TSTP Solution File: RNG008-5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : RNG008-5 : 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.Js2prQa1LG true
% Computer : n027.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 14:06:16 EDT 2023
% Result : Unsatisfiable 106.09s 15.90s
% Output : Refutation 106.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-5 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Js2prQa1LG true
% 0.13/0.34 % Computer : n027.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 : Sun Aug 27 03:06:20 EDT 2023
% 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
% 0.20/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.20/0.63 % Total configuration time : 435
% 0.20/0.63 % Estimated wc time : 1092
% 0.20/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.96/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 106.09/15.90 % Solved by fo/fo5.sh.
% 106.09/15.90 % done 19889 iterations in 15.125s
% 106.09/15.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 106.09/15.90 % SZS output start Refutation
% 106.09/15.90 thf(multiply_type, type, multiply: $i > $i > $i).
% 106.09/15.90 thf(sum_type, type, sum: $i > $i > $i > $o).
% 106.09/15.90 thf(b_type, type, b: $i).
% 106.09/15.90 thf(product_type, type, product: $i > $i > $i > $o).
% 106.09/15.90 thf(a_type, type, a: $i).
% 106.09/15.90 thf(additive_identity_type, type, additive_identity: $i).
% 106.09/15.90 thf(c_type, type, c: $i).
% 106.09/15.90 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 106.09/15.90 thf(add_type, type, add: $i > $i > $i).
% 106.09/15.90 thf(prove_b_times_a_is_c, conjecture, (product @ b @ a @ c)).
% 106.09/15.90 thf(zf_stmt_0, negated_conjecture, (~( product @ b @ a @ c )),
% 106.09/15.90 inference('cnf.neg', [status(esa)], [prove_b_times_a_is_c])).
% 106.09/15.90 thf(zip_derived_cl25, plain, (~ (product @ b @ a @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 106.09/15.90 thf(closure_of_addition, axiom, (sum @ X @ Y @ ( add @ X @ Y ))).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 106.09/15.90 thf(zip_derived_cl0, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [additive_identity1])).
% 106.09/15.90 thf(right_inverse, axiom,
% 106.09/15.90 (sum @ X @ ( additive_inverse @ X ) @ additive_identity)).
% 106.09/15.90 thf(zip_derived_cl5, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 106.09/15.90 inference('cnf', [status(esa)], [right_inverse])).
% 106.09/15.90 thf(associativity_of_addition1, axiom,
% 106.09/15.90 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 106.09/15.90 ( ~( sum @ U @ Z @ W ) ) | ( sum @ X @ V @ W ))).
% 106.09/15.90 thf(zip_derived_cl6, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (sum @ X1 @ X3 @ X4)
% 106.09/15.90 | ~ (sum @ X2 @ X3 @ X5)
% 106.09/15.90 | (sum @ X0 @ X4 @ X5))),
% 106.09/15.90 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 106.09/15.90 thf(zip_derived_cl82, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 ( (sum @ X0 @ X2 @ X1)
% 106.09/15.90 | ~ (sum @ additive_identity @ X3 @ X1)
% 106.09/15.90 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl6])).
% 106.09/15.90 thf(zip_derived_cl837, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (~ (sum @ (additive_inverse @ X2) @ X0 @ X1) | (sum @ X2 @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl82])).
% 106.09/15.90 thf(zip_derived_cl12275, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ X1 @ (add @ (additive_inverse @ X1) @ X0) @ X0)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl837])).
% 106.09/15.90 thf(commutativity_of_addition, axiom,
% 106.09/15.90 (( ~( sum @ X @ Y @ Z ) ) | ( sum @ Y @ X @ Z ))).
% 106.09/15.90 thf(zip_derived_cl8, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 106.09/15.90 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 106.09/15.90 thf(zip_derived_cl12396, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ (add @ (additive_inverse @ X1) @ X0) @ X1 @ X0)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl12275, zip_derived_cl8])).
% 106.09/15.90 thf(x_squared_is_x, axiom, (product @ X @ X @ X)).
% 106.09/15.90 thf(zip_derived_cl23, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [x_squared_is_x])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(multiply_additive_inverse, axiom,
% 106.09/15.90 (product @
% 106.09/15.90 X @ ( additive_inverse @ Y ) @ ( additive_inverse @ ( multiply @ X @ Y ) ))).
% 106.09/15.90 thf(zip_derived_cl22, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (product @ X0 @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (multiply @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiply_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl23, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [x_squared_is_x])).
% 106.09/15.90 thf(multiplication_is_well_defined, axiom,
% 106.09/15.90 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ X @ Y @ V ) ) |
% 106.09/15.90 ( ( U ) = ( V ) ))).
% 106.09/15.90 thf(zip_derived_cl16, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X1 @ X3)
% 106.09/15.90 | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl26, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (product @ X0 @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl62, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ((additive_inverse @ X0)
% 106.09/15.90 = (additive_inverse @ (multiply @ (additive_inverse @ X0) @ X0)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl26])).
% 106.09/15.90 thf(additive_inverse_additive_inverse, axiom,
% 106.09/15.90 (sum @
% 106.09/15.90 ( additive_inverse @ ( additive_inverse @ X ) ) @ additive_identity @ X)).
% 106.09/15.90 thf(zip_derived_cl18, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 (sum @ (additive_inverse @ (additive_inverse @ X0)) @
% 106.09/15.90 additive_identity @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [additive_inverse_additive_inverse])).
% 106.09/15.90 thf(additive_identity2, axiom, (sum @ X @ additive_identity @ X)).
% 106.09/15.90 thf(zip_derived_cl1, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [additive_identity2])).
% 106.09/15.90 thf(addition_is_well_defined, axiom,
% 106.09/15.90 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ X @ Y @ V ) ) | ( ( U ) = ( V ) ))).
% 106.09/15.90 thf(zip_derived_cl15, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl55, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl358, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ((additive_inverse @ (additive_inverse @ X0))
% 106.09/15.90 = (multiply @ (additive_inverse @ X0) @ X0))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl93])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl373, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (multiply @ (additive_inverse @ X0) @ X0))),
% 106.09/15.90 inference('demod', [status(thm)], [zip_derived_cl358, zip_derived_cl93])).
