TSTP Solution File: LCL158-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL158-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.wehyTrD58T true
% Computer : n002.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 08:58:26 EDT 2023
% Result : Unsatisfiable 1.43s 0.93s
% Output : Refutation 1.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL158-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.wehyTrD58T true
% 0.13/0.34 % Computer : n002.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 : Thu Aug 24 18:31:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.61 % Total configuration time : 435
% 0.21/0.61 % Estimated wc time : 1092
% 0.21/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.68 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.43/0.93 % Solved by fo/fo5.sh.
% 1.43/0.93 % done 239 iterations in 0.141s
% 1.43/0.93 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.43/0.93 % SZS output start Refutation
% 1.43/0.93 thf(and_type, type, and: $i > $i > $i).
% 1.43/0.93 thf(xor_type, type, xor: $i > $i > $i).
% 1.43/0.93 thf(x_type, type, x: $i).
% 1.43/0.93 thf(or_type, type, or: $i > $i > $i).
% 1.43/0.93 thf(truth_type, type, truth: $i).
% 1.43/0.93 thf(implies_type, type, implies: $i > $i > $i).
% 1.43/0.93 thf(falsehood_type, type, falsehood: $i).
% 1.43/0.93 thf(and_star_type, type, and_star: $i > $i > $i).
% 1.43/0.93 thf(not_type, type, not: $i > $i).
% 1.43/0.93 thf(prove_alternative_wajsberg_axiom, conjecture,
% 1.43/0.93 (( and_star @ ( xor @ truth @ x ) @ x ) = ( falsehood ))).
% 1.43/0.93 thf(zf_stmt_0, negated_conjecture,
% 1.43/0.93 (( and_star @ ( xor @ truth @ x ) @ x ) != ( falsehood )),
% 1.43/0.93 inference('cnf.neg', [status(esa)], [prove_alternative_wajsberg_axiom])).
% 1.43/0.93 thf(zip_derived_cl16, plain,
% 1.43/0.93 (((and_star @ (xor @ truth @ x) @ x) != (falsehood))),
% 1.43/0.93 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.43/0.93 thf(and_star_commutativity, axiom,
% 1.43/0.93 (( and_star @ X @ Y ) = ( and_star @ Y @ X ))).
% 1.43/0.93 thf(zip_derived_cl14, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((and_star @ X1 @ X0) = (and_star @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [and_star_commutativity])).
% 1.43/0.93 thf(zip_derived_cl17, plain,
% 1.43/0.93 (((and_star @ x @ (xor @ truth @ x)) != (falsehood))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl14])).
% 1.43/0.93 thf(xor_commutativity, axiom, (( xor @ X @ Y ) = ( xor @ Y @ X ))).
% 1.43/0.93 thf(zip_derived_cl11, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((xor @ X1 @ X0) = (xor @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [xor_commutativity])).
% 1.43/0.93 thf(or_definition, axiom, (( or @ X @ Y ) = ( implies @ ( not @ X ) @ Y ))).
% 1.43/0.93 thf(zip_derived_cl4, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X0 @ X1) = (implies @ (not @ X0) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_definition])).
% 1.43/0.93 thf(false_definition, axiom, (( not @ truth ) = ( falsehood ))).
% 1.43/0.93 thf(zip_derived_cl15, plain, (((not @ truth) = (falsehood))),
% 1.43/0.93 inference('cnf', [status(esa)], [false_definition])).
% 1.43/0.93 thf(zip_derived_cl4, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X0 @ X1) = (implies @ (not @ X0) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_definition])).
% 1.43/0.93 thf(zip_derived_cl18, plain,
% 1.43/0.93 (![X0 : $i]: ((or @ truth @ X0) = (implies @ falsehood @ X0))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl4])).
% 1.43/0.93 thf(or_commutativity, axiom, (( or @ X @ Y ) = ( or @ Y @ X ))).
% 1.43/0.93 thf(zip_derived_cl6, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X1 @ X0) = (or @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_commutativity])).
% 1.43/0.93 thf(zip_derived_cl19, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ falsehood @ X0) = (or @ X0 @ truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl6])).
% 1.43/0.93 thf(wajsberg_1, axiom, (( implies @ truth @ X ) = ( X ))).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(wajsberg_3, axiom,
% 1.43/0.93 (( implies @ ( implies @ X @ Y ) @ Y ) =
% 1.43/0.93 ( implies @ ( implies @ Y @ X ) @ X ))).
% 1.43/0.93 thf(zip_derived_cl2, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ (implies @ X1 @ X0) @ X0)
% 1.43/0.93 = (implies @ (implies @ X0 @ X1) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_3])).
