%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : CAT010-10 : TPTP v9.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mib1R9N8w8 true
% Computer : n012.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 04:29:58 PM UTC 2025
% Result : Unsatisfiable 5.20s 1.35s
% Output : Refutation 5.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : CAT010-10 : TPTP v9.2.0. Released v7.3.0.
% 0.04/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mib1R9N8w8 true
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Oct 1 10:46:23 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.38 % Number of cores: 8
% 0.15/0.38 % Python version: Python 3.6.8
% 0.15/0.38 % Running in FO mode
% 0.54/0.67 % Total configuration time : 435
% 0.54/0.67 % Estimated wc time : 1092
% 0.54/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 5.20/1.35 % Solved by fo/fo3_bce.sh.
% 5.20/1.35 % BCE start: 16
% 5.20/1.35 % BCE eliminated: 0
% 5.20/1.35 % PE start: 16
% 5.20/1.35 logic: eq
% 5.20/1.35 % PE eliminated: 0
% 5.20/1.35 % done 457 iterations in 0.572s
% 5.20/1.35 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.20/1.35 % SZS output start Refutation
% 5.20/1.35 thf(ifeq_type, type, ifeq: $i > $i > $i > $i > $i).
% 5.20/1.35 thf(codomain_type, type, codomain: $i > $i).
% 5.20/1.35 thf(there_exists_type, type, there_exists: $i > $i).
% 5.20/1.35 thf(domain_type, type, domain: $i > $i).
% 5.20/1.35 thf(compose_type, type, compose: $i > $i > $i).
% 5.20/1.35 thf(b_type, type, b: $i).
% 5.20/1.35 thf(true_type, type, true: $i).
% 5.20/1.35 thf(a_type, type, a: $i).
% 5.20/1.35 thf(ifeq2_type, type, ifeq2: $i > $i > $i > $i > $i).
% 5.20/1.35 thf(ab_exists, axiom, (( there_exists @ ( compose @ a @ b ) ) = ( true ))).
% 5.20/1.35 thf(zip_derived_cl14, plain, (((there_exists @ (compose @ a @ b)) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [ab_exists])).
% 5.20/1.35 thf(compose_codomain, axiom, (( compose @ ( codomain @ X ) @ X ) = ( X ))).
% 5.20/1.35 thf(zip_derived_cl13, plain,
% 5.20/1.35 (![X0 : $i]: ((compose @ (codomain @ X0) @ X0) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [compose_codomain])).
% 5.20/1.35 thf(associativity_of_compose, axiom,
% 5.20/1.35 (( compose @ X @ ( compose @ Y @ Z ) ) =
% 5.20/1.35 ( compose @ ( compose @ X @ Y ) @ Z ))).
% 5.20/1.35 thf(zip_derived_cl11, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.20/1.35 ((compose @ X0 @ (compose @ X1 @ X2))
% 5.20/1.35 = (compose @ (compose @ X0 @ X1) @ X2))),
% 5.20/1.35 inference('cnf', [status(esa)], [associativity_of_compose])).
% 5.20/1.35 thf(zip_derived_cl19, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((compose @ (codomain @ X0) @ (compose @ X0 @ X1))
% 5.20/1.35 = (compose @ X0 @ X1))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl11])).
% 5.20/1.35 thf(domain_codomain_composition1, axiom,
% 5.20/1.35 (( ifeq2 @
% 5.20/1.35 ( there_exists @ ( compose @ X @ Y ) ) @ true @ ( domain @ X ) @
% 5.20/1.35 ( codomain @ Y ) ) =
% 5.20/1.35 ( codomain @ Y ))).
% 5.20/1.35 thf(zip_derived_cl9, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X1 @ X0)) @ true @
% 5.20/1.35 (domain @ X1) @ (codomain @ X0)) = (codomain @ X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_codomain_composition1])).
% 5.20/1.35 thf(zip_derived_cl67, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X1 @ X0)) @ true @
% 5.20/1.35 (domain @ (codomain @ X1)) @ (codomain @ (compose @ X1 @ X0)))
% 5.20/1.35 = (codomain @ (compose @ X1 @ X0)))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl9])).
