0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.15 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.8f8aUlbN0f 0.14/0.37 % Computer : n006.cluster.edu 0.14/0.37 % Model : x86_64 x86_64 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.37 % Memory : 8042.1875MB 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.37 % CPULimit : 960 0.14/0.37 % DateTime : Thu Jul 2 08:33:15 EDT 2020 0.14/0.37 % CPUTime : 0.14/0.37 % Running portfolio for 120 s 0.14/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.37 % Number of cores: 8 0.14/0.37 % Python version: Python 3.6.8 0.14/0.37 % Running in FO mode 61.91/62.47 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 61.91/62.47 % Warning: 61.91/62.47 % To remain in the chosen logic fragment, unification with booleans has been disabled. 61.91/62.47 % 61.91/62.47 % Running /export/starexec/sandbox2/solver/bin/fo/fo8.sh for 20 61.91/62.47 % Warning: 61.91/62.47 % To remain in the chosen logic fragment, unification with booleans has been disabled. 61.91/62.47 % 61.91/62.47 % Running /export/starexec/sandbox2/solver/bin/fo/fo5.sh for 20 61.91/62.47 % Solved by: fo/fo5.sh 61.91/62.47 To remain in the chosen logic fragment, unification with booleans has been disabled. 61.91/62.47 % done 332 iterations in 16.950s 61.91/62.47 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 61.91/62.47 % SZS output start Refutation 61.91/62.47 tff(fact_89_insert__fold1SetE, axiom, 61.91/62.47 (![X_b,F_1,A_4,X_3,X_1]: 61.91/62.47 (hBOOL(hAPP(X_b,bool, 61.91/62.47 hAPP(fun(X_b,bool),fun(X_b,bool), 61.91/62.47 hAPP(fun(X_b,fun(X_b,X_b)), 61.91/62.47 fun(fun(X_b,bool),fun(X_b,bool)), 61.91/62.47 finite_fold1Set(X_b),F_1), 61.91/62.47 hAPP(fun(X_b,bool),fun(X_b,bool), 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)), 61.91/62.47 insert(X_b),A_4), 61.91/62.47 X_3)), 61.91/62.47 X_1)) => 61.91/62.47 (~ 61.91/62.47 (![A_3,A_2]: 61.91/62.47 ((hAPP(fun(X_b,bool),fun(X_b,bool), 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4), 61.91/62.47 X_3) = 61.91/62.47 hAPP(fun(X_b,bool),fun(X_b,bool), 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3), 61.91/62.47 A_2)) => 61.91/62.47 (hBOOL(hAPP(X_b,bool, 61.91/62.47 hAPP(fun(X_b,bool),fun(X_b,bool), 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)), 61.91/62.47 hAPP(fun(X_b,fun(X_b,X_b)), 61.91/62.47 fun(X_b, 61.91/62.47 fun(fun(X_b,bool),fun(X_b,bool))), 61.91/62.47 finite_fold_graph(X_b,X_b),F_1), 61.91/62.47 A_3), 61.91/62.47 A_2), 61.91/62.47 X_1)) => 61.91/62.47 hBOOL(hAPP(fun(X_b,bool),bool, 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_2))))))))). 61.91/62.47 tff('0', plain, 61.91/62.47 ![X8, X9, X10, X11, X12]: 61.91/62.47 (~ hBOOL( 61.91/62.47 hAPP(fun(X8, bool), bool, 61.91/62.47 hAPP(X8, fun(fun(X8, bool), bool), member(X8), 61.91/62.47 sk_A_3(X10, X11, X12, X9, X8)), sk_A_2(X10, X11, X12, X9, X8))) 61.91/62.47 | ~ hBOOL( 61.91/62.47 hAPP(X8, bool, 61.91/62.47 hAPP(fun(X8, bool), fun(X8, bool), 61.91/62.47 hAPP(fun(X8, fun(X8, X8)), 61.91/62.47 fun(fun(X8, bool), fun(X8, bool)), finite_fold1Set(X8), 61.91/62.47 X9), 61.91/62.47 hAPP(fun(X8, bool), fun(X8, bool), 61.91/62.47 hAPP(X8, fun(fun(X8, bool), fun(X8, bool)), insert(X8), 61.91/62.47 X12), X11)), X10))), 61.91/62.47 inference('cnf', [status(esa)], [fact_89_insert__fold1SetE])). 61.91/62.47 tff(fact_4_constant, axiom, 61.91/62.47 (![X_b,Ga,Pa,Ca,Q_1,C]: 61.91/62.47 ((hBOOL(C) => 61.91/62.47 hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool),bool), 61.91/62.47 hoare_122391849derivs(X_b),Ga), 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool), 61.91/62.47 hAPP(hoare_509422987triple(X_b), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool)), 61.91/62.47 insert(hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b))), 61.91/62.47 hoare_1008221573triple(X_b),Pa), 61.91/62.47 Ca), 61.91/62.47 Q_1)), 61.91/62.47 bot_bot(fun(hoare_509422987triple(X_b),bool)))))) => 61.91/62.47 hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool),bool), 61.91/62.47 hoare_122391849derivs(X_b),Ga), 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool), 61.91/62.47 hAPP(hoare_509422987triple(X_b), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool)), 61.91/62.47 insert(hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b))), 61.91/62.47 hoare_1008221573triple(X_b), 61.91/62.47 hAPP(bool,fun(X_b,fun(state,bool)), 61.91/62.47 hAPP(fun(X_b, 61.91/62.47 fun(bool, 61.91/62.47 fun(state,bool))), 61.91/62.47 fun(bool, 61.91/62.47 fun(X_b, 61.91/62.47 fun(state,bool))), 61.91/62.47 combc(X_b,bool, 61.91/62.47 fun(state,bool)), 61.91/62.47 hAPP(fun(X_b, 61.91/62.47 fun(state, 