%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : BOO017-10 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.lyo5fiBHaP true
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:29:48 PM UTC 2025
% Result : Unsatisfiable 104.66s 15.58s
% Output : Refutation 104.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO017-10 : TPTP v9.2.0. Released v7.5.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.lyo5fiBHaP true
% 0.13/0.34 % Computer : n026.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 : Wed Oct 1 13:56:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.56/0.66 % Total configuration time : 435
% 0.56/0.66 % Estimated wc time : 1092
% 0.56/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.57/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 104.66/15.58 % Solved by fo/fo5.sh.
% 104.66/15.58 % done 7832 iterations in 14.759s
% 104.66/15.58 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 104.66/15.58 % SZS output start Refutation
% 104.66/15.58 thf(y_type, type, y: $i).
% 104.66/15.58 thf(x_type, type, x: $i).
% 104.66/15.58 thf(z_type, type, z: $i).
% 104.66/15.58 thf(add_type, type, add: $i > $i > $i).
% 104.66/15.58 thf(multiply_type, type, multiply: $i > $i > $i).
% 104.66/15.58 thf(additive_identity_type, type, additive_identity: $i).
% 104.66/15.58 thf(sum_type, type, sum: $i > $i > $i > $i).
% 104.66/15.58 thf(ifeq2_type, type, ifeq2: $i > $i > $i > $i > $i).
% 104.66/15.58 thf(product_type, type, product: $i > $i > $i > $i).
% 104.66/15.58 thf(true_type, type, true: $i).
% 104.66/15.58 thf(inverse_type, type, inverse: $i > $i).
% 104.66/15.58 thf(ifeq_type, type, ifeq: $i > $i > $i > $i > $i).
% 104.66/15.58 thf(closure_of_multiplication, axiom,
% 104.66/15.58 (( product @ X @ Y @ ( multiply @ X @ Y ) ) = ( true ))).
% 104.66/15.58 thf(zip_derived_cl3, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 104.66/15.58 thf(closure_of_addition, axiom,
% 104.66/15.58 (( sum @ X @ Y @ ( add @ X @ Y ) ) = ( true ))).
% 104.66/15.58 thf(zip_derived_cl2, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_addition])).
% 104.66/15.58 thf(x_plus_y, axiom, (( sum @ x @ y @ z ) = ( true ))).
% 104.66/15.58 thf(zip_derived_cl24, plain, (((sum @ x @ y @ z) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [x_plus_y])).
% 104.66/15.58 thf(additive_identity2, axiom,
% 104.66/15.58 (( sum @ X @ additive_identity @ X ) = ( true ))).
% 104.66/15.58 thf(zip_derived_cl7, plain,
% 104.66/15.58 (![X0 : $i]: ((sum @ X0 @ additive_identity @ X0) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [additive_identity2])).
% 104.66/15.58 thf(distributivity5, axiom,
% 104.66/15.58 (( ifeq @
% 104.66/15.58 ( product @ Y @ Z @ V3 ) @ true @
% 104.66/15.58 ( ifeq @
% 104.66/15.58 ( sum @ X @ V3 @ V4 ) @ true @
% 104.66/15.58 ( ifeq @
% 104.66/15.58 ( sum @ X @ Z @ V2 ) @ true @
% 104.66/15.58 ( ifeq @
% 104.66/15.58 ( sum @ X @ Y @ V1 ) @ true @ ( product @ V1 @ V2 @ V4 ) @ true ) @
% 104.66/15.58 true ) @
% 104.66/15.58 true ) @
% 104.66/15.58 true ) =
% 104.66/15.58 ( true ))).
% 104.66/15.58 thf(zip_derived_cl14, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 104.66/15.58 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 104.66/15.58 (ifeq @ (sum @ X3 @ X2 @ X4) @ true @
% 104.66/15.58 (ifeq @ (sum @ X3 @ X1 @ X5) @ true @
% 104.66/15.58 (ifeq @ (sum @ X3 @ X0 @ X6) @ true @ (product @ X6 @ X5 @ X4) @
% 104.66/15.58 true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [distributivity5])).
% 104.66/15.58 thf(zip_derived_cl339, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.66/15.58 ((ifeq @ (product @ additive_identity @ X3 @ X4) @ true @
% 104.66/15.58 (ifeq @ (sum @ X2 @ X4 @ X0) @ true @
% 104.66/15.58 (ifeq @ (sum @ X2 @ X3 @ X1) @ true @
% 104.66/15.58 (ifeq @ true @ true @ (product @ X2 @ X1 @ X0) @ true) @ true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl14])).