% 106.09/15.90 thf(closure_of_multiplication, axiom,
% 106.09/15.90 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl437, plain,
% 106.09/15.90 (![X0 : $i]: (product @ (additive_inverse @ X0) @ X0 @ X0)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl373, zip_derived_cl2])).
% 106.09/15.90 thf(zip_derived_cl5, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 106.09/15.90 inference('cnf', [status(esa)], [right_inverse])).
% 106.09/15.90 thf(distributivity4, axiom,
% 106.09/15.90 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 106.09/15.90 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 106.09/15.90 ( product @ V3 @ X @ V4 ))).
% 106.09/15.90 thf(zip_derived_cl14, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X3 @ X1 @ X4)
% 106.09/15.90 | ~ (sum @ X0 @ X3 @ X5)
% 106.09/15.90 | ~ (sum @ X2 @ X4 @ X6)
% 106.09/15.90 | (product @ X5 @ X1 @ X6))),
% 106.09/15.90 inference('cnf', [status(esa)], [distributivity4])).
% 106.09/15.90 thf(zip_derived_cl166, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (product @ additive_identity @ X2 @ X1)
% 106.09/15.90 | ~ (sum @ X4 @ X3 @ X1)
% 106.09/15.90 | ~ (product @ (additive_inverse @ X0) @ X2 @ X3)
% 106.09/15.90 | ~ (product @ X0 @ X2 @ X4))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl14])).
% 106.09/15.90 thf(zip_derived_cl4545, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X0 @ X1)
% 106.09/15.90 | ~ (sum @ X1 @ X0 @ X2)
% 106.09/15.90 | (product @ additive_identity @ X0 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl166])).
% 106.09/15.90 thf(zip_derived_cl56024, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ( (product @ additive_identity @ X0 @ (add @ X1 @ X0))
% 106.09/15.90 | ~ (product @ X0 @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4545])).
% 106.09/15.90 thf(zip_derived_cl56441, plain,
% 106.09/15.90 (![X0 : $i]: (product @ additive_identity @ X0 @ (add @ X0 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl56024])).
% 106.09/15.90 thf(multiply_additive_id2, axiom,
% 106.09/15.90 (product @ additive_identity @ X @ additive_identity)).
% 106.09/15.90 thf(zip_derived_cl20, plain,
% 106.09/15.90 (![X0 : $i]: (product @ additive_identity @ X0 @ additive_identity)),
% 106.09/15.90 inference('cnf', [status(esa)], [multiply_additive_id2])).
% 106.09/15.90 thf(zip_derived_cl16, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X1 @ X3)
% 106.09/15.90 | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl29, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((additive_identity) = (X1))
% 106.09/15.90 | ~ (product @ additive_identity @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl56540, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_identity) = (add @ X0 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl56441, zip_derived_cl29])).
% 106.09/15.90 thf(distribute_additive_inverse, axiom,
% 106.09/15.90 (sum @
% 106.09/15.90 ( additive_inverse @ X ) @ ( additive_inverse @ Y ) @
% 106.09/15.90 ( additive_inverse @ ( add @ X @ Y ) ))).
% 106.09/15.90 thf(zip_derived_cl21, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ (additive_inverse @ X0) @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (add @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [distribute_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl15, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl54, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X1 @ X0 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl297, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (additive_inverse @ X1) @ (additive_inverse @ X0))
% 106.09/15.90 = (additive_inverse @ (add @ X1 @ X0)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl54])).
% 106.09/15.90 thf(zip_derived_cl12275, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ X1 @ (add @ (additive_inverse @ X1) @ X0) @ X0)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl837])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl8, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2) | (sum @ X1 @ X0 @ X2))),
% 106.09/15.90 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 106.09/15.90 thf(zip_derived_cl53, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 106.09/15.90 thf(zip_derived_cl15, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl268, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl12398, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl12275, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl12719, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (additive_inverse @ (add @ X1 @ X0)) @ X1)
% 106.09/15.90 = (additive_inverse @ X0))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl297, zip_derived_cl12398])).
% 106.09/15.90 thf(zip_derived_cl56689, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ((add @ (additive_inverse @ additive_identity) @ X0)
% 106.09/15.90 = (additive_inverse @ X0))),
% 106.09/15.90 inference('sup+', [status(thm)],
% 106.09/15.90 [zip_derived_cl56540, zip_derived_cl12719])).
% 106.09/15.90 thf(left_inverse, axiom,
% 106.09/15.90 (sum @ ( additive_inverse @ X ) @ X @ additive_identity)).
% 106.09/15.90 thf(zip_derived_cl4, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 106.09/15.90 inference('cnf', [status(esa)], [left_inverse])).
% 106.09/15.90 thf(zip_derived_cl55, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl92, plain,
% 106.09/15.90 (((additive_inverse @ additive_identity) = (additive_identity))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl0, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [additive_identity1])).
% 106.09/15.90 thf(zip_derived_cl15, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl57, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl94, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl57])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl57468, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ (add @ X1 @ X0) @ X1 @ X0)),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl12396, zip_derived_cl57069])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl23, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [x_squared_is_x])).
% 106.09/15.90 thf(a_times_b_is_c, axiom, (product @ a @ b @ c)).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(associativity_of_multiplication2, axiom,
% 106.09/15.90 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 106.09/15.90 ( ~( product @ X @ V @ W ) ) | ( product @ U @ Z @ W ))).
% 106.09/15.90 thf(zip_derived_cl10, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X1 @ X3 @ X4)
% 106.09/15.90 | ~ (product @ X0 @ X4 @ X5)
% 106.09/15.90 | (product @ X2 @ X3 @ X5))),
% 106.09/15.90 inference('cnf', [status(esa)], [associativity_of_multiplication2])).
% 106.09/15.90 thf(zip_derived_cl109, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 ( (product @ c @ X1 @ X0)
% 106.09/15.90 | ~ (product @ a @ X2 @ X0)
% 106.09/15.90 | ~ (product @ b @ X1 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl10])).
% 106.09/15.90 thf(zip_derived_cl242, plain,
% 106.09/15.90 (![X0 : $i]: (~ (product @ b @ X0 @ b) | (product @ c @ X0 @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl109])).