61.91/62.47 fun( 61.91/62.47 bool,bool))), 61.91/62.47 fun(X_b, 61.91/62.47 fun(bool, 61.91/62.47 fun( 61.91/62.47 state,bool))), 61.91/62.47 hAPP(fun(fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool)), 61.91/62.47 fun( 61.91/62.47 bool, 61.91/62.47 fun( 61.91/62.47 state,bool))), 61.91/62.47 fun(fun( 61.91/62.47 X_b, 61.91/62.47 fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool))), 61.91/62.47 fun( 61.91/62.47 X_b, 61.91/62.47 fun( 61.91/62.47 bool, 61.91/62.47 fun( 61.91/62.47 state,bool)))), 61.91/62.47 combb(fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool)), 61.91/62.47 fun( 61.91/62.47 bool, 61.91/62.47 fun( 61.91/62.47 state, 61.91/62.47 bool)), 61.91/62.47 X_b), 61.91/62.47 combc(state, 61.91/62.47 bool,bool)), 61.91/62.47 hAPP(fun(X_b, 61.91/62.47 fun( 61.91/62.47 state,bool)), 61.91/62.47 fun(X_b, 61.91/62.47 fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool))), 61.91/62.47 hAPP(fun( 61.91/62.47 fun( 61.91/62.47 state,bool), 61.91/62.47 fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool))), 61.91/62.47 fun( 61.91/62.47 fun( 61.91/62.47 X_b, 61.91/62.47 fun( 61.91/62.47 state,bool)), 61.91/62.47 fun( 61.91/62.47 X_b, 61.91/62.47 fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool)))), 61.91/62.47 combb( 61.91/62.47 fun( 61.91/62.47 state,bool), 61.91/62.47 fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool)), 61.91/62.47 X_b), 61.91/62.47 hAPP( 61.91/62.47 fun( 61.91/62.47 bool, 61.91/62.47 fun( 61.91/62.47 bool,bool)), 61.91/62.47 fun( 61.91/62.47 fun( 61.91/62.47 state,bool), 61.91/62.47 fun( 61.91/62.47 state, 61.91/62.47 fun( 61.91/62.47 bool,bool))), 61.91/62.47 combb( 61.91/62.47 bool, 61.91/62.47 fun( 61.91/62.47 bool,bool), 61.91/62.47 state), 61.91/62.47 fconj)), 61.91/62.47 Pa))), 61.91/62.47 C)), 61.91/62.47 Ca), 61.91/62.47 Q_1)), 61.91/62.47 bot_bot(fun(hoare_509422987triple(X_b),bool)))))))). 61.91/62.47 tff('1', plain, 61.91/62.47 ![X366, X367, X368, X369, X370, X371]: 61.91/62.47 ( hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(X366), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X366), bool), 61.91/62.47 fun(fun(hoare_509422987triple(X366), bool), bool), 61.91/62.47 hoare_122391849derivs(X366), X367), 61.91/62.47 hAPP(fun(hoare_509422987triple(X366), bool), 61.91/62.47 fun(hoare_509422987triple(X366), bool), 61.91/62.47 hAPP(hoare_509422987triple(X366), 61.91/62.47 fun(fun(hoare_509422987triple(X366), bool), 61.91/62.47 fun(hoare_509422987triple(X366), bool)), 61.91/62.47 insert(hoare_509422987triple(X366)), 61.91/62.47 hAPP(fun(X366, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X366), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X366, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X366)), 61.91/62.47 hAPP(fun(X366, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X366, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X366))), 61.91/62.47 hoare_1008221573triple(X366), 61.91/62.47 hAPP(bool, fun(X366, fun(state, bool)), 61.91/62.47 hAPP(fun(X366, fun(bool, fun(state, bool))), 61.91/62.47 fun(bool, fun(X366, fun(state, bool))), 61.91/62.47 combc(X366, bool, fun(state, bool)), 61.91/62.47 hAPP(fun(X366, fun(state, fun(bool, bool))), 61.91/62.47 fun(X366, fun(bool, fun(state, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, fun(bool, bool)), 61.91/62.47 fun(bool, fun(state, bool))), 61.91/62.47 fun(fun(X366, fun(state, fun(bool, bool))), 61.91/62.47 fun(X366, fun(bool, fun(state, bool)))), 61.91/62.47 combb(fun(state, fun(bool, bool)), 61.91/62.47 fun(bool, fun(state, bool)), X366), 61.91/62.47 combc(state, bool, bool)), 61.91/62.47 hAPP(fun(X366, fun(state, bool)), 61.91/62.47 fun(X366, fun(state, fun(bool, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 fun(fun(X366, fun(state, bool)), 61.91/62.47 fun(X366, fun(state, fun(bool, bool)))), 61.91/62.47 combb(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool)), X366), 61.91/62.47 hAPP(fun(bool, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 combb(bool, fun(bool, bool), state), fconj)), 61.91/62.47 X368))), X369)), X370), X371)), 61.91/62.47 bot_bot(fun(hoare_509422987triple(X366), bool))))) 61.91/62.47 | hBOOL(X369)), 61.91/62.47 inference('cnf', [status(esa)], [fact_4_constant])). 61.91/62.47 tff(fact_12_singleton__conv2, axiom, 61.91/62.47 (![X_b,A_4]: 61.91/62.47 (hAPP(fun(X_b,bool),fun(X_b,bool), 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4), 61.91/62.47 bot_bot(fun(X_b,bool))) = 61.91/62.47 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b), 61.91/62.47 hAPP(X_b,fun(X_b,bool),fequal(X_b),A_4))))). 