% 104.66/15.58 thf(ifeq_axiom_001, axiom, (( ifeq @ A @ A @ B @ C ) = ( B ))).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl366, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 104.66/15.58 ((ifeq @ (product @ additive_identity @ X3 @ X4) @ true @
% 104.66/15.58 (ifeq @ (sum @ X2 @ X4 @ X0) @ true @
% 104.66/15.58 (ifeq @ (sum @ X2 @ X3 @ X1) @ true @ (product @ X2 @ X1 @ X0) @
% 104.66/15.58 true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl339, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl15393, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq @ (product @ additive_identity @ y @ X1) @ true @
% 104.66/15.58 (ifeq @ (sum @ x @ X1 @ X0) @ true @
% 104.66/15.58 (ifeq @ true @ true @ (product @ x @ z @ X0) @ true) @ true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl366])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl15422, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq @ (product @ additive_identity @ y @ X1) @ true @
% 104.66/15.58 (ifeq @ (sum @ x @ X1 @ X0) @ true @ (product @ x @ z @ X0) @ true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl15393, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl36972, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((ifeq @ (product @ additive_identity @ y @ X0) @ true @
% 104.66/15.58 (ifeq @ true @ true @ (product @ x @ z @ (add @ x @ X0)) @ true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl15422])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl36982, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((ifeq @ (product @ additive_identity @ y @ X0) @ true @
% 104.66/15.58 (product @ x @ z @ (add @ x @ X0)) @ true) = (true))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl36972, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl36997, plain,
% 104.66/15.58 (((ifeq @ true @ true @
% 104.66/15.58 (product @ x @ z @ (add @ x @ (multiply @ additive_identity @ y))) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl36982])).
% 104.66/15.58 thf(zip_derived_cl3, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 104.66/15.58 thf(commutativity_of_multiplication, axiom,
% 104.66/15.58 (( ifeq @ ( product @ X @ Y @ Z ) @ true @ ( product @ Y @ X @ Z ) @ true ) =
% 104.66/15.58 ( true ))).
% 104.66/15.58 thf(zip_derived_cl5, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @ (product @ X1 @ X0 @ X2) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [commutativity_of_multiplication])).
% 104.66/15.58 thf(zip_derived_cl31, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq @ true @ true @ (product @ X0 @ X1 @ (multiply @ X1 @ X0)) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl45, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((true) = (product @ X0 @ X1 @ (multiply @ X1 @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl3, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 104.66/15.58 thf(multiplication_is_well_defined, axiom,
% 104.66/15.58 (( ifeq2 @
% 104.66/15.58 ( product @ X @ Y @ V ) @ true @
% 104.66/15.58 ( ifeq2 @ ( product @ X @ Y @ U ) @ true @ U @ V ) @ V ) =
% 104.66/15.58 ( V ))).
% 104.66/15.58 thf(zip_derived_cl23, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.66/15.58 ((ifeq2 @ (product @ X1 @ X2 @ X0) @ true @
% 104.66/15.58 (ifeq2 @ (product @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (
% 104.66/15.58 X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [multiplication_is_well_defined])).
% 104.66/15.58 thf(zip_derived_cl72, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @ (multiply @ X1 @ X0)) @
% 104.66/15.58 (multiply @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl23])).
% 104.66/15.58 thf(zip_derived_cl659, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ true @ true @ (multiply @ X0 @ X1) @ (multiply @ X1 @ X0)) @
% 104.66/15.58 (multiply @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl72])).
% 104.66/15.58 thf(ifeq_axiom, axiom, (( ifeq2 @ A @ A @ B @ C ) = ( B ))).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl669, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl659, zip_derived_cl0, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl37000, plain,
% 104.66/15.58 (((product @ x @ z @ (add @ x @ (multiply @ y @ additive_identity)))
% 104.66/15.58 = (true))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl36997, zip_derived_cl669, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl72, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @ (multiply @ X1 @ X0)) @
% 104.66/15.58 (multiply @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl23])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl653, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((multiply @ X1 @ X0)
% 104.66/15.58 = (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @
% 104.66/15.58 (multiply @ X1 @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl37013, plain,
% 104.66/15.58 (((multiply @ x @ z)
% 104.66/15.58 = (ifeq2 @ true @ true @
% 104.66/15.58 (add @ x @ (multiply @ y @ additive_identity)) @ (multiply @ x @ z)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl37000, zip_derived_cl653])).