% 1.43/0.93 thf(zip_derived_cl141, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((implies @ X0 @ X0) = (implies @ (implies @ X0 @ truth) @ truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(wajsberg_2, axiom,
% 1.43/0.93 (( implies @
% 1.43/0.93 ( implies @ X @ Y ) @
% 1.43/0.93 ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) =
% 1.43/0.93 ( truth ))).
% 1.43/0.93 thf(zip_derived_cl1, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.43/0.93 ((implies @ (implies @ X0 @ X1) @
% 1.43/0.93 (implies @ (implies @ X1 @ X2) @ (implies @ X0 @ X2))) = (truth))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_2])).
% 1.43/0.93 thf(zip_derived_cl29, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ (implies @ truth @ X1) @
% 1.43/0.93 (implies @ (implies @ X1 @ X0) @ X0)) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(zip_derived_cl37, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ X1 @ (implies @ (implies @ X1 @ X0) @ X0)) = (truth))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(zip_derived_cl48, plain,
% 1.43/0.93 (![X0 : $i]: ((truth) = (implies @ (implies @ truth @ X0) @ X0))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(zip_derived_cl58, plain, (![X0 : $i]: ((truth) = (implies @ X0 @ X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl151, plain,
% 1.43/0.93 (![X0 : $i]: ((truth) = (implies @ (implies @ X0 @ truth) @ truth))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl141, zip_derived_cl58])).
% 1.43/0.93 thf(zip_derived_cl37, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ X1 @ (implies @ (implies @ X1 @ X0) @ X0)) = (truth))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl237, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ X0 @ truth) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl151, zip_derived_cl37])).
% 1.43/0.93 thf(zip_derived_cl4, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X0 @ X1) = (implies @ (not @ X0) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_definition])).
% 1.43/0.93 thf(zip_derived_cl264, plain, (![X0 : $i]: ((or @ X0 @ truth) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl4])).
% 1.43/0.93 thf(zip_derived_cl274, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ falsehood @ X0) = (truth))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl264])).
% 1.43/0.93 thf(zip_derived_cl2, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ (implies @ X1 @ X0) @ X0)
% 1.43/0.93 = (implies @ (implies @ X0 @ X1) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_3])).
% 1.43/0.93 thf(zip_derived_cl284, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((implies @ (implies @ X0 @ falsehood) @ falsehood)
% 1.43/0.93 = (implies @ truth @ X0))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl274, zip_derived_cl2])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(zip_derived_cl291, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ (implies @ X0 @ falsehood) @ falsehood) = (X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl284, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl482, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ (or @ X0 @ falsehood) @ falsehood) = (not @ X0))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl291])).
% 1.43/0.93 thf(zip_derived_cl58, plain, (![X0 : $i]: ((truth) = (implies @ X0 @ X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl4, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X0 @ X1) = (implies @ (not @ X0) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_definition])).
% 1.43/0.93 thf(zip_derived_cl65, plain,
% 1.43/0.93 (![X0 : $i]: ((or @ X0 @ (not @ X0)) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl4])).
% 1.43/0.93 thf(zip_derived_cl6, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X1 @ X0) = (or @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_commutativity])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(wajsberg_4, axiom,
% 1.43/0.93 (( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) ) =
% 1.43/0.93 ( truth ))).
% 1.43/0.93 thf(zip_derived_cl3, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ (implies @ (not @ X0) @ (not @ X1)) @ (implies @ X1 @ X0))
% 1.43/0.93 = (truth))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_4])).
% 1.43/0.93 thf(zip_derived_cl4, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X0 @ X1) = (implies @ (not @ X0) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_definition])).
% 1.43/0.93 thf(zip_derived_cl99, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ (or @ X0 @ (not @ X1)) @ (implies @ X1 @ X0)) = (truth))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 1.43/0.93 thf(zip_derived_cl108, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ (or @ X0 @ (not @ truth)) @ X0) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl99])).
% 1.43/0.93 thf(zip_derived_cl15, plain, (((not @ truth) = (falsehood))),
% 1.43/0.93 inference('cnf', [status(esa)], [false_definition])).
% 1.43/0.93 thf(zip_derived_cl120, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ (or @ X0 @ falsehood) @ X0) = (truth))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl15])).
% 1.43/0.93 thf(zip_derived_cl434, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ (or @ falsehood @ X0) @ X0) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl120])).
% 1.43/0.93 thf(zip_derived_cl515, plain,
% 1.43/0.93 (((implies @ truth @ (not @ falsehood)) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl434])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(zip_derived_cl534, plain, (((truth) = (not @ falsehood))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl515, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl4, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X0 @ X1) = (implies @ (not @ X0) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_definition])).