61.91/62.47 tff('2', plain, 61.91/62.47 ![X125, X126]: 61.91/62.47 hAPP(fun(X125, bool), fun(X125, bool), 61.91/62.47 hAPP(X125, fun(fun(X125, bool), fun(X125, bool)), insert(X125), X126), 61.91/62.47 bot_bot(fun(X125, bool))) 61.91/62.47 = hAPP(fun(X125, bool), fun(X125, bool), collect(X125), 61.91/62.47 hAPP(X125, fun(X125, bool), fequal(X125), X126)), 61.91/62.47 inference('cnf', [status(esa)], [fact_12_singleton__conv2])). 61.91/62.47 tff(fact_77_Collect__def, axiom, 61.91/62.47 (![X_b,Pa]: 61.91/62.47 (ti(fun(X_b,bool),Pa) = 61.91/62.47 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)))). 61.91/62.47 tff('3', plain, 61.91/62.47 ![X52, X53]: 61.91/62.47 ti(fun(X52, bool), X53) 61.91/62.47 = hAPP(fun(X52, bool), fun(X52, bool), collect(X52), X53), 61.91/62.47 inference('cnf', [status(esa)], [fact_77_Collect__def])). 61.91/62.47 tff(tsy_c_hAPP_res, axiom, 61.91/62.47 (![X_c,X_a,B_1_1,B_2]: 61.91/62.47 (ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2)))). 61.91/62.47 tff('4', plain, 61.91/62.47 ![X222, X223, X224, X225]: 61.91/62.47 ti(X223, hAPP(X222, X223, X224, X225)) = hAPP(X222, X223, X224, X225), 61.91/62.47 inference('cnf', [status(esa)], [tsy_c_hAPP_res])). 61.91/62.47 tff('5', plain, 61.91/62.47 ![X125, X126]: 61.91/62.47 hAPP(fun(X125, bool), fun(X125, bool), 61.91/62.47 hAPP(X125, fun(fun(X125, bool), fun(X125, bool)), insert(X125), X126), 61.91/62.47 bot_bot(fun(X125, bool))) 61.91/62.47 = hAPP(X125, fun(X125, bool), fequal(X125), X126), 61.91/62.47 inference('demod', [status(thm)], ['2', '3', '4'])). 61.91/62.47 tff('6', plain, 61.91/62.47 ![X366, X367, X368, X369, X370, X371]: 61.91/62.47 ( hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(X366), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X366), bool), 61.91/62.47 fun(fun(hoare_509422987triple(X366), bool), bool), 61.91/62.47 hoare_122391849derivs(X366), X367), 61.91/62.47 hAPP(hoare_509422987triple(X366), 61.91/62.47 fun(hoare_509422987triple(X366), bool), 61.91/62.47 fequal(hoare_509422987triple(X366)), 61.91/62.47 hAPP(fun(X366, fun(state, bool)), hoare_509422987triple(X366), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X366, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X366)), 61.91/62.47 hAPP(fun(X366, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X366, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X366))), 61.91/62.47 hoare_1008221573triple(X366), 61.91/62.47 hAPP(bool, fun(X366, fun(state, bool)), 61.91/62.47 hAPP(fun(X366, fun(bool, fun(state, bool))), 61.91/62.47 fun(bool, fun(X366, fun(state, bool))), 61.91/62.47 combc(X366, bool, fun(state, bool)), 61.91/62.47 hAPP(fun(X366, fun(state, fun(bool, bool))), 61.91/62.47 fun(X366, fun(bool, fun(state, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, fun(bool, bool)), 61.91/62.47 fun(bool, fun(state, bool))), 61.91/62.47 fun(fun(X366, fun(state, fun(bool, bool))), 61.91/62.47 fun(X366, fun(bool, fun(state, bool)))), 61.91/62.47 combb(fun(state, fun(bool, bool)), 61.91/62.47 fun(bool, fun(state, bool)), X366), 61.91/62.47 combc(state, bool, bool)), 61.91/62.47 hAPP(fun(X366, fun(state, bool)), 61.91/62.47 fun(X366, fun(state, fun(bool, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 fun(fun(X366, fun(state, bool)), 61.91/62.47 fun(X366, fun(state, fun(bool, bool)))), 61.91/62.47 combb(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool)), X366), 61.91/62.47 hAPP(fun(bool, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 combb(bool, fun(bool, bool), state), fconj)), 61.91/62.47 X368))), X369)), X370), X371)))) 61.91/62.47 | hBOOL(X369)), 61.91/62.47 inference('demod', [status(thm)], ['1', '5'])). 61.91/62.47 tff(fact_7_conseq1, axiom, 61.91/62.47 (![X_b,Pa,Ga,P_2,Ca,Q_1]: 61.91/62.47 (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool),bool), 61.91/62.47 hoare_122391849derivs(X_b),Ga), 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool), 61.91/62.47 hAPP(hoare_509422987triple(X_b), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool)), 61.91/62.47 insert(hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b))), 61.91/62.47 hoare_1008221573triple(X_b),P_2), 61.91/62.47 Ca), 61.91/62.47 Q_1)), 61.91/62.47 bot_bot(fun(hoare_509422987triple(X_b),bool))))) => 61.91/62.47 ((![Z_1,S]: 61.91/62.47 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S)) => 61.91/62.47 hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_2,Z_1),S)))) => 61.91/62.47 hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool),bool), 61.91/62.47 hoare_122391849derivs(X_b),Ga), 61.91/62.47 hAPP(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool), 61.91/62.47 hAPP(hoare_509422987triple(X_b), 61.91/62.47 fun(fun(hoare_509422987triple(X_b),bool), 61.91/62.47 fun(hoare_509422987triple(X_b),bool)), 61.91/62.47 insert(hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b)), 61.91/62.47 hAPP(fun(X_b,fun(state,bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X_b,fun(state,bool)), 61.91/62.47 hoare_509422987triple(X_b))), 61.91/62.47 hoare_1008221573triple(X_b),Pa), 61.91/62.47 Ca), 61.91/62.47 Q_1)), 61.91/62.47 bot_bot(fun(hoare_509422987triple(X_b),bool))))))))). 