% 106.09/15.90 thf(zip_derived_cl243, plain, ( (product @ c @ b @ c)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl242])).
% 106.09/15.90 thf(zip_derived_cl437, plain,
% 106.09/15.90 (![X0 : $i]: (product @ (additive_inverse @ X0) @ X0 @ X0)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl373, zip_derived_cl2])).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl10, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X1 @ X3 @ X4)
% 106.09/15.90 | ~ (product @ X0 @ X4 @ X5)
% 106.09/15.90 | (product @ X2 @ X3 @ X5))),
% 106.09/15.90 inference('cnf', [status(esa)], [associativity_of_multiplication2])).
% 106.09/15.90 thf(zip_derived_cl105, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 106.09/15.90 | ~ (product @ X1 @ X4 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X3 @ X4))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl10])).
% 106.09/15.90 thf(zip_derived_cl1185, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (~ (product @ X1 @ X0 @ b) | (product @ (multiply @ a @ X1) @ X0 @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl105])).
% 106.09/15.90 thf(zip_derived_cl1193, plain,
% 106.09/15.90 ( (product @ (multiply @ a @ (additive_inverse @ b)) @ b @ c)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl1185])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(zip_derived_cl16, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X1 @ X3)
% 106.09/15.90 | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl30, plain,
% 106.09/15.90 (![X0 : $i]: (((c) = (X0)) | ~ (product @ a @ b @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl32, plain, (((c) = (multiply @ a @ b))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl30])).
% 106.09/15.90 thf(zip_derived_cl22, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (product @ X0 @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (multiply @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiply_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl64, plain,
% 106.09/15.90 ( (product @ a @ (additive_inverse @ b) @ (additive_inverse @ c))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl22])).
% 106.09/15.90 thf(zip_derived_cl16, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X1 @ X3)
% 106.09/15.90 | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl187, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 (((additive_inverse @ c) = (X0))
% 106.09/15.90 | ~ (product @ a @ (additive_inverse @ b) @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl191, plain,
% 106.09/15.90 (((additive_inverse @ c) = (multiply @ a @ (additive_inverse @ b)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl187])).
% 106.09/15.90 thf(zip_derived_cl1195, plain, ( (product @ (additive_inverse @ c) @ b @ c)),
% 106.09/15.90 inference('demod', [status(thm)], [zip_derived_cl1193, zip_derived_cl191])).
% 106.09/15.90 thf(zip_derived_cl166, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (product @ additive_identity @ X2 @ X1)
% 106.09/15.90 | ~ (sum @ X4 @ X3 @ X1)
% 106.09/15.90 | ~ (product @ (additive_inverse @ X0) @ X2 @ X3)
% 106.09/15.90 | ~ (product @ X0 @ X2 @ X4))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl14])).
% 106.09/15.90 thf(zip_derived_cl4548, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (~ (product @ c @ b @ X0)
% 106.09/15.90 | ~ (sum @ X0 @ c @ X1)
% 106.09/15.90 | (product @ additive_identity @ b @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl1195, zip_derived_cl166])).
% 106.09/15.90 thf(zip_derived_cl4559, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ( (product @ additive_identity @ b @ X0) | ~ (sum @ c @ c @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl4548])).
% 106.09/15.90 thf(zip_derived_cl4561, plain,
% 106.09/15.90 ( (product @ additive_identity @ b @ (add @ c @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl4559])).
% 106.09/15.90 thf(zip_derived_cl29, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((additive_identity) = (X1))
% 106.09/15.90 | ~ (product @ additive_identity @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl4591, plain, (((additive_identity) = (add @ c @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4561, zip_derived_cl29])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl4610, plain, ( (sum @ c @ c @ additive_identity)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl4591, zip_derived_cl3])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl6, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (sum @ X1 @ X3 @ X4)
% 106.09/15.90 | ~ (sum @ X2 @ X3 @ X5)
% 106.09/15.90 | (sum @ X0 @ X4 @ X5))),
% 106.09/15.90 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 106.09/15.90 thf(zip_derived_cl80, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (sum @ X1 @ X3 @ X2)
% 106.09/15.90 | ~ (sum @ (add @ X1 @ X0) @ X4 @ X2)
% 106.09/15.90 | ~ (sum @ X0 @ X4 @ X3))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 106.09/15.90 thf(zip_derived_cl783, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (sum @ X1 @ X0 @ X3)
% 106.09/15.90 | (sum @ X2 @ X3 @ (add @ (add @ X2 @ X1) @ X0)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl80])).
% 106.09/15.90 thf(zip_derived_cl11635, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ (add @ (add @ X0 @ c) @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4610, zip_derived_cl783])).
% 106.09/15.90 thf(zip_derived_cl53, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 106.09/15.90 thf(zip_derived_cl54, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X1 @ X0 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl292, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl54])).
% 106.09/15.90 thf(zip_derived_cl11641, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ (add @ c @ (add @ X0 @ c)))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl11635, zip_derived_cl292])).
% 106.09/15.90 thf(zip_derived_cl55, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((X0) = (X1)) | ~ (sum @ X0 @ additive_identity @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl11739, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (add @ c @ (add @ X0 @ c)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl11641, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl11799, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ c @ (add @ X0 @ c) @ X0)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl11739, zip_derived_cl3])).
% 106.09/15.90 thf(zip_derived_cl23, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [x_squared_is_x])).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(zip_derived_cl23, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [x_squared_is_x])).
% 106.09/15.90 thf(associativity_of_multiplication1, axiom,
% 106.09/15.90 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 106.09/15.90 ( ~( product @ U @ Z @ W ) ) | ( product @ X @ V @ W ))).
% 106.09/15.90 thf(zip_derived_cl9, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X1 @ X3 @ X4)
% 106.09/15.90 | ~ (product @ X2 @ X3 @ X5)
% 106.09/15.90 | (product @ X0 @ X4 @ X5))),
% 106.09/15.90 inference('cnf', [status(esa)], [associativity_of_multiplication1])).