% 5.20/1.35 thf(zip_derived_cl2975, plain,
% 5.20/1.35 (((ifeq2 @ true @ true @ (domain @ (codomain @ a)) @
% 5.20/1.35 (codomain @ (compose @ a @ b))) = (codomain @ (compose @ a @ b)))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl67])).
% 5.20/1.35 thf(ifeq_axiom_001, axiom, (( ifeq2 @ A @ A @ B @ C ) = ( B ))).
% 5.20/1.35 thf(zip_derived_cl1, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 5.20/1.35 thf(zip_derived_cl3043, plain,
% 5.20/1.35 (((domain @ (codomain @ a)) = (codomain @ (compose @ a @ b)))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl2975, zip_derived_cl1])).
% 5.20/1.35 thf(zip_derived_cl13, plain,
% 5.20/1.35 (![X0 : $i]: ((compose @ (codomain @ X0) @ X0) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [compose_codomain])).
% 5.20/1.35 thf(zip_derived_cl3080, plain,
% 5.20/1.35 (((compose @ (domain @ (codomain @ a)) @ (compose @ a @ b))
% 5.20/1.35 = (compose @ a @ b))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl3043, zip_derived_cl13])).
% 5.20/1.35 thf(zip_derived_cl11, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.20/1.35 ((compose @ X0 @ (compose @ X1 @ X2))
% 5.20/1.35 = (compose @ (compose @ X0 @ X1) @ X2))),
% 5.20/1.35 inference('cnf', [status(esa)], [associativity_of_compose])).
% 5.20/1.35 thf(zip_derived_cl9, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X1 @ X0)) @ true @
% 5.20/1.35 (domain @ X1) @ (codomain @ X0)) = (codomain @ X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_codomain_composition1])).
% 5.20/1.35 thf(zip_derived_cl68, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X2 @ (compose @ X1 @ X0))) @
% 5.20/1.35 true @ (domain @ (compose @ X2 @ X1)) @ (codomain @ X0))
% 5.20/1.35 = (codomain @ X0))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl9])).
% 5.20/1.35 thf(zip_derived_cl3237, plain,
% 5.20/1.35 (((ifeq2 @ (there_exists @ (compose @ a @ b)) @ true @
% 5.20/1.35 (domain @ (compose @ (domain @ (codomain @ a)) @ a)) @ (codomain @ b))
% 5.20/1.35 = (codomain @ b))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl3080, zip_derived_cl68])).
% 5.20/1.35 thf(zip_derived_cl14, plain, (((there_exists @ (compose @ a @ b)) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [ab_exists])).
% 5.20/1.35 thf(zip_derived_cl14, plain, (((there_exists @ (compose @ a @ b)) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [ab_exists])).
% 5.20/1.35 thf(zip_derived_cl9, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X1 @ X0)) @ true @
% 5.20/1.35 (domain @ X1) @ (codomain @ X0)) = (codomain @ X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_codomain_composition1])).
% 5.20/1.35 thf(zip_derived_cl60, plain,
% 5.20/1.35 (((ifeq2 @ true @ true @ (domain @ a) @ (codomain @ b)) = (codomain @ b))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl9])).
% 5.20/1.35 thf(zip_derived_cl1, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 5.20/1.35 thf(zip_derived_cl69, plain, (((domain @ a) = (codomain @ b))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 5.20/1.35 thf(zip_derived_cl1, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 5.20/1.35 thf(zip_derived_cl69, plain, (((domain @ a) = (codomain @ b))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 5.20/1.35 thf(zip_derived_cl3329, plain,
% 5.20/1.35 (((domain @ (compose @ (domain @ (codomain @ a)) @ a)) = (domain @ a))),
% 5.20/1.35 inference('demod', [status(thm)],
% 5.20/1.35 [zip_derived_cl3237, zip_derived_cl14, zip_derived_cl69,
% 5.20/1.35 zip_derived_cl1, zip_derived_cl69])).
% 5.20/1.35 thf(domain_has_elements, axiom,
% 5.20/1.35 (( ifeq @
% 5.20/1.35 ( there_exists @ ( domain @ X ) ) @ true @ ( there_exists @ X ) @ true ) =
% 5.20/1.35 ( true ))).