61.91/62.47 tff('7', plain, 61.91/62.47 ![X226, X227, X228, X229, X230, X231]: 61.91/62.47 ( hBOOL( 61.91/62.47 hAPP(state, bool, 61.91/62.47 hAPP(X226, fun(state, bool), X228, sk_Z_1_1(X227, X228, X226)), 61.91/62.47 sk_S_1(X227, X228, X226))) 61.91/62.47 | ~ hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(fun(hoare_509422987triple(X226), bool), bool), 61.91/62.47 hoare_122391849derivs(X226), X229), 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(hoare_509422987triple(X226), bool), 61.91/62.47 hAPP(hoare_509422987triple(X226), 61.91/62.47 fun(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(hoare_509422987triple(X226), bool)), 61.91/62.47 insert(hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226))), 61.91/62.47 hoare_1008221573triple(X226), X227), X230), X231)), 61.91/62.47 bot_bot(fun(hoare_509422987triple(X226), bool))))) 61.91/62.47 | hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(fun(hoare_509422987triple(X226), bool), bool), 61.91/62.47 hoare_122391849derivs(X226), X229), 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(hoare_509422987triple(X226), bool), 61.91/62.47 hAPP(hoare_509422987triple(X226), 61.91/62.47 fun(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(hoare_509422987triple(X226), bool)), 61.91/62.47 insert(hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226))), 61.91/62.47 hoare_1008221573triple(X226), X228), X230), X231)), 61.91/62.47 bot_bot(fun(hoare_509422987triple(X226), bool)))))), 61.91/62.47 inference('cnf', [status(esa)], [fact_7_conseq1])). 61.91/62.47 tff('8', plain, 61.91/62.47 ![X125, X126]: 61.91/62.47 hAPP(fun(X125, bool), fun(X125, bool), 61.91/62.47 hAPP(X125, fun(fun(X125, bool), fun(X125, bool)), insert(X125), X126), 61.91/62.47 bot_bot(fun(X125, bool))) 61.91/62.47 = hAPP(X125, fun(X125, bool), fequal(X125), X126), 61.91/62.47 inference('demod', [status(thm)], ['2', '3', '4'])). 61.91/62.47 tff('9', plain, 61.91/62.47 ![X125, X126]: 61.91/62.47 hAPP(fun(X125, bool), fun(X125, bool), 61.91/62.47 hAPP(X125, fun(fun(X125, bool), fun(X125, bool)), insert(X125), X126), 61.91/62.47 bot_bot(fun(X125, bool))) 61.91/62.47 = hAPP(X125, fun(X125, bool), fequal(X125), X126), 61.91/62.47 inference('demod', [status(thm)], ['2', '3', '4'])). 61.91/62.47 tff('10', plain, 61.91/62.47 ![X226, X227, X228, X229, X230, X231]: 61.91/62.47 ( hBOOL( 61.91/62.47 hAPP(state, bool, 61.91/62.47 hAPP(X226, fun(state, bool), X228, sk_Z_1_1(X227, X228, X226)), 61.91/62.47 sk_S_1(X227, X228, X226))) 61.91/62.47 | ~ hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(fun(hoare_509422987triple(X226), bool), bool), 61.91/62.47 hoare_122391849derivs(X226), X229), 61.91/62.47 hAPP(hoare_509422987triple(X226), 61.91/62.47 fun(hoare_509422987triple(X226), bool), 61.91/62.47 fequal(hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226))), 61.91/62.47 hoare_1008221573triple(X226), X227), X230), X231)))) 61.91/62.47 | hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(X226), bool), 61.91/62.47 fun(fun(hoare_509422987triple(X226), bool), bool), 61.91/62.47 hoare_122391849derivs(X226), X229), 61.91/62.47 hAPP(hoare_509422987triple(X226), 61.91/62.47 fun(hoare_509422987triple(X226), bool), 61.91/62.47 fequal(hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226)), 61.91/62.47 hAPP(fun(X226, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(X226, fun(state, bool)), 61.91/62.47 hoare_509422987triple(X226))), 61.91/62.47 hoare_1008221573triple(X226), X228), X230), X231))))), 61.91/62.47 inference('demod', [status(thm)], ['7', '8', '9'])). 