% 104.66/15.58 thf(zip_derived_cl669, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl659, zip_derived_cl0, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl669, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl659, zip_derived_cl0, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl37357, plain,
% 104.66/15.58 (((multiply @ z @ x) = (add @ x @ (multiply @ y @ additive_identity)))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl37013, zip_derived_cl669, zip_derived_cl669,
% 104.66/15.58 zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl3, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 104.66/15.58 thf(multiplicative_inverse2, axiom,
% 104.66/15.58 (( product @ X @ ( inverse @ X ) @ additive_identity ) = ( true ))).
% 104.66/15.58 thf(zip_derived_cl21, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((product @ X0 @ (inverse @ X0) @ additive_identity) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 104.66/15.58 thf(zip_derived_cl7, plain,
% 104.66/15.58 (![X0 : $i]: ((sum @ X0 @ additive_identity @ X0) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [additive_identity2])).
% 104.66/15.58 thf(zip_derived_cl3, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((product @ X0 @ X1 @ (multiply @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_multiplication])).
% 104.66/15.58 thf(distributivity1, axiom,
% 104.66/15.58 (( ifeq @
% 104.66/15.58 ( product @ X @ V3 @ V4 ) @ true @
% 104.66/15.58 ( ifeq @
% 104.66/15.58 ( product @ X @ Z @ V2 ) @ true @
% 104.66/15.58 ( ifeq @
% 104.66/15.58 ( product @ X @ Y @ V1 ) @ true @
% 104.66/15.58 ( ifeq @ ( sum @ Y @ Z @ V3 ) @ true @ ( sum @ V1 @ V2 @ V4 ) @ true ) @
% 104.66/15.58 true ) @
% 104.66/15.58 true ) @
% 104.66/15.58 true ) =
% 104.66/15.58 ( true ))).
% 104.66/15.58 thf(zip_derived_cl10, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 104.66/15.58 ((ifeq @ (product @ X0 @ X1 @ X2) @ true @
% 104.66/15.58 (ifeq @ (product @ X0 @ X3 @ X4) @ true @
% 104.66/15.58 (ifeq @ (product @ X0 @ X5 @ X6) @ true @
% 104.66/15.58 (ifeq @ (sum @ X5 @ X3 @ X1) @ true @ (sum @ X6 @ X4 @ X2) @ true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [distributivity1])).
% 104.66/15.58 thf(zip_derived_cl123, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 104.66/15.58 ((ifeq @ true @ true @
% 104.66/15.58 (ifeq @ (product @ X1 @ X4 @ X2) @ true @
% 104.66/15.58 (ifeq @ (product @ X1 @ X5 @ X3) @ true @
% 104.66/15.58 (ifeq @ (sum @ X5 @ X4 @ X0) @ true @
% 104.66/15.58 (sum @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl10])).
% 104.66/15.58 thf(zip_derived_cl1796, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.66/15.58 ((ifeq @ true @ true @
% 104.66/15.58 (ifeq @ (product @ X1 @ additive_identity @ X2) @ true @
% 104.66/15.58 (ifeq @ (product @ X1 @ X0 @ X3) @ true @
% 104.66/15.58 (ifeq @ true @ true @ (sum @ X3 @ X2 @ (multiply @ X1 @ X0)) @
% 104.66/15.58 true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl123])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl1816, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.66/15.58 ((ifeq @ (product @ X1 @ additive_identity @ X2) @ true @
% 104.66/15.58 (ifeq @ (product @ X1 @ X0 @ X3) @ true @
% 104.66/15.58 (sum @ X3 @ X2 @ (multiply @ X1 @ X0)) @ true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl1796, zip_derived_cl1, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl68291, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq @ (product @ X0 @ additive_identity @ X1) @ true @
% 104.66/15.58 (ifeq @ true @ true @
% 104.66/15.58 (sum @ additive_identity @ X1 @ (multiply @ X0 @ (inverse @ X0))) @
% 104.66/15.58 true) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1816])).
% 104.66/15.58 thf(zip_derived_cl21, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((product @ X0 @ (inverse @ X0) @ additive_identity) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [multiplicative_inverse2])).