% 5.20/1.35 thf(zip_derived_cl6, plain,
% 5.20/1.35 (![X0 : $i]:
% 5.20/1.35 ((ifeq @ (there_exists @ (domain @ X0)) @ true @
% 5.20/1.35 (there_exists @ X0) @ true) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_has_elements])).
% 5.20/1.35 thf(zip_derived_cl5618, plain,
% 5.20/1.35 (((ifeq @ (there_exists @ (domain @ a)) @ true @
% 5.20/1.35 (there_exists @ (compose @ (domain @ (codomain @ a)) @ a)) @ true)
% 5.20/1.35 = (true))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl3329, zip_derived_cl6])).
% 5.20/1.35 thf(zip_derived_cl14, plain, (((there_exists @ (compose @ a @ b)) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [ab_exists])).
% 5.20/1.35 thf(composition_implies_domain, axiom,
% 5.20/1.35 (( ifeq @
% 5.20/1.35 ( there_exists @ ( compose @ X @ Y ) ) @ true @
% 5.20/1.35 ( there_exists @ ( domain @ X ) ) @ true ) =
% 5.20/1.35 ( true ))).
% 5.20/1.35 thf(zip_derived_cl8, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq @ (there_exists @ (compose @ X0 @ X1)) @ true @
% 5.20/1.35 (there_exists @ (domain @ X0)) @ true) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [composition_implies_domain])).
% 5.20/1.35 thf(zip_derived_cl51, plain,
% 5.20/1.35 (((ifeq @ true @ true @ (there_exists @ (domain @ a)) @ true) = (true))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl8])).
% 5.20/1.35 thf(ifeq_axiom_002, axiom, (( ifeq @ A @ A @ B @ C ) = ( B ))).
% 5.20/1.35 thf(zip_derived_cl2, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_002])).
% 5.20/1.35 thf(zip_derived_cl603, plain, (((true) = (there_exists @ (domain @ a)))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl2])).
% 5.20/1.35 thf(zip_derived_cl2, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_002])).
% 5.20/1.35 thf(zip_derived_cl5653, plain,
% 5.20/1.35 (((there_exists @ (compose @ (domain @ (codomain @ a)) @ a)) = (true))),
% 5.20/1.35 inference('demod', [status(thm)],
% 5.20/1.35 [zip_derived_cl5618, zip_derived_cl603, zip_derived_cl2])).
% 5.20/1.35 thf(zip_derived_cl9, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X1 @ X0)) @ true @
% 5.20/1.35 (domain @ X1) @ (codomain @ X0)) = (codomain @ X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_codomain_composition1])).
% 5.20/1.35 thf(zip_derived_cl5829, plain,
% 5.20/1.35 (((ifeq2 @ true @ true @ (domain @ (domain @ (codomain @ a))) @
% 5.20/1.35 (codomain @ a)) = (codomain @ a))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl5653, zip_derived_cl9])).
% 5.20/1.35 thf(zip_derived_cl603, plain, (((true) = (there_exists @ (domain @ a)))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl2])).
% 5.20/1.35 thf(zip_derived_cl6, plain,
% 5.20/1.35 (![X0 : $i]:
% 5.20/1.35 ((ifeq @ (there_exists @ (domain @ X0)) @ true @
% 5.20/1.35 (there_exists @ X0) @ true) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_has_elements])).
% 5.20/1.35 thf(zip_derived_cl609, plain,
% 5.20/1.35 (((ifeq @ true @ true @ (there_exists @ a) @ true) = (true))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl603, zip_derived_cl6])).
% 5.20/1.35 thf(zip_derived_cl2, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_002])).
% 5.20/1.35 thf(zip_derived_cl648, plain, (((true) = (there_exists @ a))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl609, zip_derived_cl2])).
% 5.20/1.35 thf(zip_derived_cl13, plain,
% 5.20/1.35 (![X0 : $i]: ((compose @ (codomain @ X0) @ X0) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [compose_codomain])).