61.91/62.47 tff(conj_0, conjecture, 61.91/62.47 (hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a),bool), 61.91/62.47 fun(fun(hoare_509422987triple(x_a),bool),bool), 61.91/62.47 hoare_122391849derivs(x_a),g), 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a),bool), 61.91/62.47 fun(hoare_509422987triple(x_a),bool), 61.91/62.47 hAPP(hoare_509422987triple(x_a), 61.91/62.47 fun(fun(hoare_509422987triple(x_a),bool), 61.91/62.47 fun(hoare_509422987triple(x_a),bool)), 61.91/62.47 insert(hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a,fun(state,bool)), 61.91/62.47 hoare_509422987triple(x_a), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(x_a,fun(state,bool)), 61.91/62.47 hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a,fun(state,bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(x_a,fun(state,bool)), 61.91/62.47 hoare_509422987triple(x_a))), 61.91/62.47 hoare_1008221573triple(x_a), 61.91/62.47 hAPP(fun(state,bool), 61.91/62.47 fun(x_a,fun(state,bool)), 61.91/62.47 combk(fun(state,bool),x_a), 61.91/62.47 hAPP(bool,fun(state,bool), 61.91/62.47 combk(bool,state),fFalse))), 61.91/62.47 c), 61.91/62.47 hAPP(fun(state,bool),fun(x_a,fun(state,bool)), 61.91/62.47 hAPP(fun(x_a, 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool))), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(x_a,fun(state,bool))), 61.91/62.47 combc(x_a,fun(state,bool), 61.91/62.47 fun(state,bool)), 61.91/62.47 hAPP(fun(x_a,fun(state,fun(bool,bool))), 61.91/62.47 fun(x_a, 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool))), 61.91/62.47 hAPP(fun(fun(state,fun(bool,bool)), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool))), 61.91/62.47 fun(fun(x_a, 61.91/62.47 fun(state, 61.91/62.47 fun(bool,bool))), 61.91/62.47 fun(x_a, 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool)))), 61.91/62.47 combb(fun(state, 61.91/62.47 fun(bool,bool)), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool)), 61.91/62.47 x_a), 61.91/62.47 combs(state,bool,bool)), 61.91/62.47 hAPP(fun(x_a,fun(state,bool)), 61.91/62.47 fun(x_a, 61.91/62.47 fun(state,fun(bool,bool))), 61.91/62.47 hAPP(fun(fun(state,bool), 61.91/62.47 fun(state, 61.91/62.47 fun(bool,bool))), 61.91/62.47 fun(fun(x_a, 61.91/62.47 fun(state,bool)), 61.91/62.47 fun(x_a, 61.91/62.47 fun(state, 61.91/62.47 fun( 61.91/62.47 bool,bool)))), 61.91/62.47 combb(fun(state,bool), 61.91/62.47 fun(state, 61.91/62.47 fun(bool,bool)), 61.91/62.47 x_a), 61.91/62.47 hAPP(fun(bool, 61.91/62.47 fun(bool,bool)), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state, 61.91/62.47 fun( 61.91/62.47 bool,bool))), 61.91/62.47 combb(bool, 61.91/62.47 fun( 61.91/62.47 bool,bool), 61.91/62.47 state), 61.91/62.47 fconj)), 61.91/62.47 p))), 61.91/62.47 hAPP(fun(state,bool),fun(state,bool), 61.91/62.47 hAPP(fun(bool,bool), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool)), 61.91/62.47 combb(bool,bool,state),fNot), 61.91/62.47 b)))), 61.91/62.47 bot_bot(fun(hoare_509422987triple(x_a),bool))))))). 61.91/62.47 tff(zf_stmt_0, negated_conjecture, 61.91/62.47 (~ 61.91/62.47 hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a),bool), 61.91/62.47 fun(fun(hoare_509422987triple(x_a),bool),bool), 61.91/62.47 hoare_122391849derivs(x_a),g), 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a),bool), 61.91/62.47 fun(hoare_509422987triple(x_a),bool), 61.91/62.47 hAPP(hoare_509422987triple(x_a), 61.91/62.47 fun(fun(hoare_509422987triple(x_a),bool), 61.91/62.47 fun(hoare_509422987triple(x_a),bool)), 61.91/62.47 insert(hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a,fun(state,bool)), 61.91/62.47 hoare_509422987triple(x_a), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(x_a,fun(state,bool)), 61.91/62.47 hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a,fun(state,bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(x_a,fun(state,bool)), 61.91/62.47 hoare_509422987triple(x_a))), 61.91/62.47 hoare_1008221573triple(x_a), 61.91/62.47 hAPP(fun(state,bool), 61.91/62.47 fun(x_a,fun(state,bool)), 61.91/62.47 combk(fun(state,bool),x_a), 61.91/62.47 hAPP(bool,fun(state,bool), 61.91/62.47 combk(bool,state),fFalse))), 61.91/62.47 c), 61.91/62.47 hAPP(fun(state,bool),fun(x_a,fun(state,bool)), 61.91/62.47 hAPP(fun(x_a, 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool))), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(x_a,fun(state,bool))), 61.91/62.47 combc(x_a,fun(state,bool), 61.91/62.47 fun(state,bool)), 61.91/62.47 hAPP(fun(x_a, 61.91/62.47 fun(state,fun(bool,bool))), 61.91/62.47 fun(x_a, 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool))), 61.91/62.47 hAPP(fun(fun(state, 61.91/62.47 fun(bool,bool)), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool))), 61.91/62.47 fun(fun(x_a, 61.91/62.47 fun(state, 61.91/62.47 fun(bool,bool))), 61.91/62.47 fun(x_a, 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool)))), 61.91/62.47 combb(fun(state, 61.91/62.47 fun(bool,bool)), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool)), 61.91/62.47 x_a), 61.91/62.47 combs(state,bool,bool)), 61.91/62.47 hAPP(fun(x_a,fun(state,bool)), 61.91/62.47 fun(x_a, 61.91/62.47 fun(state, 61.91/62.47 fun(bool,bool))), 61.91/62.47 hAPP(fun(fun(state,bool), 61.91/62.47 fun(state, 61.91/62.47 fun(bool,bool))), 