% 106.09/15.90 thf(zip_derived_cl65, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 ( (product @ X0 @ X2 @ X1)
% 106.09/15.90 | ~ (product @ X0 @ X3 @ X1)
% 106.09/15.90 | ~ (product @ X0 @ X3 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl9])).
% 106.09/15.90 thf(zip_derived_cl462, plain,
% 106.09/15.90 (![X0 : $i]: (~ (product @ a @ b @ X0) | (product @ a @ X0 @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl65])).
% 106.09/15.90 thf(zip_derived_cl470, plain, ( (product @ a @ c @ c)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl462])).
% 106.09/15.90 thf(distributivity1, axiom,
% 106.09/15.90 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 106.09/15.90 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 106.09/15.90 ( sum @ V1 @ V2 @ V4 ))).
% 106.09/15.90 thf(zip_derived_cl11, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X3 @ X4)
% 106.09/15.90 | ~ (sum @ X1 @ X3 @ X5)
% 106.09/15.90 | ~ (product @ X0 @ X5 @ X6)
% 106.09/15.90 | (sum @ X2 @ X4 @ X6))),
% 106.09/15.90 inference('cnf', [status(esa)], [distributivity1])).
% 106.09/15.90 thf(zip_derived_cl474, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 ( (sum @ c @ X1 @ X0)
% 106.09/15.90 | ~ (product @ a @ X2 @ X0)
% 106.09/15.90 | ~ (sum @ c @ X3 @ X2)
% 106.09/15.90 | ~ (product @ a @ X3 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl470, zip_derived_cl11])).
% 106.09/15.90 thf(zip_derived_cl6203, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (~ (product @ a @ X1 @ X0)
% 106.09/15.90 | ~ (sum @ c @ X1 @ a)
% 106.09/15.90 | (sum @ c @ X0 @ a))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl474])).
% 106.09/15.90 thf(zip_derived_cl11921, plain,
% 106.09/15.90 (![X0 : $i]: ( (sum @ c @ X0 @ a) | ~ (product @ a @ (add @ a @ c) @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl11799, zip_derived_cl6203])).
% 106.09/15.90 thf(zip_derived_cl11948, plain,
% 106.09/15.90 ( (sum @ c @ (multiply @ a @ (add @ a @ c)) @ a)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl11921])).
% 106.09/15.90 thf(zip_derived_cl268, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl13755, plain,
% 106.09/15.90 (((add @ (multiply @ a @ (add @ a @ c)) @ c) = (a))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl11948, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl11799, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ c @ (add @ X0 @ c) @ X0)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl11739, zip_derived_cl3])).
% 106.09/15.90 thf(zip_derived_cl268, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl11901, plain,
% 106.09/15.90 (![X0 : $i]: ((add @ (add @ X0 @ c) @ c) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl11799, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl15441, plain,
% 106.09/15.90 (((add @ a @ c) = (multiply @ a @ (add @ a @ c)))),
% 106.09/15.90 inference('sup+', [status(thm)],
% 106.09/15.90 [zip_derived_cl13755, zip_derived_cl11901])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl16288, plain,
% 106.09/15.90 ( (product @ a @ (add @ a @ c) @ (add @ a @ c))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl15441, zip_derived_cl2])).
% 106.09/15.90 thf(zip_derived_cl56540, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_identity) = (add @ X0 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl56441, zip_derived_cl29])).
% 106.09/15.90 thf(zip_derived_cl3, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_addition])).
% 106.09/15.90 thf(zip_derived_cl56663, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ X0 @ additive_identity)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl56540, zip_derived_cl3])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl26, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (product @ X0 @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl36, plain, (![X0 : $i]: ((X0) = (multiply @ X0 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl26])).
% 106.09/15.90 thf(zip_derived_cl22, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (product @ X0 @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (multiply @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiply_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl75, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 (product @ X0 @ (additive_inverse @ X0) @ (additive_inverse @ X0))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl22])).
% 106.09/15.90 thf(zip_derived_cl21, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ (additive_inverse @ X0) @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (add @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [distribute_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl14, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X3 @ X1 @ X4)
% 106.09/15.90 | ~ (sum @ X0 @ X3 @ X5)
% 106.09/15.90 | ~ (sum @ X2 @ X4 @ X6)
% 106.09/15.90 | (product @ X5 @ X1 @ X6))),
% 106.09/15.90 inference('cnf', [status(esa)], [distributivity4])).
% 106.09/15.90 thf(zip_derived_cl169, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 ( (product @ (additive_inverse @ (add @ X1 @ X0)) @ X3 @ X2)
% 106.09/15.90 | ~ (sum @ X5 @ X4 @ X2)
% 106.09/15.90 | ~ (product @ (additive_inverse @ X0) @ X3 @ X4)
% 106.09/15.90 | ~ (product @ (additive_inverse @ X1) @ X3 @ X5))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl14])).
% 106.09/15.90 thf(zip_derived_cl4945, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ (additive_inverse @ X2) @
% 106.09/15.90 (additive_inverse @ (additive_inverse @ X0)) @ X1)
% 106.09/15.90 | ~ (sum @ X1 @ (additive_inverse @ (additive_inverse @ X0)) @ X3)
% 106.09/15.90 | (product @ (additive_inverse @ (add @ X2 @ X0)) @
% 106.09/15.90 (additive_inverse @ (additive_inverse @ X0)) @ X3))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl169])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl4957, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ (additive_inverse @ X2) @ X0 @ X1)
% 106.09/15.90 | ~ (sum @ X1 @ X0 @ X3)
% 106.09/15.90 | (product @ (additive_inverse @ (add @ X2 @ X0)) @ X0 @ X3))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl4945, zip_derived_cl93, zip_derived_cl93,
% 106.09/15.90 zip_derived_cl93])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl76416, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X2 @ X0 @ X1)
% 106.09/15.90 | ~ (sum @ X1 @ X0 @ X3)
% 106.09/15.90 | (product @ (add @ X2 @ X0) @ X0 @ X3))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl4957, zip_derived_cl57069, zip_derived_cl57069])).
% 106.09/15.90 thf(zip_derived_cl76417, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ( (product @ (add @ X1 @ X0) @ X0 @ additive_identity)
% 106.09/15.90 | ~ (product @ X1 @ X0 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl56663, zip_derived_cl76416])).
