TSTP Solution File: RNG001-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BS5ACS6XIV true
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:06:12 EDT 2023
% Result : Unsatisfiable 25.56s 4.23s
% Output : Refutation 25.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BS5ACS6XIV true
% 0.13/0.36 % Computer : n031.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Aug 27 02:24:09 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 1.02/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 1.02/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 1.02/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.02/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.02/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.30/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.30/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 25.56/4.23 % Solved by fo/fo3_bce.sh.
% 25.56/4.23 % BCE start: 8
% 25.56/4.23 % BCE eliminated: 0
% 25.56/4.23 % PE start: 8
% 25.56/4.23 logic: neq
% 25.56/4.23 % PE eliminated: 0
% 25.56/4.23 % done 6387 iterations in 3.474s
% 25.56/4.23 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 25.56/4.23 % SZS output start Refutation
% 25.56/4.23 thf(sum_type, type, sum: $i > $i > $i > $o).
% 25.56/4.23 thf(additive_inverse_type, type, additive_inverse: $i > $i).
% 25.56/4.23 thf(additive_identity_type, type, additive_identity: $i).
% 25.56/4.23 thf(multiply_type, type, multiply: $i > $i > $i).
% 25.56/4.23 thf(a_type, type, a: $i).
% 25.56/4.23 thf(product_type, type, product: $i > $i > $i > $o).
% 25.56/4.23 thf(prove_a_times_additive_id_is_additive_id, conjecture,
% 25.56/4.23 (product @ a @ additive_identity @ additive_identity)).
% 25.56/4.23 thf(zf_stmt_0, negated_conjecture,
% 25.56/4.23 (~( product @ a @ additive_identity @ additive_identity )),
% 25.56/4.23 inference('cnf.neg', [status(esa)],
% 25.56/4.23 [prove_a_times_additive_id_is_additive_id])).
% 25.56/4.23 thf(zip_derived_cl7, plain,
% 25.56/4.23 (~ (product @ a @ additive_identity @ additive_identity)),
% 25.56/4.23 inference('cnf', [status(esa)], [zf_stmt_0])).
% 25.56/4.23 thf(additive_identity1, axiom, (sum @ additive_identity @ X @ X)).
% 25.56/4.23 thf(zip_derived_cl0, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_identity1])).
% 25.56/4.23 thf(additive_inverse1, axiom,
% 25.56/4.23 (sum @ ( additive_inverse @ X ) @ X @ additive_identity)).
% 25.56/4.23 thf(zip_derived_cl1, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_inverse1])).
% 25.56/4.23 thf(associativity_of_addition1, axiom,
% 25.56/4.23 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 25.56/4.23 ( ~( sum @ U @ Z @ W ) ) | ( sum @ X @ V @ W ))).
% 25.56/4.23 thf(zip_derived_cl2, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X2 @ X3 @ X5)
% 25.56/4.23 | (sum @ X0 @ X4 @ X5))),
% 25.56/4.23 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 25.56/4.23 thf(zip_derived_cl9, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (sum @ (additive_inverse @ X0) @ X2 @ X1)
% 25.56/4.23 | ~ (sum @ additive_identity @ X3 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X2))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 25.56/4.23 thf(zip_derived_cl51, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ additive_identity @ X1 @ X0)
% 25.56/4.23 | (sum @ (additive_inverse @ additive_identity) @ X0 @ X0))),
% 25.56/4.23 inference('eq_fact', [status(thm)], [zip_derived_cl9])).
% 25.56/4.23 thf(zip_derived_cl56, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ (additive_inverse @ additive_identity) @ X0 @ X0)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl51])).
% 25.56/4.23 thf(zip_derived_cl1, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_inverse1])).
% 25.56/4.23 thf(zip_derived_cl1, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_inverse1])).
% 25.56/4.23 thf(associativity_of_addition2, axiom,
% 25.56/4.23 (( ~( sum @ X @ Y @ U ) ) | ( ~( sum @ Y @ Z @ V ) ) |
% 25.56/4.23 ( ~( sum @ X @ V @ W ) ) | ( sum @ U @ Z @ W ))).
% 25.56/4.23 thf(zip_derived_cl3, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X0 @ X4 @ X5)
% 25.56/4.23 | (sum @ X2 @ X3 @ X5))),
% 25.56/4.23 inference('cnf', [status(esa)], [associativity_of_addition2])).