61.91/62.47 fun(fun(x_a, 61.91/62.47 fun(state,bool)), 61.91/62.47 fun(x_a, 61.91/62.47 fun(state, 61.91/62.47 fun( 61.91/62.47 bool,bool)))), 61.91/62.47 combb(fun(state,bool), 61.91/62.47 fun(state, 61.91/62.47 fun( 61.91/62.47 bool,bool)), 61.91/62.47 x_a), 61.91/62.47 hAPP(fun(bool, 61.91/62.47 fun(bool,bool)), 61.91/62.47 fun(fun(state, 61.91/62.47 bool), 61.91/62.47 fun(state, 61.91/62.47 fun( 61.91/62.47 bool,bool))), 61.91/62.47 combb(bool, 61.91/62.47 fun( 61.91/62.47 bool,bool), 61.91/62.47 state), 61.91/62.47 fconj)), 61.91/62.47 p))), 61.91/62.47 hAPP(fun(state,bool),fun(state,bool), 61.91/62.47 hAPP(fun(bool,bool), 61.91/62.47 fun(fun(state,bool), 61.91/62.47 fun(state,bool)), 61.91/62.47 combb(bool,bool,state),fNot), 61.91/62.47 b)))), 61.91/62.47 bot_bot(fun(hoare_509422987triple(x_a),bool))))))). 61.91/62.47 tff('11', plain, 61.91/62.47 ~ hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fun(fun(hoare_509422987triple(x_a), bool), bool), 61.91/62.47 hoare_122391849derivs(x_a), g), 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fun(hoare_509422987triple(x_a), bool), 61.91/62.47 hAPP(hoare_509422987triple(x_a), 61.91/62.47 fun(fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fun(hoare_509422987triple(x_a), bool)), 61.91/62.47 insert(hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 hoare_509422987triple(x_a))), 61.91/62.47 hoare_1008221573triple(x_a), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 combk(fun(state, bool), x_a), 61.91/62.47 hAPP(bool, fun(state, bool), combk(bool, state), 61.91/62.47 fFalse))), c), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(state, bool), fun(x_a, fun(state, bool))), 61.91/62.47 combc(x_a, fun(state, bool), fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool)))), 61.91/62.47 combb(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), x_a), 61.91/62.47 combs(state, bool, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, bool), fun(state, fun(bool, bool))), 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool)))), 61.91/62.47 combb(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool)), x_a), 61.91/62.47 hAPP(fun(bool, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 combb(bool, fun(bool, bool), state), fconj)), p))), 61.91/62.47 hAPP(fun(state, bool), fun(state, bool), 61.91/62.47 hAPP(fun(bool, bool), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), 61.91/62.47 combb(bool, bool, state), fNot), b)))), 61.91/62.47 bot_bot(fun(hoare_509422987triple(x_a), bool))))), 61.91/62.47 inference('cnf', [status(esa)], [zf_stmt_0])). 61.91/62.47 tff(fact_23_empty__def, axiom, 61.91/62.47 (![X_b]: 61.91/62.47 (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b), 61.91/62.47 hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) = 61.91/62.47 bot_bot(fun(X_b,bool))))). 61.91/62.47 tff('12', plain, 61.91/62.47 ![X317]: 61.91/62.47 hAPP(fun(X317, bool), fun(X317, bool), collect(X317), 61.91/62.47 hAPP(bool, fun(X317, bool), combk(bool, X317), fFalse)) 61.91/62.47 = bot_bot(fun(X317, bool)), 61.91/62.47 inference('cnf', [status(esa)], [fact_23_empty__def])). 61.91/62.47 tff('13', plain, 61.91/62.47 ![X52, X53]: 61.91/62.47 ti(fun(X52, bool), X53) 61.91/62.47 = hAPP(fun(X52, bool), fun(X52, bool), collect(X52), X53), 61.91/62.47 inference('cnf', [status(esa)], [fact_77_Collect__def])). 61.91/62.47 tff('14', plain, 61.91/62.47 ![X222, X223, X224, X225]: 61.91/62.47 ti(X223, hAPP(X222, X223, X224, X225)) = hAPP(X222, X223, X224, X225), 61.91/62.47 inference('cnf', [status(esa)], [tsy_c_hAPP_res])). 61.91/62.47 tff('15', plain, 61.91/62.47 ![X317]: 61.91/62.47 hAPP(bool, fun(X317, bool), combk(bool, X317), fFalse) 61.91/62.47 = bot_bot(fun(X317, bool)), 61.91/62.47 inference('demod', [status(thm)], ['12', '13', '14'])). 61.91/62.47 tff('16', plain, 61.91/62.47 ![X125, X126]: 61.91/62.47 hAPP(fun(X125, bool), fun(X125, bool), 61.91/62.47 hAPP(X125, fun(fun(X125, bool), fun(X125, bool)), insert(X125), X126), 61.91/62.47 bot_bot(fun(X125, bool))) 61.91/62.47 = hAPP(X125, fun(X125, bool), fequal(X125), X126), 61.91/62.47 inference('demod', [status(thm)], ['2', '3', '4'])). 