% 106.09/15.90 thf(zip_derived_cl83265, plain,
% 106.09/15.90 ( (product @ (add @ a @ (add @ a @ c)) @ (add @ a @ c) @
% 106.09/15.90 additive_identity)),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl16288, zip_derived_cl76417])).
% 106.09/15.90 thf(zip_derived_cl12398, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl12275, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl292, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl54])).
% 106.09/15.90 thf(zip_derived_cl57470, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X1 @ (add @ X1 @ X0)) = (X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl12398, zip_derived_cl57069, zip_derived_cl292])).
% 106.09/15.90 thf(zip_derived_cl83278, plain,
% 106.09/15.90 ( (product @ c @ (add @ a @ c) @ additive_identity)),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl83265, zip_derived_cl57470])).
% 106.09/15.90 thf(zip_derived_cl0, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [additive_identity1])).
% 106.09/15.90 thf(zip_derived_cl437, plain,
% 106.09/15.90 (![X0 : $i]: (product @ (additive_inverse @ X0) @ X0 @ X0)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl373, zip_derived_cl2])).
% 106.09/15.90 thf(zip_derived_cl21, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ (additive_inverse @ X0) @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (add @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [distribute_additive_inverse])).
% 106.09/15.90 thf(distributivity2, axiom,
% 106.09/15.90 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 106.09/15.90 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 106.09/15.90 ( product @ X @ V3 @ V4 ))).
% 106.09/15.90 thf(zip_derived_cl12, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X3 @ X4)
% 106.09/15.90 | ~ (sum @ X1 @ X3 @ X5)
% 106.09/15.90 | ~ (sum @ X2 @ X4 @ X6)
% 106.09/15.90 | (product @ X0 @ X5 @ X6))),
% 106.09/15.90 inference('cnf', [status(esa)], [distributivity2])).
% 106.09/15.90 thf(zip_derived_cl142, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 ( (product @ X3 @ (additive_inverse @ (add @ X1 @ X0)) @ X2)
% 106.09/15.90 | ~ (sum @ X5 @ X4 @ X2)
% 106.09/15.90 | ~ (product @ X3 @ (additive_inverse @ X0) @ X4)
% 106.09/15.90 | ~ (product @ X3 @ (additive_inverse @ X1) @ X5))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl12])).
% 106.09/15.90 thf(zip_derived_cl3570, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ (additive_inverse @ (additive_inverse @ X0)) @
% 106.09/15.90 (additive_inverse @ X2) @ X1)
% 106.09/15.90 | ~ (sum @ X1 @ (additive_inverse @ X0) @ X3)
% 106.09/15.90 | (product @ (additive_inverse @ (additive_inverse @ X0)) @
% 106.09/15.90 (additive_inverse @ (add @ X2 @ X0)) @ X3))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl142])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl3584, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X0 @ (additive_inverse @ X2) @ X1)
% 106.09/15.90 | ~ (sum @ X1 @ (additive_inverse @ X0) @ X3)
% 106.09/15.90 | (product @ X0 @ (additive_inverse @ (add @ X2 @ X0)) @ X3))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl3570, zip_derived_cl93, zip_derived_cl93])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl67105, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X2 @ X1)
% 106.09/15.90 | ~ (sum @ X1 @ X0 @ X3)
% 106.09/15.90 | (product @ X0 @ (add @ X2 @ X0) @ X3))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl3584, zip_derived_cl57069, zip_derived_cl57069,
% 106.09/15.90 zip_derived_cl57069])).
% 106.09/15.90 thf(zip_derived_cl67114, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ( (product @ X0 @ (add @ X1 @ X0) @ X0)
% 106.09/15.90 | ~ (product @ X0 @ X1 @ additive_identity))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl67105])).
% 106.09/15.90 thf(zip_derived_cl83329, plain,
% 106.09/15.90 ( (product @ c @ (add @ (add @ a @ c) @ c) @ c)),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl83278, zip_derived_cl67114])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl21, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ (additive_inverse @ X0) @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (add @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [distribute_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl268, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl960, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (additive_inverse @ X0) @ (additive_inverse @ X1))
% 106.09/15.90 = (additive_inverse @ (add @ X1 @ X0)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl1038, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ X0 @ (additive_inverse @ X1))
% 106.09/15.90 = (additive_inverse @ (add @ X1 @ (additive_inverse @ X0))))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl960])).
% 106.09/15.90 thf(zip_derived_cl1, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [additive_identity2])).
% 106.09/15.90 thf(zip_derived_cl4591, plain, (((additive_identity) = (add @ c @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4561, zip_derived_cl29])).
% 106.09/15.90 thf(zip_derived_cl21, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ (additive_inverse @ X0) @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (add @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [distribute_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl4611, plain,
% 106.09/15.90 ( (sum @ (additive_inverse @ c) @ (additive_inverse @ c) @
% 106.09/15.90 (additive_inverse @ additive_identity))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl4591, zip_derived_cl21])).
% 106.09/15.90 thf(zip_derived_cl92, plain,
% 106.09/15.90 (((additive_inverse @ additive_identity) = (additive_identity))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl4618, plain,
% 106.09/15.90 ( (sum @ (additive_inverse @ c) @ (additive_inverse @ c) @
% 106.09/15.90 additive_identity)),
% 106.09/15.90 inference('demod', [status(thm)], [zip_derived_cl4611, zip_derived_cl92])).
% 106.09/15.90 thf(zip_derived_cl5, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ X0) @ additive_identity)),
% 106.09/15.90 inference('cnf', [status(esa)], [right_inverse])).
% 106.09/15.90 thf(associativity_of_addition2, axiom,
% 106.09/15.90 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 106.09/15.90 ( ~( sum @ X @ V @ W ) ) | ( sum @ U @ Z @ W ))).
% 106.09/15.90 thf(zip_derived_cl7, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (sum @ X1 @ X3 @ X4)
% 106.09/15.90 | ~ (sum @ X0 @ X4 @ X5)
% 106.09/15.90 | (sum @ X2 @ X3 @ X5))),
% 106.09/15.90 inference('cnf', [status(esa)], [associativity_of_addition2])).