% 25.56/4.23 thf(zip_derived_cl14, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (sum @ additive_identity @ X2 @ X1)
% 25.56/4.23 | ~ (sum @ (additive_inverse @ X0) @ X3 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X2 @ X3))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 25.56/4.23 thf(zip_derived_cl82, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X0)
% 25.56/4.23 | (sum @ additive_identity @ X1 @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl14])).
% 25.56/4.23 thf(zip_derived_cl85, plain,
% 25.56/4.23 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 25.56/4.23 additive_identity)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl82])).
% 25.56/4.23 thf(zip_derived_cl0, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_identity1])).
% 25.56/4.23 thf(zip_derived_cl0, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_identity1])).
% 25.56/4.23 thf(zip_derived_cl2, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X2 @ X3 @ X5)
% 25.56/4.23 | (sum @ X0 @ X4 @ X5))),
% 25.56/4.23 inference('cnf', [status(esa)], [associativity_of_addition1])).
% 25.56/4.23 thf(zip_derived_cl8, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (sum @ additive_identity @ X2 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X2))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 25.56/4.23 thf(zip_derived_cl42, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ additive_identity @ X0 @ X1)
% 25.56/4.23 | (sum @ additive_identity @ X1 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl8])).
% 25.56/4.23 thf(zip_derived_cl106, plain,
% 25.56/4.23 ( (sum @ additive_identity @ additive_identity @
% 25.56/4.23 (additive_inverse @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl42])).
% 25.56/4.23 thf(zip_derived_cl85, plain,
% 25.56/4.23 ( (sum @ additive_identity @ (additive_inverse @ additive_identity) @
% 25.56/4.23 additive_identity)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl82])).
% 25.56/4.23 thf(zip_derived_cl1, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_inverse1])).
% 25.56/4.23 thf(zip_derived_cl0, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_identity1])).
% 25.56/4.23 thf(zip_derived_cl9, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (sum @ (additive_inverse @ X0) @ X2 @ X1)
% 25.56/4.23 | ~ (sum @ additive_identity @ X3 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X2))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 25.56/4.23 thf(zip_derived_cl50, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1) | (sum @ (additive_inverse @ X2) @ X1 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 25.56/4.23 thf(zip_derived_cl3, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X0 @ X4 @ X5)
% 25.56/4.23 | (sum @ X2 @ X3 @ X5))),
% 25.56/4.23 inference('cnf', [status(esa)], [associativity_of_addition2])).
% 25.56/4.23 thf(zip_derived_cl16, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (sum @ X0 @ X3 @ X0)
% 25.56/4.23 | ~ (sum @ X2 @ X1 @ X0)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X1))),
% 25.56/4.23 inference('eq_fact', [status(thm)], [zip_derived_cl3])).
% 25.56/4.23 thf(zip_derived_cl175, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X1)
% 25.56/4.23 | (sum @ X0 @ X3 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl16])).
% 25.56/4.23 thf(zip_derived_cl250, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 ( (sum @ X0 @ X1 @ X0)
% 25.56/4.23 | ~ (sum @ additive_identity @ X1 @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl175])).
% 25.56/4.23 thf(zip_derived_cl266, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ X0 @ (additive_inverse @ additive_identity) @ X0)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl250])).
% 25.56/4.23 thf(distributivity1, axiom,
% 25.56/4.23 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 25.56/4.23 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( product @ X @ V3 @ V4 ) ) |
% 25.56/4.23 ( sum @ V1 @ V2 @ V4 ))).
% 25.56/4.23 thf(zip_derived_cl5, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 25.56/4.23 (~ (product @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (product @ X0 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X5)
% 25.56/4.23 | ~ (product @ X0 @ X5 @ X6)
% 25.56/4.23 | (sum @ X2 @ X4 @ X6))),
% 25.56/4.23 inference('cnf', [status(esa)], [distributivity1])).
% 25.56/4.23 thf(zip_derived_cl22, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 25.56/4.23 ( (sum @ X0 @ X0 @ X3)
% 25.56/4.23 | ~ (product @ X2 @ X4 @ X3)
% 25.56/4.23 | ~ (sum @ X1 @ X1 @ X4)
% 25.56/4.23 | ~ (product @ X2 @ X1 @ X0))),
% 25.56/4.23 inference('eq_fact', [status(thm)], [zip_derived_cl5])).