% 5.20/1.35 thf(zip_derived_cl8, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq @ (there_exists @ (compose @ X0 @ X1)) @ true @
% 5.20/1.35 (there_exists @ (domain @ X0)) @ true) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [composition_implies_domain])).
% 5.20/1.35 thf(zip_derived_cl53, plain,
% 5.20/1.35 (![X0 : $i]:
% 5.20/1.35 ((ifeq @ (there_exists @ X0) @ true @
% 5.20/1.35 (there_exists @ (domain @ (codomain @ X0))) @ true) = (true))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl8])).
% 5.20/1.35 thf(zip_derived_cl1642, plain,
% 5.20/1.35 (((ifeq @ true @ true @ (there_exists @ (domain @ (codomain @ a))) @ true)
% 5.20/1.35 = (true))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl648, zip_derived_cl53])).
% 5.20/1.35 thf(zip_derived_cl2, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_002])).
% 5.20/1.35 thf(zip_derived_cl2358, plain,
% 5.20/1.35 (((true) = (there_exists @ (domain @ (codomain @ a))))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl1642, zip_derived_cl2])).
% 5.20/1.35 thf(zip_derived_cl6, plain,
% 5.20/1.35 (![X0 : $i]:
% 5.20/1.35 ((ifeq @ (there_exists @ (domain @ X0)) @ true @
% 5.20/1.35 (there_exists @ X0) @ true) = (true))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_has_elements])).
% 5.20/1.35 thf(zip_derived_cl2370, plain,
% 5.20/1.35 (((ifeq @ true @ true @ (there_exists @ (codomain @ a)) @ true) = (true))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl2358, zip_derived_cl6])).
% 5.20/1.35 thf(zip_derived_cl2, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_002])).
% 5.20/1.35 thf(zip_derived_cl2377, plain, (((true) = (there_exists @ (codomain @ a)))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl2370, zip_derived_cl2])).
% 5.20/1.35 thf(compose_domain, axiom, (( compose @ X @ ( domain @ X ) ) = ( X ))).
% 5.20/1.35 thf(zip_derived_cl12, plain,
% 5.20/1.35 (![X0 : $i]: ((compose @ X0 @ (domain @ X0)) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [compose_domain])).
% 5.20/1.35 thf(zip_derived_cl9, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X1 @ X0)) @ true @
% 5.20/1.35 (domain @ X1) @ (codomain @ X0)) = (codomain @ X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_codomain_composition1])).
% 5.20/1.35 thf(zip_derived_cl61, plain,
% 5.20/1.35 (![X0 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ X0) @ true @ (domain @ X0) @
% 5.20/1.35 (codomain @ (domain @ X0))) = (codomain @ (domain @ X0)))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl9])).
% 5.20/1.35 thf(zip_derived_cl2434, plain,
% 5.20/1.35 (((ifeq2 @ true @ true @ (domain @ (codomain @ a)) @
% 5.20/1.35 (codomain @ (domain @ (codomain @ a))))
% 5.20/1.35 = (codomain @ (domain @ (codomain @ a))))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl2377, zip_derived_cl61])).
% 5.20/1.35 thf(zip_derived_cl1, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 5.20/1.35 thf(zip_derived_cl2448, plain,
% 5.20/1.35 (((domain @ (codomain @ a)) = (codomain @ (domain @ (codomain @ a))))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl2434, zip_derived_cl1])).
% 5.20/1.35 thf(zip_derived_cl13, plain,
% 5.20/1.35 (![X0 : $i]: ((compose @ (codomain @ X0) @ X0) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [compose_codomain])).
% 5.20/1.35 thf(zip_derived_cl9, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ (compose @ X1 @ X0)) @ true @
% 5.20/1.35 (domain @ X1) @ (codomain @ X0)) = (codomain @ X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [domain_codomain_composition1])).
% 5.20/1.35 thf(zip_derived_cl62, plain,
% 5.20/1.35 (![X0 : $i]:
% 5.20/1.35 ((ifeq2 @ (there_exists @ X0) @ true @ (domain @ (codomain @ X0)) @
% 5.20/1.35 (codomain @ X0)) = (codomain @ X0))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl9])).