% 106.09/15.90 thf(zip_derived_cl120, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 ( (sum @ additive_identity @ X2 @ X1)
% 106.09/15.90 | ~ (sum @ X0 @ X3 @ X1)
% 106.09/15.90 | ~ (sum @ (additive_inverse @ X0) @ X2 @ X3))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl7])).
% 106.09/15.90 thf(zip_derived_cl4652, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 (~ (sum @ c @ additive_identity @ X0)
% 106.09/15.90 | (sum @ additive_identity @ (additive_inverse @ c) @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4618, zip_derived_cl120])).
% 106.09/15.90 thf(zip_derived_cl4743, plain,
% 106.09/15.90 ( (sum @ additive_identity @ (additive_inverse @ c) @ c)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl4652])).
% 106.09/15.90 thf(zip_derived_cl57, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl4760, plain, (((additive_inverse @ c) = (c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4743, zip_derived_cl57])).
% 106.09/15.90 thf(zip_derived_cl960, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (additive_inverse @ X0) @ (additive_inverse @ X1))
% 106.09/15.90 = (additive_inverse @ (add @ X1 @ X0)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl4918, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ((add @ c @ (additive_inverse @ X0))
% 106.09/15.90 = (additive_inverse @ (add @ X0 @ c)))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl4760, zip_derived_cl960])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl5237, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ((additive_inverse @ (add @ c @ (additive_inverse @ X0)))
% 106.09/15.90 = (add @ X0 @ c))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl4918, zip_derived_cl93])).
% 106.09/15.90 thf(zip_derived_cl5521, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((additive_inverse @ (add @ c @ (add @ X1 @ (additive_inverse @ X0))))
% 106.09/15.90 = (add @ (add @ X0 @ (additive_inverse @ X1)) @ c))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5237])).
% 106.09/15.90 thf(zip_derived_cl292, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl54])).
% 106.09/15.90 thf(zip_derived_cl5534, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((additive_inverse @ (add @ c @ (add @ X1 @ (additive_inverse @ X0))))
% 106.09/15.90 = (add @ c @ (add @ X0 @ (additive_inverse @ X1))))),
% 106.09/15.90 inference('demod', [status(thm)], [zip_derived_cl5521, zip_derived_cl292])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl53, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (sum @ X0 @ X1 @ (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl8])).
% 106.09/15.90 thf(zip_derived_cl4760, plain, (((additive_inverse @ c) = (c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4743, zip_derived_cl57])).
% 106.09/15.90 thf(zip_derived_cl21, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (sum @ (additive_inverse @ X0) @ (additive_inverse @ X1) @
% 106.09/15.90 (additive_inverse @ (add @ X0 @ X1)))),
% 106.09/15.90 inference('cnf', [status(esa)], [distribute_additive_inverse])).
% 106.09/15.90 thf(zip_derived_cl15, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (sum @ X0 @ X1 @ X2) | ~ (sum @ X0 @ X1 @ X3) | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl115, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((additive_inverse @ (add @ X1 @ X0)) = (X2))
% 106.09/15.90 | ~ (sum @ (additive_inverse @ X1) @ (additive_inverse @ X0) @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl4925, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (~ (sum @ c @ (additive_inverse @ X1) @ X0)
% 106.09/15.90 | ((additive_inverse @ (add @ c @ X1)) = (X0)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4760, zip_derived_cl115])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl57405, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (~ (sum @ c @ X1 @ X0) | ((additive_inverse @ (add @ c @ X1)) = (X0)))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl4925, zip_derived_cl57069])).
% 106.09/15.90 thf(zip_derived_cl66992, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (add @ c @ X0)) = (add @ X0 @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl57405])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl80145, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (add @ X1 @ X0) @ c) = (add @ c @ (add @ X0 @ X1)))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl5534, zip_derived_cl57069, zip_derived_cl66992,
% 106.09/15.90 zip_derived_cl57069])).
% 106.09/15.90 thf(zip_derived_cl292, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl54])).
% 106.09/15.90 thf(zip_derived_cl292, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl54])).
% 106.09/15.90 thf(zip_derived_cl12398, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (add @ (additive_inverse @ X1) @ X0) @ X1) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl12275, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl12714, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl292, zip_derived_cl12398])).
% 106.09/15.90 thf(zip_derived_cl57069, plain,
% 106.09/15.90 (![X0 : $i]: ((X0) = (additive_inverse @ X0))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl56689, zip_derived_cl92, zip_derived_cl94])).
% 106.09/15.90 thf(zip_derived_cl292, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl54])).
% 106.09/15.90 thf(zip_derived_cl57478, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: ((add @ X0 @ (add @ X1 @ X0)) = (X1))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl12714, zip_derived_cl57069, zip_derived_cl292])).
% 106.09/15.90 thf(zip_derived_cl83371, plain, ( (product @ c @ a @ c)),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl83329, zip_derived_cl80145, zip_derived_cl292,
% 106.09/15.90 zip_derived_cl57478])).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl9, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X1 @ X3 @ X4)
% 106.09/15.90 | ~ (product @ X2 @ X3 @ X5)
% 106.09/15.90 | (product @ X0 @ X4 @ X5))),
% 106.09/15.90 inference('cnf', [status(esa)], [associativity_of_multiplication1])).
% 106.09/15.90 thf(zip_derived_cl66, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (product @ X1 @ X3 @ X2)
% 106.09/15.90 | ~ (product @ (multiply @ X1 @ X0) @ X4 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X4 @ X3))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 106.09/15.90 thf(zip_derived_cl502, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X1 @ X0 @ X3)
% 106.09/15.90 | (product @ X2 @ X3 @ (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl66])).
% 106.09/15.90 thf(zip_derived_cl6390, plain,
% 106.09/15.90 (![X0 : $i]: (product @ X0 @ c @ (multiply @ (multiply @ X0 @ a) @ b))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl502])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl16, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X1 @ X3)
% 106.09/15.90 | ((X2) = (X3)))),
% 106.09/15.90 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 106.09/15.90 thf(zip_derived_cl27, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl7389, plain,
% 106.09/15.90 (![X0 : $i]: ((multiply @ X0 @ c) = (multiply @ (multiply @ X0 @ a) @ b))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl6390, zip_derived_cl27])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl23, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [x_squared_is_x])).