% 25.56/4.23 thf(zip_derived_cl164, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 25.56/4.23 (~ (product @ X2 @ X1 @ X0)
% 25.56/4.23 | ~ (sum @ X1 @ X1 @ X1)
% 25.56/4.23 | (sum @ X0 @ X0 @ X0))),
% 25.56/4.23 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 25.56/4.23 thf(closure_of_multiplication, axiom,
% 25.56/4.23 (product @ X @ Y @ ( multiply @ X @ Y ))).
% 25.56/4.23 thf(zip_derived_cl4, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 25.56/4.23 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 25.56/4.23 thf(zip_derived_cl165, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 ( (sum @ (multiply @ X1 @ X0) @ (multiply @ X1 @ X0) @
% 25.56/4.23 (multiply @ X1 @ X0))
% 25.56/4.23 | ~ (sum @ X0 @ X0 @ X0))),
% 25.56/4.23 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl4])).
% 25.56/4.23 thf(zip_derived_cl82, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X0)
% 25.56/4.23 | (sum @ additive_identity @ X1 @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl14])).
% 25.56/4.23 thf(zip_derived_cl1116, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X0 @ X0)
% 25.56/4.23 | (sum @ additive_identity @ (multiply @ X1 @ X0) @
% 25.56/4.23 additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl165, zip_derived_cl82])).
% 25.56/4.23 thf(zip_derived_cl1809, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (sum @ additive_identity @
% 25.56/4.23 (multiply @ X0 @ (additive_inverse @ additive_identity)) @
% 25.56/4.23 additive_identity)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl266, zip_derived_cl1116])).
% 25.56/4.23 thf(zip_derived_cl0, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ additive_identity @ X0 @ X0)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_identity1])).
% 25.56/4.23 thf(zip_derived_cl250, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 ( (sum @ X0 @ X1 @ X0)
% 25.56/4.23 | ~ (sum @ additive_identity @ X1 @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl175])).
% 25.56/4.23 thf(zip_derived_cl265, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl250])).
% 25.56/4.23 thf(zip_derived_cl1, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_inverse1])).
% 25.56/4.23 thf(zip_derived_cl50, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1) | (sum @ (additive_inverse @ X2) @ X1 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 25.56/4.23 thf(zip_derived_cl3, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X0 @ X4 @ X5)
% 25.56/4.23 | (sum @ X2 @ X3 @ X5))),
% 25.56/4.23 inference('cnf', [status(esa)], [associativity_of_addition2])).
% 25.56/4.23 thf(zip_derived_cl168, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1)
% 25.56/4.23 | (sum @ X0 @ X4 @ X3)
% 25.56/4.23 | ~ (sum @ (additive_inverse @ X2) @ X5 @ X3)
% 25.56/4.23 | ~ (sum @ X1 @ X4 @ X5))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl3])).
% 25.56/4.23 thf(zip_derived_cl1246, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X1 @ X0)
% 25.56/4.23 | (sum @ X3 @ X1 @ additive_identity)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X2))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl168])).
% 25.56/4.23 thf(zip_derived_cl1541, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X0)
% 25.56/4.23 | (sum @ X1 @ additive_identity @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl265, zip_derived_cl1246])).
% 25.56/4.23 thf(zip_derived_cl4412, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (sum @ (multiply @ X0 @ (additive_inverse @ additive_identity)) @
% 25.56/4.23 additive_identity @ additive_identity)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1809, zip_derived_cl1541])).
% 25.56/4.23 thf(zip_derived_cl4, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 25.56/4.23 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 25.56/4.23 thf(zip_derived_cl50, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1) | (sum @ (additive_inverse @ X2) @ X1 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 25.56/4.23 thf(distributivity2, axiom,
% 25.56/4.23 (( ~( product @ X @ Y @ V1 ) ) | ( ~( product @ X @ Z @ V2 ) ) |
% 25.56/4.23 ( ~( sum @ Y @ Z @ V3 ) ) | ( ~( sum @ V1 @ V2 @ V4 ) ) |
% 25.56/4.23 ( product @ X @ V3 @ V4 ))).