61.91/62.47 tff('17', plain, 61.91/62.47 ~ hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fun(fun(hoare_509422987triple(x_a), bool), bool), 61.91/62.47 hoare_122391849derivs(x_a), g), 61.91/62.47 hAPP(hoare_509422987triple(x_a), 61.91/62.47 fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fequal(hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 hoare_509422987triple(x_a))), 61.91/62.47 hoare_1008221573triple(x_a), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 combk(fun(state, bool), x_a), bot_bot(fun(state, bool)))), 61.91/62.47 c), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(state, bool), fun(x_a, fun(state, bool))), 61.91/62.47 combc(x_a, fun(state, bool), fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool)))), 61.91/62.47 combb(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), x_a), 61.91/62.47 combs(state, bool, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, bool), fun(state, fun(bool, bool))), 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool)))), 61.91/62.47 combb(fun(state, bool), fun(state, fun(bool, bool)), 61.91/62.47 x_a), 61.91/62.47 hAPP(fun(bool, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, fun(bool, bool))), 61.91/62.47 combb(bool, fun(bool, bool), state), fconj)), p))), 61.91/62.47 hAPP(fun(state, bool), fun(state, bool), 61.91/62.47 hAPP(fun(bool, bool), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), 61.91/62.47 combb(bool, bool, state), fNot), b)))))), 61.91/62.47 inference('demod', [status(thm)], ['11', '15', '16'])). 61.91/62.47 tff('18', plain, 61.91/62.47 ![X0]: 61.91/62.47 (~ hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fun(fun(hoare_509422987triple(x_a), bool), bool), 61.91/62.47 hoare_122391849derivs(x_a), g), 61.91/62.47 hAPP(hoare_509422987triple(x_a), 61.91/62.47 fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fequal(hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 hoare_509422987triple(x_a))), 61.91/62.47 hoare_1008221573triple(x_a), X0), c), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(state, bool), fun(x_a, fun(state, bool))), 61.91/62.47 combc(x_a, fun(state, bool), fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool)))), 61.91/62.47 combb(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), x_a), 61.91/62.47 combs(state, bool, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, bool), fun(state, fun(bool, bool))), 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool)))), 61.91/62.47 combb(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool)), x_a), 61.91/62.47 hAPP(fun(bool, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 combb(bool, fun(bool, bool), state), fconj)), p))), 61.91/62.47 hAPP(fun(state, bool), fun(state, bool), 61.91/62.47 hAPP(fun(bool, bool), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), 61.91/62.47 combb(bool, bool, state), fNot), b)))))) 61.91/62.47 | hBOOL( 61.91/62.47 hAPP(state, bool, 61.91/62.47 hAPP(x_a, fun(state, bool), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 combk(fun(state, bool), x_a), bot_bot(fun(state, bool))), 61.91/62.47 sk_Z_1_1(X0, 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 combk(fun(state, bool), x_a), bot_bot(fun(state, bool))), 61.91/62.47 x_a)), 61.91/62.47 sk_S_1(X0, 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 combk(fun(state, bool), x_a), bot_bot(fun(state, bool))), 61.91/62.47 x_a)))), 61.91/62.47 inference('s_sup-', [status(thm)], ['10', '17'])). 61.91/62.47 tff(help_COMBK_1_1_U, axiom, 61.91/62.47 (![X_b,X_a,P,Q]: 61.91/62.47 (ti(X_a,P) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)))). 61.91/62.47 tff('19', plain, 61.91/62.47 ![X256, X257, X258, X259]: 61.91/62.47 ti(X257, X258) 61.91/62.47 = hAPP(X256, X257, 61.91/62.47 hAPP(X257, fun(X256, X257), combk(X257, X256), X258), X259), 61.91/62.47 inference('cnf', [status(esa)], [help_COMBK_1_1_U])). 61.91/62.47 tff(tsy_c_hAPP_arg1, axiom, 61.91/62.47 (![X_a,X_c,B_1_1,B_2]: 61.91/62.47 (hAPP(X_a,X_c,B_1_1,B_2) = hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2)))). 61.91/62.47 tff('20', plain, 61.91/62.47 ![X274, X275, X276, X277]: 61.91/62.47 hAPP(X274, X275, X276, X277) 61.91/62.47 = hAPP(X274, X275, ti(fun(X274, X275), X276), X277), 61.91/62.47 inference('cnf', [status(esa)], [tsy_c_hAPP_arg1])). 61.91/62.47 tff('21', plain, 61.91/62.47 ![X0]: 61.91/62.47 (~ hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fun(fun(hoare_509422987triple(x_a), bool), bool), 61.91/62.47 hoare_122391849derivs(x_a), g), 61.91/62.47 hAPP(hoare_509422987triple(x_a), 61.91/62.47 fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fequal(hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 hoare_509422987triple(x_a))), 61.91/62.47 hoare_1008221573triple(x_a), X0), c), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(state, bool), fun(x_a, fun(state, bool))), 61.91/62.47 combc(x_a, fun(state, bool), fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool)))), 61.91/62.47 combb(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), x_a), 61.91/62.47 combs(state, bool, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, bool), fun(state, fun(bool, bool))), 