% 106.09/15.90 thf(zip_derived_cl105, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 106.09/15.90 | ~ (product @ X1 @ X4 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X3 @ X4))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl10])).
% 106.09/15.90 thf(zip_derived_cl1175, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (~ (product @ X2 @ X1 @ X0)
% 106.09/15.90 | (product @ (multiply @ X0 @ X2) @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl105])).
% 106.09/15.90 thf(zip_derived_cl3771, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (product @ (multiply @ (multiply @ X1 @ X0) @ X1) @ X0 @
% 106.09/15.90 (multiply @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl1175])).
% 106.09/15.90 thf(zip_derived_cl68115, plain,
% 106.09/15.90 ( (product @ (multiply @ b @ c) @ a @ (multiply @ b @ a))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl7389, zip_derived_cl3771])).
% 106.09/15.90 thf(zip_derived_cl66, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (product @ X1 @ X3 @ X2)
% 106.09/15.90 | ~ (product @ (multiply @ X1 @ X0) @ X4 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X4 @ X3))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 106.09/15.90 thf(zip_derived_cl68685, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 (~ (product @ c @ a @ X0) | (product @ b @ X0 @ (multiply @ b @ a)))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl68115, zip_derived_cl66])).
% 106.09/15.90 thf(zip_derived_cl83451, plain, ( (product @ b @ c @ (multiply @ b @ a))),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl83371, zip_derived_cl68685])).
% 106.09/15.90 thf(zip_derived_cl23, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 106.09/15.90 inference('cnf', [status(esa)], [x_squared_is_x])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(distributivity3, axiom,
% 106.09/15.90 (( ~( product @ Y @ X @ V1 ) ) | ( ~( product @ Z @ X @ V2 ) ) |
% 106.09/15.90 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ V3 @ X @ V4 ) ) |
% 106.09/15.90 ( sum @ V1 @ V2 @ V4 ))).
% 106.09/15.90 thf(zip_derived_cl13, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 106.09/15.90 (~ (product @ X0 @ X1 @ X2)
% 106.09/15.90 | ~ (product @ X3 @ X1 @ X4)
% 106.09/15.90 | ~ (sum @ X0 @ X3 @ X5)
% 106.09/15.90 | ~ (product @ X5 @ X1 @ X6)
% 106.09/15.90 | (sum @ X2 @ X4 @ X6))),
% 106.09/15.90 inference('cnf', [status(esa)], [distributivity3])).
% 106.09/15.90 thf(zip_derived_cl145, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 106.09/15.90 ( (sum @ (multiply @ X1 @ X0) @ X3 @ X2)
% 106.09/15.90 | ~ (product @ X4 @ X0 @ X2)
% 106.09/15.90 | ~ (sum @ X1 @ X5 @ X4)
% 106.09/15.90 | ~ (product @ X5 @ X0 @ X3))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 106.09/15.90 thf(zip_derived_cl3892, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 (~ (product @ X2 @ X0 @ X1)
% 106.09/15.90 | ~ (sum @ X3 @ X2 @ X0)
% 106.09/15.90 | (sum @ (multiply @ X3 @ X0) @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl145])).
% 106.09/15.90 thf(zip_derived_cl85078, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ( (sum @ (multiply @ X0 @ c) @ (multiply @ b @ a) @ c)
% 106.09/15.90 | ~ (sum @ X0 @ b @ c))),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl83451, zip_derived_cl3892])).
% 106.09/15.90 thf(zip_derived_cl112028, plain,
% 106.09/15.90 ( (sum @ (multiply @ (add @ b @ c) @ c) @ (multiply @ b @ a) @ c)),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl57468, zip_derived_cl85078])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl11799, plain,
% 106.09/15.90 (![X0 : $i]: (sum @ c @ (add @ X0 @ c) @ X0)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl11739, zip_derived_cl3])).
% 106.09/15.90 thf(zip_derived_cl24, plain, ( (product @ a @ b @ c)),
% 106.09/15.90 inference('cnf', [status(esa)], [a_times_b_is_c])).
% 106.09/15.90 thf(zip_derived_cl474, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 106.09/15.90 ( (sum @ c @ X1 @ X0)
% 106.09/15.90 | ~ (product @ a @ X2 @ X0)
% 106.09/15.90 | ~ (sum @ c @ X3 @ X2)
% 106.09/15.90 | ~ (product @ a @ X3 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl470, zip_derived_cl11])).
% 106.09/15.90 thf(zip_derived_cl6215, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (~ (product @ a @ X1 @ X0)
% 106.09/15.90 | ~ (sum @ c @ X1 @ b)
% 106.09/15.90 | (sum @ c @ X0 @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl474])).
% 106.09/15.90 thf(zip_derived_cl11924, plain,
% 106.09/15.90 (![X0 : $i]: ( (sum @ c @ X0 @ c) | ~ (product @ a @ (add @ b @ c) @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl11799, zip_derived_cl6215])).
% 106.09/15.90 thf(zip_derived_cl12040, plain,
% 106.09/15.90 ( (sum @ c @ (multiply @ a @ (add @ b @ c)) @ c)),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl11924])).
% 106.09/15.90 thf(zip_derived_cl268, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((add @ X1 @ X0) = (X2)) | ~ (sum @ X0 @ X1 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl14115, plain,
% 106.09/15.90 (((add @ (multiply @ a @ (add @ b @ c)) @ c) = (c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl12040, zip_derived_cl268])).
% 106.09/15.90 thf(zip_derived_cl93, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_inverse @ (additive_inverse @ X0)) = (X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 106.09/15.90 thf(zip_derived_cl12714, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (add @ X1 @ (additive_inverse @ X0)) @ X0) = (X1))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl292, zip_derived_cl12398])).
% 106.09/15.90 thf(zip_derived_cl12970, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 ((add @ (add @ X1 @ X0) @ (additive_inverse @ X0)) = (X1))),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl12714])).