% 1.43/0.93 thf(zip_derived_cl546, plain,
% 1.43/0.93 (![X0 : $i]: ((or @ falsehood @ X0) = (implies @ truth @ X0))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl4])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(zip_derived_cl554, plain, (![X0 : $i]: ((or @ falsehood @ X0) = (X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl546, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl6, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X1 @ X0) = (or @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_commutativity])).
% 1.43/0.93 thf(zip_derived_cl561, plain, (![X0 : $i]: ((or @ X0 @ falsehood) = (X0))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl554, zip_derived_cl6])).
% 1.43/0.93 thf(zip_derived_cl840, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ X0 @ falsehood) = (not @ X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl482, zip_derived_cl561])).
% 1.43/0.93 thf(zip_derived_cl2, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((implies @ (implies @ X1 @ X0) @ X0)
% 1.43/0.93 = (implies @ (implies @ X0 @ X1) @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_3])).
% 1.43/0.93 thf(zip_derived_cl855, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((implies @ (implies @ falsehood @ X0) @ X0)
% 1.43/0.93 = (not @ (implies @ X0 @ falsehood)))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl840, zip_derived_cl2])).
% 1.43/0.93 thf(zip_derived_cl274, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ falsehood @ X0) = (truth))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl264])).
% 1.43/0.93 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 1.43/0.93 inference('cnf', [status(esa)], [wajsberg_1])).
% 1.43/0.93 thf(zip_derived_cl840, plain,
% 1.43/0.93 (![X0 : $i]: ((implies @ X0 @ falsehood) = (not @ X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl482, zip_derived_cl561])).
% 1.43/0.93 thf(zip_derived_cl874, plain, (![X0 : $i]: ((X0) = (not @ (not @ X0)))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl855, zip_derived_cl274, zip_derived_cl0,
% 1.43/0.93 zip_derived_cl840])).
% 1.43/0.93 thf(zip_derived_cl534, plain, (((truth) = (not @ falsehood))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl515, zip_derived_cl0])).
% 1.43/0.93 thf(and_star_definition, axiom,
% 1.43/0.93 (( and_star @ X @ Y ) = ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ))).
% 1.43/0.93 thf(zip_derived_cl12, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((and_star @ X0 @ X1) = (not @ (or @ (not @ X0) @ (not @ X1))))),
% 1.43/0.93 inference('cnf', [status(esa)], [and_star_definition])).
% 1.43/0.93 thf(zip_derived_cl551, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((and_star @ X0 @ falsehood) = (not @ (or @ (not @ X0) @ truth)))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl12])).
% 1.43/0.93 thf(zip_derived_cl264, plain, (![X0 : $i]: ((or @ X0 @ truth) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl4])).
% 1.43/0.93 thf(zip_derived_cl15, plain, (((not @ truth) = (falsehood))),
% 1.43/0.93 inference('cnf', [status(esa)], [false_definition])).
% 1.43/0.93 thf(zip_derived_cl556, plain,
% 1.43/0.93 (![X0 : $i]: ((and_star @ X0 @ falsehood) = (falsehood))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl551, zip_derived_cl264, zip_derived_cl15])).
% 1.43/0.93 thf(xor_definition, axiom,
% 1.43/0.93 (( xor @ X @ Y ) =
% 1.43/0.93 ( or @ ( and @ X @ ( not @ Y ) ) @ ( and @ ( not @ X ) @ Y ) ))).
% 1.43/0.93 thf(zip_derived_cl10, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((xor @ X0 @ X1)
% 1.43/0.93 = (or @ (and @ X0 @ (not @ X1)) @ (and @ (not @ X0) @ X1)))),
% 1.43/0.93 inference('cnf', [status(esa)], [xor_definition])).
% 1.43/0.93 thf(and_definition, axiom,
% 1.43/0.93 (( and @ X @ Y ) = ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ))).
% 1.43/0.93 thf(zip_derived_cl7, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((and @ X0 @ X1) = (not @ (or @ (not @ X0) @ (not @ X1))))),
% 1.43/0.93 inference('cnf', [status(esa)], [and_definition])).
% 1.43/0.93 thf(zip_derived_cl12, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((and_star @ X0 @ X1) = (not @ (or @ (not @ X0) @ (not @ X1))))),
% 1.43/0.93 inference('cnf', [status(esa)], [and_star_definition])).
% 1.43/0.93 thf(zip_derived_cl97, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((and @ X0 @ X1) = (and_star @ X0 @ X1))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl12])).