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool)))), 61.91/62.47 combb(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool)), x_a), 61.91/62.47 hAPP(fun(bool, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 combb(bool, fun(bool, bool), state), fconj)), p))), 61.91/62.47 hAPP(fun(state, bool), fun(state, bool), 61.91/62.47 hAPP(fun(bool, bool), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), 61.91/62.47 combb(bool, bool, state), fNot), b)))))) 61.91/62.47 | hBOOL( 61.91/62.47 hAPP(state, bool, bot_bot(fun(state, bool)), 61.91/62.47 sk_S_1(X0, 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 combk(fun(state, bool), x_a), bot_bot(fun(state, bool))), 61.91/62.47 x_a)))), 61.91/62.47 inference('demod', [status(thm)], ['18', '19', '20'])). 61.91/62.47 tff(fact_66_bot__empty__eq, axiom, 61.91/62.47 (![X_b,X_2]: 61.91/62.47 (hBOOL(hAPP(fun(X_b,bool),bool, 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2), 61.91/62.47 bot_bot(fun(X_b,bool)))) <=> 61.91/62.47 hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2))))). 61.91/62.47 tff('22', plain, 61.91/62.47 ![X478, X480]: 61.91/62.47 ( hBOOL( 61.91/62.47 hAPP(fun(X478, bool), bool, 61.91/62.47 hAPP(X478, fun(fun(X478, bool), bool), member(X478), X480), 61.91/62.47 bot_bot(fun(X478, bool)))) 61.91/62.47 | ~ hBOOL(hAPP(X478, bool, bot_bot(fun(X478, bool)), X480))), 61.91/62.47 inference('cnf', [status(esa)], [fact_66_bot__empty__eq])). 61.91/62.47 tff(fact_11_emptyE, axiom, 61.91/62.47 (![X_b,A_4]: 61.91/62.47 (~ 61.91/62.47 hBOOL(hAPP(fun(X_b,bool),bool, 61.91/62.47 hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4), 61.91/62.47 bot_bot(fun(X_b,bool))))))). 61.91/62.47 tff('23', plain, 61.91/62.47 ![X334, X335]: 61.91/62.47 ~ hBOOL( 61.91/62.47 hAPP(fun(X334, bool), bool, 61.91/62.47 hAPP(X334, fun(fun(X334, bool), bool), member(X334), X335), 61.91/62.47 bot_bot(fun(X334, bool)))), 61.91/62.47 inference('cnf', [status(esa)], [fact_11_emptyE])). 61.91/62.47 tff('24', plain, 61.91/62.47 ![X478, X480]: ~ hBOOL(hAPP(X478, bool, bot_bot(fun(X478, bool)), X480)), 61.91/62.47 inference('clc', [status(thm)], ['22', '23'])). 61.91/62.47 tff('25', plain, 61.91/62.47 ![X0]: 61.91/62.47 ~ hBOOL( 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), bool, 61.91/62.47 hAPP(fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fun(fun(hoare_509422987triple(x_a), bool), bool), 61.91/62.47 hoare_122391849derivs(x_a), g), 61.91/62.47 hAPP(hoare_509422987triple(x_a), 61.91/62.47 fun(hoare_509422987triple(x_a), bool), 61.91/62.47 fequal(hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a), 61.91/62.47 hAPP(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), hoare_509422987triple(x_a)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(com, 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 hoare_509422987triple(x_a))), 61.91/62.47 hoare_1008221573triple(x_a), X0), c), 61.91/62.47 hAPP(fun(state, bool), fun(x_a, fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(state, bool), fun(x_a, fun(state, bool))), 61.91/62.47 combc(x_a, fun(state, bool), fun(state, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool))), 61.91/62.47 fun(fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 fun(x_a, fun(fun(state, bool), fun(state, bool)))), 61.91/62.47 combb(fun(state, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), x_a), 61.91/62.47 combs(state, bool, bool)), 61.91/62.47 hAPP(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool))), 61.91/62.47 hAPP( 61.91/62.47 fun(fun(state, bool), fun(state, fun(bool, bool))), 61.91/62.47 fun(fun(x_a, fun(state, bool)), 61.91/62.47 fun(x_a, fun(state, fun(bool, bool)))), 61.91/62.47 combb(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool)), x_a), 61.91/62.47 hAPP(fun(bool, fun(bool, bool)), 61.91/62.47 fun(fun(state, bool), 61.91/62.47 fun(state, fun(bool, bool))), 61.91/62.47 combb(bool, fun(bool, bool), state), fconj)), p))), 61.91/62.47 hAPP(fun(state, bool), fun(state, bool), 61.91/62.47 hAPP(fun(bool, bool), 61.91/62.47 fun(fun(state, bool), fun(state, bool)), 61.91/62.47 combb(bool, bool, state), fNot), b)))))), 61.91/62.47 inference('clc', [status(thm)], ['21', '24'])). 61.91/62.47 tff('26', plain, ![X0]: hBOOL(X0), 61.91/62.47 inference('s_sup-', [status(thm)], ['6', '25'])). 61.91/62.47 tff('27', plain, ![X0]: hBOOL(X0), 61.91/62.47 inference('s_sup-', [status(thm)], ['6', '25'])). 61.91/62.47 tff('28', plain, $false, inference('demod', [status(thm)], ['0', '26', '27'])). 61.91/62.47 61.91/62.47 % SZS output end Refutation 61.91/62.47 61.91/62.48 % Zipperpin 1.5 exiting 61.91/62.48 EOF