% 106.09/15.90 thf(zip_derived_cl16028, plain,
% 106.09/15.90 (((add @ c @ (additive_inverse @ c)) = (multiply @ a @ (add @ b @ c)))),
% 106.09/15.90 inference('sup+', [status(thm)],
% 106.09/15.90 [zip_derived_cl14115, zip_derived_cl12970])).
% 106.09/15.90 thf(zip_derived_cl4760, plain, (((additive_inverse @ c) = (c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4743, zip_derived_cl57])).
% 106.09/15.90 thf(zip_derived_cl4591, plain, (((additive_identity) = (add @ c @ c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl4561, zip_derived_cl29])).
% 106.09/15.90 thf(zip_derived_cl16048, plain,
% 106.09/15.90 (((additive_identity) = (multiply @ a @ (add @ b @ c)))),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl16028, zip_derived_cl4760, zip_derived_cl4591])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl16065, plain,
% 106.09/15.90 ( (product @ a @ (add @ b @ c) @ additive_identity)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl16048, zip_derived_cl2])).
% 106.09/15.90 thf(multiply_additive_id1, axiom,
% 106.09/15.90 (product @ X @ additive_identity @ additive_identity)).
% 106.09/15.90 thf(zip_derived_cl19, plain,
% 106.09/15.90 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 106.09/15.90 inference('cnf', [status(esa)], [multiply_additive_id1])).
% 106.09/15.90 thf(zip_derived_cl105, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 106.09/15.90 ( (product @ (multiply @ X1 @ X0) @ X3 @ X2)
% 106.09/15.90 | ~ (product @ X1 @ X4 @ X2)
% 106.09/15.90 | ~ (product @ X0 @ X3 @ X4))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl10])).
% 106.09/15.90 thf(zip_derived_cl1177, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (~ (product @ X2 @ X1 @ additive_identity)
% 106.09/15.90 | (product @ (multiply @ X0 @ X2) @ X1 @ additive_identity))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl105])).
% 106.09/15.90 thf(zip_derived_cl21207, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 (product @ (multiply @ X0 @ a) @ (add @ b @ c) @ additive_identity)),
% 106.09/15.90 inference('sup-', [status(thm)],
% 106.09/15.90 [zip_derived_cl16065, zip_derived_cl1177])).
% 106.09/15.90 thf(zip_derived_cl27, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 106.09/15.90 (((multiply @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl26540, plain,
% 106.09/15.90 (![X0 : $i]:
% 106.09/15.90 ((multiply @ (multiply @ X0 @ a) @ (add @ b @ c))
% 106.09/15.90 = (additive_identity))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl21207, zip_derived_cl27])).
% 106.09/15.90 thf(zip_derived_cl3771, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (product @ (multiply @ (multiply @ X1 @ X0) @ X1) @ X0 @
% 106.09/15.90 (multiply @ X1 @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl1175])).
% 106.09/15.90 thf(zip_derived_cl68112, plain,
% 106.09/15.90 ( (product @ additive_identity @ a @ (multiply @ (add @ b @ c) @ a))),
% 106.09/15.90 inference('sup+', [status(thm)],
% 106.09/15.90 [zip_derived_cl26540, zip_derived_cl3771])).
% 106.09/15.90 thf(zip_derived_cl29, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((additive_identity) = (X1))
% 106.09/15.90 | ~ (product @ additive_identity @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl68990, plain,
% 106.09/15.90 (((additive_identity) = (multiply @ (add @ b @ c) @ a))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl68112, zip_derived_cl29])).
% 106.09/15.90 thf(zip_derived_cl7389, plain,
% 106.09/15.90 (![X0 : $i]: ((multiply @ X0 @ c) = (multiply @ (multiply @ X0 @ a) @ b))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl6390, zip_derived_cl27])).
% 106.09/15.90 thf(zip_derived_cl69054, plain,
% 106.09/15.90 (((multiply @ (add @ b @ c) @ c) = (multiply @ additive_identity @ b))),
% 106.09/15.90 inference('sup+', [status(thm)],
% 106.09/15.90 [zip_derived_cl68990, zip_derived_cl7389])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl29, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((additive_identity) = (X1))
% 106.09/15.90 | ~ (product @ additive_identity @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl16])).
% 106.09/15.90 thf(zip_derived_cl44, plain,
% 106.09/15.90 (![X0 : $i]: ((additive_identity) = (multiply @ additive_identity @ X0))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl29])).
% 106.09/15.90 thf(zip_derived_cl69091, plain,
% 106.09/15.90 (((multiply @ (add @ b @ c) @ c) = (additive_identity))),
% 106.09/15.90 inference('demod', [status(thm)], [zip_derived_cl69054, zip_derived_cl44])).
% 106.09/15.90 thf(zip_derived_cl112030, plain,
% 106.09/15.90 ( (sum @ additive_identity @ (multiply @ b @ a) @ c)),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl112028, zip_derived_cl69091])).
% 106.09/15.90 thf(zip_derived_cl57, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]:
% 106.09/15.90 (((X0) = (X1)) | ~ (sum @ additive_identity @ X0 @ X1))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl15])).
% 106.09/15.90 thf(zip_derived_cl112071, plain, (((multiply @ b @ a) = (c))),
% 106.09/15.90 inference('sup-', [status(thm)], [zip_derived_cl112030, zip_derived_cl57])).
% 106.09/15.90 thf(zip_derived_cl2, plain,
% 106.09/15.90 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 106.09/15.90 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 106.09/15.90 thf(zip_derived_cl112306, plain, ( (product @ b @ a @ c)),
% 106.09/15.90 inference('sup+', [status(thm)], [zip_derived_cl112071, zip_derived_cl2])).
% 106.09/15.90 thf(zip_derived_cl112713, plain, ($false),
% 106.09/15.90 inference('demod', [status(thm)],
% 106.09/15.90 [zip_derived_cl25, zip_derived_cl112306])).
% 106.09/15.90
% 106.09/15.90 % SZS output end Refutation
% 106.09/15.90
% 106.09/15.90
% 106.09/15.90 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 106.09/15.91 % Terminating...
% 106.93/15.97 % Runner terminated.
% 106.93/15.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------