% 104.66/15.58 thf(zip_derived_cl72, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ (product @ X1 @ X0 @ X2) @ true @ X2 @ (multiply @ X1 @ X0)) @
% 104.66/15.58 (multiply @ X1 @ X0)) = (multiply @ X1 @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl23])).
% 104.66/15.58 thf(zip_derived_cl661, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ true @ true @ additive_identity @
% 104.66/15.58 (multiply @ X0 @ (inverse @ X0))) @
% 104.66/15.58 (multiply @ X0 @ (inverse @ X0))) = (multiply @ X0 @ (inverse @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl72])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl671, plain,
% 104.66/15.58 (![X0 : $i]: ((additive_identity) = (multiply @ X0 @ (inverse @ X0)))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl661, zip_derived_cl0, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl68327, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq @ (product @ X0 @ additive_identity @ X1) @ true @
% 104.66/15.58 (sum @ additive_identity @ X1 @ additive_identity) @ true) = (
% 104.66/15.58 true))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl68291, zip_derived_cl671, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl71162, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((ifeq @ true @ true @
% 104.66/15.58 (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 104.66/15.58 additive_identity) @
% 104.66/15.58 true) = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl68327])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl71186, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((true)
% 104.66/15.58 = (sum @ additive_identity @ (multiply @ X0 @ additive_identity) @
% 104.66/15.58 additive_identity))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl71162, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl2, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_addition])).
% 104.66/15.58 thf(commutativity_of_addition, axiom,
% 104.66/15.58 (( ifeq @ ( sum @ X @ Y @ Z ) @ true @ ( sum @ Y @ X @ Z ) @ true ) =
% 104.66/15.58 ( true ))).
% 104.66/15.58 thf(zip_derived_cl4, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((ifeq @ (sum @ X0 @ X1 @ X2) @ true @ (sum @ X1 @ X0 @ X2) @ true)
% 104.66/15.58 = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [commutativity_of_addition])).
% 104.66/15.58 thf(zip_derived_cl53, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq @ true @ true @ (sum @ X0 @ X1 @ (add @ X1 @ X0)) @ true)
% 104.66/15.58 = (true))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl4])).
% 104.66/15.58 thf(zip_derived_cl1, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 104.66/15.58 thf(zip_derived_cl588, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((true) = (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl2, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_addition])).
% 104.66/15.58 thf(addition_is_well_defined, axiom,
% 104.66/15.58 (( ifeq2 @
% 104.66/15.58 ( sum @ X @ Y @ V ) @ true @
% 104.66/15.58 ( ifeq2 @ ( sum @ X @ Y @ U ) @ true @ U @ V ) @ V ) =
% 104.66/15.58 ( V ))).
% 104.66/15.58 thf(zip_derived_cl22, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.66/15.58 ((ifeq2 @ (sum @ X1 @ X2 @ X0) @ true @
% 104.66/15.58 (ifeq2 @ (sum @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 104.66/15.58 thf(zip_derived_cl88, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ (sum @ X1 @ X0 @ X2) @ true @ X2 @ (add @ X1 @ X0)) @
% 104.66/15.58 (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl22])).
% 104.66/15.58 thf(zip_derived_cl941, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ true @ true @ (add @ X0 @ X1) @ (add @ X1 @ X0)) @
% 104.66/15.58 (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl588, zip_derived_cl88])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl961, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((add @ X0 @ X1) = (add @ X1 @ X0))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl941, zip_derived_cl0, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl88, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @
% 104.66/15.58 (ifeq2 @ (sum @ X1 @ X0 @ X2) @ true @ X2 @ (add @ X1 @ X0)) @
% 104.66/15.58 (add @ X1 @ X0)) = (add @ X1 @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl22])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl926, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((add @ X1 @ X0)
% 104.66/15.58 = (ifeq2 @ (sum @ X1 @ X0 @ X2) @ true @ X2 @ (add @ X1 @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl88, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl1286, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 104.66/15.58 ((add @ X0 @ X1)
% 104.66/15.58 = (ifeq2 @ (sum @ X0 @ X1 @ X2) @ true @ X2 @ (add @ X1 @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl961, zip_derived_cl926])).
% 104.66/15.58 thf(zip_derived_cl71287, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((add @ additive_identity @ (multiply @ X0 @ additive_identity))
% 104.66/15.58 = (ifeq2 @ true @ true @ additive_identity @
% 104.66/15.58 (add @ (multiply @ X0 @ additive_identity) @ additive_identity)))),
% 104.66/15.58 inference('sup+', [status(thm)],
% 104.66/15.58 [zip_derived_cl71186, zip_derived_cl1286])).
