TSTP Solution File: BOO004-10 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO004-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.IzgVz6NPon true
% Computer : n028.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 : Wed Aug 30 18:13:12 EDT 2023
% Result : Unsatisfiable 15.88s 2.89s
% Output : Refutation 15.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO004-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.IzgVz6NPon true
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 08:53:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.35/0.80 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 15.88/2.89 % Solved by fo/fo5.sh.
% 15.88/2.89 % done 1925 iterations in 2.089s
% 15.88/2.89 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 15.88/2.89 % SZS output start Refutation
% 15.88/2.89 thf(x_type, type, x: $i).
% 15.88/2.89 thf(add_type, type, add: $i > $i > $i).
% 15.88/2.89 thf(sum_type, type, sum: $i > $i > $i > $i).
% 15.88/2.89 thf(ifeq2_type, type, ifeq2: $i > $i > $i > $i > $i).
% 15.88/2.89 thf(product_type, type, product: $i > $i > $i > $i).
% 15.88/2.89 thf(true_type, type, true: $i).
% 15.88/2.89 thf(multiplicative_identity_type, type, multiplicative_identity: $i).
% 15.88/2.89 thf(inverse_type, type, inverse: $i > $i).
% 15.88/2.89 thf(ifeq_type, type, ifeq: $i > $i > $i > $i > $i).
% 15.88/2.89 thf(prove_both_equalities, conjecture, (( sum @ x @ x @ x ) = ( true ))).
% 15.88/2.89 thf(zf_stmt_0, negated_conjecture, (( sum @ x @ x @ x ) != ( true )),
% 15.88/2.89 inference('cnf.neg', [status(esa)], [prove_both_equalities])).
% 15.88/2.89 thf(zip_derived_cl24, plain, (((sum @ x @ x @ x) != (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [zf_stmt_0])).
% 15.88/2.89 thf(multiplicative_identity2, axiom,
% 15.88/2.89 (( product @ X @ multiplicative_identity @ X ) = ( true ))).
% 15.88/2.89 thf(zip_derived_cl9, plain,
% 15.88/2.89 (![X0 : $i]: ((product @ X0 @ multiplicative_identity @ X0) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 15.88/2.89 thf(zip_derived_cl9, plain,
% 15.88/2.89 (![X0 : $i]: ((product @ X0 @ multiplicative_identity @ X0) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 15.88/2.89 thf(zip_derived_cl9, plain,
% 15.88/2.89 (![X0 : $i]: ((product @ X0 @ multiplicative_identity @ X0) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 15.88/2.89 thf(distributivity1, axiom,
% 15.88/2.89 (( ifeq @
% 15.88/2.89 ( product @ X @ V3 @ V4 ) @ true @
% 15.88/2.89 ( ifeq @
% 15.88/2.89 ( product @ X @ Z @ V2 ) @ true @
% 15.88/2.89 ( ifeq @
% 15.88/2.89 ( product @ X @ Y @ V1 ) @ true @
% 15.88/2.89 ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @
% 15.88/2.89 true ) @
% 15.88/2.89 true ) @
% 15.88/2.89 true ) =
% 15.88/2.89 ( true ))).
% 15.88/2.89 thf(zip_derived_cl10, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 15.88/2.89 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 15.88/2.89 (ifeq @ (product @ X0 @ X3 @ X4) @ true @
% 15.88/2.89 (ifeq @ (product @ X0 @ X5 @ X6) @ true @
% 15.88/2.89 (ifeq @ (sum @ X5 @ X3 @ X1) @ true @ (sum @ X6 @ X4 @ X2) @ true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [distributivity1])).
% 15.88/2.89 thf(zip_derived_cl274, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 15.88/2.89 ((ifeq @ true @ true @
% 15.88/2.89 (ifeq @ (product @ X0 @ X3 @ X1) @ true @
% 15.88/2.89 (ifeq @ (product @ X0 @ X4 @ X2) @ true @
% 15.88/2.89 (ifeq @ (sum @ X4 @ X3 @ multiplicative_identity) @ true @
% 15.88/2.89 (sum @ X2 @ X1 @ X0) @ true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl10])).
% 15.88/2.89 thf(zip_derived_cl13822, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((ifeq @ true @ true @
% 15.88/2.89 (ifeq @ (product @ X0 @ X2 @ X1) @ true @
% 15.88/2.89 (ifeq @ true @ true @
% 15.88/2.89 (ifeq @
% 15.88/2.89 (sum @ multiplicative_identity @ X2 @ multiplicative_identity) @
% 15.88/2.89 true @ (sum @ X0 @ X1 @ X0) @ true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl274])).