% 1.43/0.93 thf(zip_derived_cl97, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((and @ X0 @ X1) = (and_star @ X0 @ X1))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl12])).
% 1.43/0.93 thf(zip_derived_cl213, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((xor @ X0 @ X1)
% 1.43/0.93 = (or @ (and_star @ X0 @ (not @ X1)) @ (and_star @ (not @ X0) @ X1)))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl10, zip_derived_cl97, zip_derived_cl97])).
% 1.43/0.93 thf(zip_derived_cl579, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((xor @ X0 @ falsehood)
% 1.43/0.93 = (or @ (and_star @ X0 @ (not @ falsehood)) @ falsehood))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl556, zip_derived_cl213])).
% 1.43/0.93 thf(zip_derived_cl534, plain, (((truth) = (not @ falsehood))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl515, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl6, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X1 @ X0) = (or @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_commutativity])).
% 1.43/0.93 thf(zip_derived_cl554, plain, (![X0 : $i]: ((or @ falsehood @ X0) = (X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl546, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl582, plain,
% 1.43/0.93 (![X0 : $i]: ((xor @ X0 @ falsehood) = (and_star @ X0 @ truth))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl579, zip_derived_cl534, zip_derived_cl6,
% 1.43/0.93 zip_derived_cl554])).
% 1.43/0.93 thf(zip_derived_cl874, plain, (![X0 : $i]: ((X0) = (not @ (not @ X0)))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl855, zip_derived_cl274, zip_derived_cl0,
% 1.43/0.93 zip_derived_cl840])).
% 1.43/0.93 thf(zip_derived_cl65, plain,
% 1.43/0.93 (![X0 : $i]: ((or @ X0 @ (not @ X0)) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl4])).
% 1.43/0.93 thf(zip_derived_cl12, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((and_star @ X0 @ X1) = (not @ (or @ (not @ X0) @ (not @ X1))))),
% 1.43/0.93 inference('cnf', [status(esa)], [and_star_definition])).
% 1.43/0.93 thf(zip_derived_cl90, plain,
% 1.43/0.93 (![X0 : $i]: ((and_star @ X0 @ (not @ X0)) = (not @ truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl65, zip_derived_cl12])).
% 1.43/0.93 thf(zip_derived_cl15, plain, (((not @ truth) = (falsehood))),
% 1.43/0.93 inference('cnf', [status(esa)], [false_definition])).
% 1.43/0.93 thf(zip_derived_cl95, plain,
% 1.43/0.93 (![X0 : $i]: ((and_star @ X0 @ (not @ X0)) = (falsehood))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl15])).
% 1.43/0.93 thf(zip_derived_cl883, plain,
% 1.43/0.93 (![X0 : $i]: ((and_star @ (not @ X0) @ X0) = (falsehood))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl874, zip_derived_cl95])).
% 1.43/0.93 thf(and_star_associativity, axiom,
% 1.43/0.93 (( and_star @ ( and_star @ X @ Y ) @ Z ) =
% 1.43/0.93 ( and_star @ X @ ( and_star @ Y @ Z ) ))).
% 1.43/0.93 thf(zip_derived_cl13, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.43/0.93 ((and_star @ (and_star @ X0 @ X1) @ X2)
% 1.43/0.93 = (and_star @ X0 @ (and_star @ X1 @ X2)))),
% 1.43/0.93 inference('cnf', [status(esa)], [and_star_associativity])).
% 1.43/0.93 thf(zip_derived_cl985, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((and_star @ falsehood @ X0)
% 1.43/0.93 = (and_star @ (not @ X1) @ (and_star @ X1 @ X0)))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl883, zip_derived_cl13])).
% 1.43/0.93 thf(zip_derived_cl534, plain, (((truth) = (not @ falsehood))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl515, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl12, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((and_star @ X0 @ X1) = (not @ (or @ (not @ X0) @ (not @ X1))))),
% 1.43/0.93 inference('cnf', [status(esa)], [and_star_definition])).
% 1.43/0.93 thf(zip_derived_cl547, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((and_star @ falsehood @ X0) = (not @ (or @ truth @ (not @ X0))))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl12])).
% 1.43/0.93 thf(zip_derived_cl264, plain, (![X0 : $i]: ((or @ X0 @ truth) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl4])).
% 1.43/0.93 thf(zip_derived_cl6, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((or @ X1 @ X0) = (or @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [or_commutativity])).
% 1.43/0.93 thf(zip_derived_cl276, plain, (![X0 : $i]: ((or @ truth @ X0) = (truth))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl264, zip_derived_cl6])).
