.23 (((quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [identity_divide_idQ_idQa])).
% 18.19/3.23 thf(divisor_existence, axiom,
% 18.19/3.23 (( ifeq @ ( quotient @ X @ Y @ Z ) @ true @ ( less_equal @ Z @ X ) @ true ) =
% 18.19/3.23 ( true ))).
% 18.19/3.23 thf(zip_derived_cl4, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.19/3.23 ((ifeq @ (quotient @ X0 @ X1 @ X2) @ true @ (less_equal @ X2 @ X0) @
% 18.19/3.23 true) = (true))),
% 18.19/3.23 inference('cnf', [status(esa)], [divisor_existence])).
% 18.19/3.23 thf(zip_derived_cl51, plain,
% 18.19/3.23 (((ifeq @ true @ true @ (less_equal @ idQa_Q__idQ_idQa @ idQa) @ true)
% 18.19/3.23 = (true))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl4])).
% 18.19/3.23 thf(zip_derived_cl1, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 18.19/3.23 thf(zip_derived_cl148, plain,
% 18.19/3.23 (((true) = (less_equal @ idQa_Q__idQ_idQa @ idQa))),
% 18.19/3.23 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl1])).
% 18.19/3.23 thf(zip_derived_cl20574, plain, (((divide @ idQa @ a) = (idQa))),
% 18.19/3.23 inference('demod', [status(thm)],
% 18.19/3.23 [zip_derived_cl20462, zip_derived_cl7297, zip_derived_cl0,
% 18.19/3.23 zip_derived_cl0])).
% 18.19/3.23 thf(zip_derived_cl0, plain,
% 18.19/3.23 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 18.19/3.23 inference('cnf', [status(esa)], [ifeq_axiom])).
% 18.19/3.23 thf(zip_derived_cl20672, plain, (((idQa) = (idQa_Q__idQ_idQa))),
% 18.19/3.23 inference('demod', [status(thm)],
% 18.19/3.23 [zip_derived_cl11192, zip_derived_cl20574, zip_derived_cl148,
% 18.19/3.23 zip_derived_cl20574, zip_derived_cl0])).
% 18.19/3.23 thf(prove_idQa_equals_idQa_Q__idQ_idQa, conjecture,
% 18.19/3.23 (( idQa ) = ( idQa_Q__idQ_idQa ))).
% 18.19/3.23 thf(zf_stmt_0, negated_conjecture, (( idQa ) != ( idQa_Q__idQ_idQa )),
% 18.19/3.23 inference('cnf.neg', [status(esa)], [prove_idQa_equals_idQa_Q__idQ_idQa])).
% 18.19/3.23 thf(zip_derived_cl22, plain, (((idQa) != (idQa_Q__idQ_idQa))),
% 18.19/3.23 inference('cnf', [status(esa)], [zf_stmt_0])).
% 18.19/3.23 thf(zip_derived_cl20673, plain, ($false),
% 18.19/3.23 inference('simplify_reflect-', [status(thm)],
% 18.19/3.23 [zip_derived_cl20672, zip_derived_cl22])).
% 18.19/3.23
% 18.19/3.23 % SZS output end Refutation
% 18.19/3.23
% 18.19/3.23
% 18.19/3.23 % Terminating...
% 18.19/3.29 % Runner terminated.
% 18.22/3.31 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------