% 15.88/2.89 thf(additive_inverse2, axiom,
% 15.88/2.89 (( sum @ X @ ( inverse @ X ) @ multiplicative_identity ) = ( true ))).
% 15.88/2.89 thf(zip_derived_cl19, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((sum @ X0 @ (inverse @ X0) @ multiplicative_identity) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [additive_inverse2])).
% 15.88/2.89 thf(closure_of_addition, axiom,
% 15.88/2.89 (( sum @ X @ Y @ ( add @ X @ Y ) ) = ( true ))).
% 15.88/2.89 thf(zip_derived_cl2, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [closure_of_addition])).
% 15.88/2.89 thf(multiplicative_identity1, axiom,
% 15.88/2.89 (( product @ multiplicative_identity @ X @ X ) = ( true ))).
% 15.88/2.89 thf(zip_derived_cl8, plain,
% 15.88/2.89 (![X0 : $i]: ((product @ multiplicative_identity @ X0 @ X0) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [multiplicative_identity1])).
% 15.88/2.89 thf(zip_derived_cl9, plain,
% 15.88/2.89 (![X0 : $i]: ((product @ X0 @ multiplicative_identity @ X0) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [multiplicative_identity2])).
% 15.88/2.89 thf(distributivity6, axiom,
% 15.88/2.89 (( ifeq @
% 15.88/2.89 ( product @ V1 @ V2 @ V4 ) @ true @
% 15.88/2.89 ( ifeq @
% 15.88/2.89 ( product @ Y @ Z @ V3 ) @ true @
% 15.88/2.89 ( ifeq @
% 15.88/2.89 ( sum @ X @ Z @ V2 ) @ true @
% 15.88/2.89 ( ifeq @ ( sum @ X @ Y @ V1 ) @ true @ ( sum @ X @ V3 @ V4 ) @ true ) @
% 15.88/2.89 true ) @
% 15.88/2.89 true ) @
% 15.88/2.89 true ) =
% 15.88/2.89 ( true ))).
% 15.88/2.89 thf(zip_derived_cl15, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 15.88/2.89 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 15.88/2.89 (ifeq @ (product @ X3 @ X4 @ X5) @ true @
% 15.88/2.89 (ifeq @ (sum @ X6 @ X4 @ X1) @ true @
% 15.88/2.89 (ifeq @ (sum @ X6 @ X3 @ X0) @ true @ (sum @ X6 @ X5 @ X2) @ true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [distributivity6])).
% 15.88/2.89 thf(zip_derived_cl156, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 15.88/2.89 ((ifeq @ true @ true @
% 15.88/2.89 (ifeq @ (product @ X3 @ X4 @ X1) @ true @
% 15.88/2.89 (ifeq @ (sum @ X2 @ X4 @ multiplicative_identity) @ true @
% 15.88/2.89 (ifeq @ (sum @ X2 @ X3 @ X0) @ true @ (sum @ X2 @ X1 @ X0) @ true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl15])).
% 15.88/2.89 thf(zip_derived_cl4468, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((ifeq @ true @ true @
% 15.88/2.89 (ifeq @ true @ true @
% 15.88/2.89 (ifeq @ (sum @ X2 @ X1 @ multiplicative_identity) @ true @
% 15.88/2.89 (ifeq @ (sum @ X2 @ multiplicative_identity @ X0) @ true @
% 15.88/2.89 (sum @ X2 @ X1 @ X0) @ true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl156])).
% 15.88/2.89 thf(ifeq_axiom_001, axiom, (( ifeq @ A @ A @ B @ C ) = ( B ))).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl4491, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((ifeq @ (sum @ X2 @ X1 @ multiplicative_identity) @ true @
% 15.88/2.89 (ifeq @ (sum @ X2 @ multiplicative_identity @ X0) @ true @
% 15.88/2.89 (sum @ X2 @ X1 @ X0) @ true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('demod', [status(thm)],
% 15.88/2.89 [zip_derived_cl4468, zip_derived_cl1, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl7299, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]:
% 15.88/2.89 ((ifeq @ (sum @ X0 @ X1 @ multiplicative_identity) @ true @
% 15.88/2.89 (ifeq @ true @ true @
% 15.88/2.89 (sum @ X0 @ X1 @ (add @ X0 @ multiplicative_identity)) @ true) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl4491])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl7315, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]:
% 15.88/2.89 ((ifeq @ (sum @ X0 @ X1 @ multiplicative_identity) @ true @
% 15.88/2.89 (sum @ X0 @ X1 @ (add @ X0 @ multiplicative_identity)) @ true)
% 15.88/2.89 = (true))),
% 15.88/2.89 inference('demod', [status(thm)], [zip_derived_cl7299, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl7355, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((ifeq @ true @ true @
% 15.88/2.89 (sum @ X0 @ (inverse @ X0) @ (add @ X0 @ multiplicative_identity)) @
% 15.88/2.89 true) = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl7315])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl8512, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((true)
% 15.88/2.89 = (sum @ X0 @ (inverse @ X0) @ (add @ X0 @ multiplicative_identity)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl7355, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl2, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [closure_of_addition])).