% 104.66/15.58 thf(zip_derived_cl588, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((true) = (sum @ X0 @ X1 @ (add @ X1 @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl7, plain,
% 104.66/15.58 (![X0 : $i]: ((sum @ X0 @ additive_identity @ X0) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [additive_identity2])).
% 104.66/15.58 thf(zip_derived_cl22, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 104.66/15.58 ((ifeq2 @ (sum @ X1 @ X2 @ X0) @ true @
% 104.66/15.58 (ifeq2 @ (sum @ X1 @ X2 @ X3) @ true @ X3 @ X0) @ X0) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [addition_is_well_defined])).
% 104.66/15.58 thf(zip_derived_cl83, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq2 @ (sum @ X1 @ additive_identity @ X0) @ true @
% 104.66/15.58 (ifeq2 @ true @ true @ X1 @ X0) @ X0) = (X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl95, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq2 @ (sum @ X1 @ additive_identity @ X0) @ true @ X1 @ X0) = (X0))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl623, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @ X0 @ (add @ additive_identity @ X0))
% 104.66/15.58 = (add @ additive_identity @ X0))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl588, zip_derived_cl95])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl646, plain,
% 104.66/15.58 (![X0 : $i]: ((X0) = (add @ additive_identity @ X0))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl623, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl2, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]: ((sum @ X0 @ X1 @ (add @ X0 @ X1)) = (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [closure_of_addition])).
% 104.66/15.58 thf(zip_derived_cl95, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((ifeq2 @ (sum @ X1 @ additive_identity @ X0) @ true @ X1 @ X0) = (X0))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl582, plain,
% 104.66/15.58 (![X0 : $i]:
% 104.66/15.58 ((ifeq2 @ true @ true @ X0 @ (add @ X0 @ additive_identity))
% 104.66/15.58 = (add @ X0 @ additive_identity))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl95])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl586, plain,
% 104.66/15.58 (![X0 : $i]: ((X0) = (add @ X0 @ additive_identity))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl0, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 104.66/15.58 inference('cnf', [status(esa)], [ifeq_axiom])).
% 104.66/15.58 thf(zip_derived_cl71736, plain,
% 104.66/15.58 (![X0 : $i]: ((multiply @ X0 @ additive_identity) = (additive_identity))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl71287, zip_derived_cl646, zip_derived_cl586,
% 104.66/15.58 zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl586, plain,
% 104.66/15.58 (![X0 : $i]: ((X0) = (add @ X0 @ additive_identity))),
% 104.66/15.58 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 104.66/15.58 thf(zip_derived_cl72144, plain, (((multiply @ z @ x) = (x))),
% 104.66/15.58 inference('demod', [status(thm)],
% 104.66/15.58 [zip_derived_cl37357, zip_derived_cl71736, zip_derived_cl586])).
% 104.66/15.58 thf(zip_derived_cl45, plain,
% 104.66/15.58 (![X0 : $i, X1 : $i]:
% 104.66/15.58 ((true) = (product @ X0 @ X1 @ (multiply @ X1 @ X0)))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl1])).
% 104.66/15.58 thf(zip_derived_cl72411, plain, (((true) = (product @ x @ z @ x))),
% 104.66/15.58 inference('sup+', [status(thm)], [zip_derived_cl72144, zip_derived_cl45])).
% 104.66/15.58 thf(prove_product, conjecture, (( product @ x @ z @ x ) = ( true ))).
% 104.66/15.58 thf(zf_stmt_0, negated_conjecture, (( product @ x @ z @ x ) != ( true )),
% 104.66/15.58 inference('cnf.neg', [status(esa)], [prove_product])).
% 104.66/15.58 thf(zip_derived_cl25, plain, (((product @ x @ z @ x) != (true))),
% 104.66/15.58 inference('cnf', [status(esa)], [zf_stmt_0])).
% 104.66/15.58 thf(zip_derived_cl72489, plain, ($false),
% 104.66/15.58 inference('simplify_reflect-', [status(thm)],
% 104.66/15.58 [zip_derived_cl72411, zip_derived_cl25])).
% 104.66/15.58
% 104.66/15.58 % SZS output end Refutation
% 104.66/15.58
% 104.66/15.58
% 104.66/15.58 % Terminating...
% 105.12/15.68 % Runner terminated.
% 105.12/15.70 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------