% 25.56/4.23 thf(zip_derived_cl6, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 25.56/4.23 (~ (product @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (product @ X0 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X5)
% 25.56/4.23 | ~ (sum @ X2 @ X4 @ X6)
% 25.56/4.23 | (product @ X0 @ X5 @ X6))),
% 25.56/4.23 inference('cnf', [status(esa)], [distributivity2])).
% 25.56/4.23 thf(zip_derived_cl170, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1)
% 25.56/4.23 | (product @ X4 @ X0 @ X3)
% 25.56/4.23 | ~ (sum @ X6 @ X5 @ X3)
% 25.56/4.23 | ~ (product @ X4 @ X1 @ X5)
% 25.56/4.23 | ~ (product @ X4 @ (additive_inverse @ X2) @ X6))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl6])).
% 25.56/4.23 thf(zip_derived_cl1322, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 25.56/4.23 (~ (product @ X1 @ X3 @ X2)
% 25.56/4.23 | ~ (sum @ (multiply @ X1 @ (additive_inverse @ X0)) @ X2 @ X4)
% 25.56/4.23 | (product @ X1 @ X5 @ X4)
% 25.56/4.23 | ~ (sum @ X0 @ X5 @ X3))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl170])).
% 25.56/4.23 thf(zip_derived_cl19214, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 25.56/4.23 (~ (sum @ additive_identity @ X2 @ X1)
% 25.56/4.23 | (product @ X0 @ X2 @ additive_identity)
% 25.56/4.23 | ~ (product @ X0 @ X1 @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl4412, zip_derived_cl1322])).
% 25.56/4.23 thf(zip_derived_cl20084, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (~ (product @ X0 @ (additive_inverse @ additive_identity) @
% 25.56/4.23 additive_identity)
% 25.56/4.23 | (product @ X0 @ additive_identity @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl19214])).
% 25.56/4.23 thf(zip_derived_cl4, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 25.56/4.23 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 25.56/4.23 thf(zip_derived_cl265, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ X0 @ additive_identity @ X0)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl250])).
% 25.56/4.23 thf(zip_derived_cl1116, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X0 @ X0)
% 25.56/4.23 | (sum @ additive_identity @ (multiply @ X1 @ X0) @
% 25.56/4.23 additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl165, zip_derived_cl82])).
% 25.56/4.23 thf(zip_derived_cl1808, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 25.56/4.23 additive_identity)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl265, zip_derived_cl1116])).
% 25.56/4.23 thf(zip_derived_cl1, plain,
% 25.56/4.23 (![X0 : $i]: (sum @ (additive_inverse @ X0) @ X0 @ additive_identity)),
% 25.56/4.23 inference('cnf', [status(esa)], [additive_inverse1])).
% 25.56/4.23 thf(zip_derived_cl50, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1) | (sum @ (additive_inverse @ X2) @ X1 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 25.56/4.23 thf(zip_derived_cl8, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (sum @ additive_identity @ X2 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X2))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 25.56/4.23 thf(zip_derived_cl171, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X0 @ X1)
% 25.56/4.23 | ~ (sum @ (additive_inverse @ X2) @ X1 @ X3)
% 25.56/4.23 | (sum @ additive_identity @ X3 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl8])).
% 25.56/4.23 thf(zip_derived_cl1340, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 ( (sum @ additive_identity @ additive_identity @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X1 @ X0))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl171])).
% 25.56/4.23 thf(zip_derived_cl1843, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (sum @ additive_identity @ additive_identity @
% 25.56/4.23 (multiply @ X0 @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1808, zip_derived_cl1340])).
% 25.56/4.23 thf(zip_derived_cl106, plain,
% 25.56/4.23 ( (sum @ additive_identity @ additive_identity @
% 25.56/4.23 (additive_inverse @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl42])).
% 25.56/4.23 thf(zip_derived_cl9, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (sum @ (additive_inverse @ X0) @ X2 @ X1)
% 25.56/4.23 | ~ (sum @ additive_identity @ X3 @ X1)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X2))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 25.56/4.23 thf(zip_derived_cl117, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ X1 @ additive_identity @ X0)
% 25.56/4.23 | (sum @ (additive_inverse @ X1) @ X0 @
% 25.56/4.23 (additive_inverse @ additive_identity)))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl9])).