% 15.88/2.89 thf(commutativity_of_addition, axiom,
% 15.88/2.89 (( ifeq @ ( sum @ X @ Y @ Z ) @ true @ ( sum @ Y @ X @ Z ) @ true ) =
% 15.88/2.89 ( true ))).
% 15.88/2.89 thf(zip_derived_cl4, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((ifeq @ (sum @ X0 @ X1 @ X2) @ true @ (sum @ X1 @ X0 @ X2) @ true)
% 15.88/2.89 = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 15.88/2.89 thf(zip_derived_cl30, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]:
% 15.88/2.89 ((ifeq @ true @ true @ (sum @ X0 @ X1 @ (add @ X1 @ X0)) @ true)
% 15.88/2.89 = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl44, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((true) = (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl2, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [closure_of_addition])).
% 15.88/2.89 thf(addition_is_well_defined, axiom,
% 15.88/2.89 (( ifeq2 @
% 15.88/2.89 ( sum @ X @ Y @ V ) @ true @
% 15.88/2.89 ( ifeq2 @ ( sum @ X @ Y @ U ) @ true @ U @ V ) @ V ) =
% 15.88/2.89 ( V ))).
% 15.88/2.89 thf(zip_derived_cl22, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 15.88/2.89 ((ifeq2 @ (sum @ X1 @ X2 @ X0) @ true @
% 15.88/2.89 (ifeq2 @ (sum @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 15.88/2.89 thf(zip_derived_cl69, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((ifeq2 @ true @ true @
% 15.88/2.89 (ifeq2 @ (sum @ X1 @ X0 @ X2) @ true @ X2 @ (add @ X1 @ X0)) @
% 15.88/2.89 (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl22])).
% 15.88/2.89 thf(zip_derived_cl589, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]:
% 15.88/2.89 ((ifeq2 @ true @ true @
% 15.88/2.89 (ifeq2 @ true @ true @ (add @ X0 @ X1) @ (add @ X1 @ X0)) @
% 15.88/2.89 (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl69])).
% 15.88/2.89 thf(ifeq_axiom, axiom, (( ifeq2 @ A @ A @ B @ C ) = ( B ))).
% 15.88/2.89 thf(zip_derived_cl0, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom])).
% 15.88/2.89 thf(zip_derived_cl0, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom])).
% 15.88/2.89 thf(zip_derived_cl601, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 15.88/2.89 inference('demod', [status(thm)],
% 15.88/2.89 [zip_derived_cl589, zip_derived_cl0, zip_derived_cl0])).
% 15.88/2.89 thf(zip_derived_cl69, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((ifeq2 @ true @ true @
% 15.88/2.89 (ifeq2 @ (sum @ X1 @ X0 @ X2) @ true @ X2 @ (add @ X1 @ X0)) @
% 15.88/2.89 (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl22])).
% 15.88/2.89 thf(zip_derived_cl0, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom])).
% 15.88/2.89 thf(zip_derived_cl581, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((add @ X1 @ X0)
% 15.88/2.89 = (ifeq2 @ (sum @ X1 @ X0 @ X2) @ true @ X2 @ (add @ X1 @ X0)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl0])).
% 15.88/2.89 thf(zip_derived_cl996, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((add @ X0 @ X1)
% 15.88/2.89 = (ifeq2 @ (sum @ X0 @ X1 @ X2) @ true @ X2 @ (add @ X1 @ X0)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl601, zip_derived_cl581])).
% 15.88/2.89 thf(zip_derived_cl8527, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((add @ X0 @ (inverse @ X0))
% 15.88/2.89 = (ifeq2 @ true @ true @ (add @ X0 @ multiplicative_identity) @
% 15.88/2.89 (add @ (inverse @ X0) @ X0)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl8512, zip_derived_cl996])).
% 15.88/2.89 thf(zip_derived_cl2, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [closure_of_addition])).
% 15.88/2.89 thf(zip_derived_cl19, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((sum @ X0 @ (inverse @ X0) @ multiplicative_identity) = (true))),
% 15.88/2.89 inference('cnf', [status(esa)], [additive_inverse2])).