% 5.20/1.35 thf(zip_derived_cl2720, plain,
% 5.20/1.35 (((ifeq2 @ (there_exists @ (domain @ (codomain @ a))) @ true @
% 5.20/1.35 (domain @ (codomain @ (domain @ (codomain @ a)))) @
% 5.20/1.35 (domain @ (codomain @ a))) = (codomain @ (domain @ (codomain @ a))))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl2448, zip_derived_cl62])).
% 5.20/1.35 thf(zip_derived_cl2358, plain,
% 5.20/1.35 (((true) = (there_exists @ (domain @ (codomain @ a))))),
% 5.20/1.35 inference('sup+', [status(thm)], [zip_derived_cl1642, zip_derived_cl2])).
% 5.20/1.35 thf(zip_derived_cl2448, plain,
% 5.20/1.35 (((domain @ (codomain @ a)) = (codomain @ (domain @ (codomain @ a))))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl2434, zip_derived_cl1])).
% 5.20/1.35 thf(zip_derived_cl1, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 5.20/1.35 thf(zip_derived_cl2448, plain,
% 5.20/1.35 (((domain @ (codomain @ a)) = (codomain @ (domain @ (codomain @ a))))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl2434, zip_derived_cl1])).
% 5.20/1.35 thf(zip_derived_cl2748, plain,
% 5.20/1.35 (((domain @ (domain @ (codomain @ a))) = (domain @ (codomain @ a)))),
% 5.20/1.35 inference('demod', [status(thm)],
% 5.20/1.35 [zip_derived_cl2720, zip_derived_cl2358, zip_derived_cl2448,
% 5.20/1.35 zip_derived_cl1, zip_derived_cl2448])).
% 5.20/1.35 thf(zip_derived_cl1, plain,
% 5.20/1.35 (![X0 : $i, X1 : $i, X2 : $i]: ((ifeq2 @ X1 @ X1 @ X0 @ X2) = (X0))),
% 5.20/1.35 inference('cnf', [status(esa)], [ifeq_axiom_001])).
% 5.20/1.35 thf(zip_derived_cl5839, plain,
% 5.20/1.35 (((domain @ (codomain @ a)) = (codomain @ a))),
% 5.20/1.35 inference('demod', [status(thm)],
% 5.20/1.35 [zip_derived_cl5829, zip_derived_cl2748, zip_derived_cl1])).
% 5.20/1.35 thf(prove_codomain_of_ab_equals_codomain_of_a, conjecture,
% 5.20/1.35 (( codomain @ ( compose @ a @ b ) ) = ( codomain @ a ))).
% 5.20/1.35 thf(zf_stmt_0, negated_conjecture,
% 5.20/1.35 (( codomain @ ( compose @ a @ b ) ) != ( codomain @ a )),
% 5.20/1.35 inference('cnf.neg', [status(esa)],
% 5.20/1.35 [prove_codomain_of_ab_equals_codomain_of_a])).
% 5.20/1.35 thf(zip_derived_cl15, plain,
% 5.20/1.35 (((codomain @ (compose @ a @ b)) != (codomain @ a))),
% 5.20/1.35 inference('cnf', [status(esa)], [zf_stmt_0])).
% 5.20/1.35 thf(zip_derived_cl3043, plain,
% 5.20/1.35 (((domain @ (codomain @ a)) = (codomain @ (compose @ a @ b)))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl2975, zip_derived_cl1])).
% 5.20/1.35 thf(zip_derived_cl3076, plain,
% 5.20/1.35 (((domain @ (codomain @ a)) != (codomain @ a))),
% 5.20/1.35 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl3043])).
% 5.20/1.35 thf(zip_derived_cl5840, plain, ($false),
% 5.20/1.35 inference('simplify_reflect-', [status(thm)],
% 5.20/1.35 [zip_derived_cl5839, zip_derived_cl3076])).
% 5.20/1.35
% 5.20/1.35 % SZS output end Refutation
% 5.20/1.35
% 5.20/1.35
% 5.20/1.35 % Terminating...
% 5.34/1.41 % Runner terminated.
% 5.34/1.42 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------