% 25.56/4.23 thf(zip_derived_cl1246, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 (~ (sum @ X2 @ X1 @ X0)
% 25.56/4.23 | (sum @ X3 @ X1 @ additive_identity)
% 25.56/4.23 | ~ (sum @ X0 @ X3 @ X2))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl168])).
% 25.56/4.23 thf(zip_derived_cl1562, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (sum @ X0 @ X1 @ X0) | (sum @ X1 @ X1 @ additive_identity))),
% 25.56/4.23 inference('eq_fact', [status(thm)], [zip_derived_cl1246])).
% 25.56/4.23 thf(zip_derived_cl1572, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (~ (sum @ additive_identity @ additive_identity @ X0)
% 25.56/4.23 | (sum @ X0 @ X0 @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl1562])).
% 25.56/4.23 thf(zip_derived_cl1905, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (sum @ (multiply @ X0 @ additive_identity) @
% 25.56/4.23 (multiply @ X0 @ additive_identity) @ additive_identity)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1843, zip_derived_cl1572])).
% 25.56/4.23 thf(zip_derived_cl106, plain,
% 25.56/4.23 ( (sum @ additive_identity @ additive_identity @
% 25.56/4.23 (additive_inverse @ additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl42])).
% 25.56/4.23 thf(zip_derived_cl6, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 25.56/4.23 (~ (product @ X0 @ X1 @ X2)
% 25.56/4.23 | ~ (product @ X0 @ X3 @ X4)
% 25.56/4.23 | ~ (sum @ X1 @ X3 @ X5)
% 25.56/4.23 | ~ (sum @ X2 @ X4 @ X6)
% 25.56/4.23 | (product @ X0 @ X5 @ X6))),
% 25.56/4.23 inference('cnf', [status(esa)], [distributivity2])).
% 25.56/4.23 thf(zip_derived_cl113, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 25.56/4.23 ( (product @ X1 @ (additive_inverse @ additive_identity) @ X0)
% 25.56/4.23 | ~ (sum @ X3 @ X2 @ X0)
% 25.56/4.23 | ~ (product @ X1 @ additive_identity @ X2)
% 25.56/4.23 | ~ (product @ X1 @ additive_identity @ X3))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl6])).
% 25.56/4.23 thf(zip_derived_cl27170, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 (~ (product @ X1 @ additive_identity @
% 25.56/4.23 (multiply @ X0 @ additive_identity))
% 25.56/4.23 | ~ (product @ X1 @ additive_identity @
% 25.56/4.23 (multiply @ X0 @ additive_identity))
% 25.56/4.23 | (product @ X1 @ (additive_inverse @ additive_identity) @
% 25.56/4.23 additive_identity))),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl1905, zip_derived_cl113])).
% 25.56/4.23 thf(zip_derived_cl27213, plain,
% 25.56/4.23 (![X0 : $i, X1 : $i]:
% 25.56/4.23 ( (product @ X1 @ (additive_inverse @ additive_identity) @
% 25.56/4.23 additive_identity)
% 25.56/4.23 | ~ (product @ X1 @ additive_identity @
% 25.56/4.23 (multiply @ X0 @ additive_identity)))),
% 25.56/4.23 inference('simplify', [status(thm)], [zip_derived_cl27170])).
% 25.56/4.23 thf(zip_derived_cl27413, plain,
% 25.56/4.23 (![X0 : $i]:
% 25.56/4.23 (product @ X0 @ (additive_inverse @ additive_identity) @
% 25.56/4.23 additive_identity)),
% 25.56/4.23 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl27213])).
% 25.56/4.23 thf(zip_derived_cl27416, plain,
% 25.56/4.23 (![X0 : $i]: (product @ X0 @ additive_identity @ additive_identity)),
% 25.56/4.23 inference('demod', [status(thm)],
% 25.56/4.23 [zip_derived_cl20084, zip_derived_cl27413])).
% 25.56/4.23 thf(zip_derived_cl27442, plain, ($false),
% 25.56/4.23 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl27416])).
% 25.56/4.23
% 25.56/4.23 % SZS output end Refutation
% 25.56/4.23
% 25.56/4.23
% 25.56/4.23 % Terminating...
% 25.74/4.27 % Runner terminated.
% 25.74/4.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------