% 15.88/2.89 thf(zip_derived_cl22, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 15.88/2.89 ((ifeq2 @ (sum @ X1 @ X2 @ X0) @ true @
% 15.88/2.89 (ifeq2 @ (sum @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 15.88/2.89 thf(zip_derived_cl66, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]:
% 15.88/2.89 ((ifeq2 @ (sum @ X1 @ (inverse @ X1) @ X0) @ true @
% 15.88/2.89 (ifeq2 @ true @ true @ multiplicative_identity @ X0) @ X0) = (
% 15.88/2.89 X0))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl22])).
% 15.88/2.89 thf(zip_derived_cl0, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom])).
% 15.88/2.89 thf(zip_derived_cl76, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]:
% 15.88/2.89 ((ifeq2 @ (sum @ X1 @ (inverse @ X1) @ X0) @ true @
% 15.88/2.89 multiplicative_identity @ X0) = (X0))),
% 15.88/2.89 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl0])).
% 15.88/2.89 thf(zip_derived_cl566, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((ifeq2 @ true @ true @ multiplicative_identity @
% 15.88/2.89 (add @ X0 @ (inverse @ X0))) = (add @ X0 @ (inverse @ X0)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl76])).
% 15.88/2.89 thf(zip_derived_cl0, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom])).
% 15.88/2.89 thf(zip_derived_cl572, plain,
% 15.88/2.89 (![X0 : $i]: ((multiplicative_identity) = (add @ X0 @ (inverse @ X0)))),
% 15.88/2.89 inference('demod', [status(thm)], [zip_derived_cl566, zip_derived_cl0])).
% 15.88/2.89 thf(zip_derived_cl44, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((true) = (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl76, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]:
% 15.88/2.89 ((ifeq2 @ (sum @ X1 @ (inverse @ X1) @ X0) @ true @
% 15.88/2.89 multiplicative_identity @ X0) = (X0))),
% 15.88/2.89 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl0])).
% 15.88/2.89 thf(zip_derived_cl567, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((ifeq2 @ true @ true @ multiplicative_identity @
% 15.88/2.89 (add @ (inverse @ X0) @ X0)) = (add @ (inverse @ X0) @ X0))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl76])).
% 15.88/2.89 thf(zip_derived_cl0, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom])).
% 15.88/2.89 thf(zip_derived_cl573, plain,
% 15.88/2.89 (![X0 : $i]: ((multiplicative_identity) = (add @ (inverse @ X0) @ X0))),
% 15.88/2.89 inference('demod', [status(thm)], [zip_derived_cl567, zip_derived_cl0])).
% 15.88/2.89 thf(zip_derived_cl0, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom])).
% 15.88/2.89 thf(zip_derived_cl8706, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((multiplicative_identity) = (add @ X0 @ multiplicative_identity))),
% 15.88/2.89 inference('demod', [status(thm)],
% 15.88/2.89 [zip_derived_cl8527, zip_derived_cl572, zip_derived_cl573,
% 15.88/2.89 zip_derived_cl0])).
% 15.88/2.89 thf(zip_derived_cl44, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i]: ((true) = (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl8886, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((true)
% 15.88/2.89 = (sum @ multiplicative_identity @ X0 @ multiplicative_identity))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl8706, zip_derived_cl44])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl13845, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 15.88/2.89 ((ifeq @ (product @ X0 @ X2 @ X1) @ true @ (sum @ X0 @ X1 @ X0) @ true)
% 15.88/2.89 = (true))),
% 15.88/2.89 inference('demod', [status(thm)],
% 15.88/2.89 [zip_derived_cl13822, zip_derived_cl8886, zip_derived_cl1,
% 15.88/2.89 zip_derived_cl1, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl13862, plain,
% 15.88/2.89 (![X0 : $i]:
% 15.88/2.89 ((ifeq @ true @ true @ (sum @ X0 @ X0 @ X0) @ true) = (true))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl13845])).
% 15.88/2.89 thf(zip_derived_cl1, plain,
% 15.88/2.89 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 15.88/2.89 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 15.88/2.89 thf(zip_derived_cl13870, plain,
% 15.88/2.89 (![X0 : $i]: ((true) = (sum @ X0 @ X0 @ X0))),
% 15.88/2.89 inference('sup+', [status(thm)], [zip_derived_cl13862, zip_derived_cl1])).
% 15.88/2.89 thf(zip_derived_cl13875, plain, (((true) != (true))),
% 15.88/2.89 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl13870])).
% 15.88/2.89 thf(zip_derived_cl13876, plain, ($false),
% 15.88/2.89 inference('simplify', [status(thm)], [zip_derived_cl13875])).
% 15.88/2.89
% 15.88/2.89 % SZS output end Refutation
% 15.88/2.89
% 15.88/2.89
% 15.88/2.89 % Terminating...
% 16.43/2.98 % Runner terminated.
% 16.43/2.99 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------