% 1.43/0.93 thf(zip_derived_cl15, plain, (((not @ truth) = (falsehood))),
% 1.43/0.93 inference('cnf', [status(esa)], [false_definition])).
% 1.43/0.93 thf(zip_derived_cl555, plain,
% 1.43/0.93 (![X0 : $i]: ((and_star @ falsehood @ X0) = (falsehood))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl547, zip_derived_cl276, zip_derived_cl15])).
% 1.43/0.93 thf(zip_derived_cl996, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((falsehood) = (and_star @ (not @ X1) @ (and_star @ X1 @ X0)))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl985, zip_derived_cl555])).
% 1.43/0.93 thf(zip_derived_cl1249, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((falsehood) = (and_star @ (not @ X0) @ (xor @ X0 @ falsehood)))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl582, zip_derived_cl996])).
% 1.43/0.93 thf(zip_derived_cl1281, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((falsehood) = (and_star @ X0 @ (xor @ (not @ X0) @ falsehood)))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl874, zip_derived_cl1249])).
% 1.43/0.93 thf(zip_derived_cl11, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((xor @ X1 @ X0) = (xor @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [xor_commutativity])).
% 1.43/0.93 thf(zip_derived_cl582, plain,
% 1.43/0.93 (![X0 : $i]: ((xor @ X0 @ falsehood) = (and_star @ X0 @ truth))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl579, zip_derived_cl534, zip_derived_cl6,
% 1.43/0.93 zip_derived_cl554])).
% 1.43/0.93 thf(zip_derived_cl213, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]:
% 1.43/0.93 ((xor @ X0 @ X1)
% 1.43/0.93 = (or @ (and_star @ X0 @ (not @ X1)) @ (and_star @ (not @ X0) @ X1)))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl10, zip_derived_cl97, zip_derived_cl97])).
% 1.43/0.93 thf(zip_derived_cl606, plain,
% 1.43/0.93 (![X0 : $i]:
% 1.43/0.93 ((xor @ X0 @ truth)
% 1.43/0.93 = (or @ (and_star @ X0 @ (not @ truth)) @
% 1.43/0.93 (xor @ (not @ X0) @ falsehood)))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl582, zip_derived_cl213])).
% 1.43/0.93 thf(zip_derived_cl15, plain, (((not @ truth) = (falsehood))),
% 1.43/0.93 inference('cnf', [status(esa)], [false_definition])).
% 1.43/0.93 thf(zip_derived_cl556, plain,
% 1.43/0.93 (![X0 : $i]: ((and_star @ X0 @ falsehood) = (falsehood))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl551, zip_derived_cl264, zip_derived_cl15])).
% 1.43/0.93 thf(zip_derived_cl11, plain,
% 1.43/0.93 (![X0 : $i, X1 : $i]: ((xor @ X1 @ X0) = (xor @ X0 @ X1))),
% 1.43/0.93 inference('cnf', [status(esa)], [xor_commutativity])).
% 1.43/0.93 thf(zip_derived_cl554, plain, (![X0 : $i]: ((or @ falsehood @ X0) = (X0))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl546, zip_derived_cl0])).
% 1.43/0.93 thf(zip_derived_cl610, plain,
% 1.43/0.93 (![X0 : $i]: ((xor @ X0 @ truth) = (xor @ falsehood @ (not @ X0)))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl606, zip_derived_cl15, zip_derived_cl556,
% 1.43/0.93 zip_derived_cl11, zip_derived_cl554])).
% 1.43/0.93 thf(zip_derived_cl1286, plain,
% 1.43/0.93 (![X0 : $i]: ((falsehood) = (and_star @ X0 @ (xor @ X0 @ truth)))),
% 1.43/0.93 inference('demod', [status(thm)],
% 1.43/0.93 [zip_derived_cl1281, zip_derived_cl11, zip_derived_cl610])).
% 1.43/0.93 thf(zip_derived_cl1297, plain,
% 1.43/0.93 (![X0 : $i]: ((falsehood) = (and_star @ X0 @ (xor @ truth @ X0)))),
% 1.43/0.93 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1286])).
% 1.43/0.93 thf(zip_derived_cl1306, plain, (((falsehood) != (falsehood))),
% 1.43/0.93 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl1297])).
% 1.43/0.93 thf(zip_derived_cl1307, plain, ($false),
% 1.43/0.93 inference('simplify', [status(thm)], [zip_derived_cl1306])).
% 1.43/0.93
% 1.43/0.93 % SZS output end Refutation
% 1.43/0.93
% 1.43/0.93
% 1.43/0.93 % Terminating...
% 1.46/1.06 % Runner terminated.
% 1.59/1.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------