%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW469+5 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 : Tue May 5 05:32:26 PM UTC 2026
% Result : Theorem 0.43s 1.62s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 123)
% Comments :
%------------------------------------------------------------------------------
fof(fact_23_type__definition_OAbs__cases,axiom,
! [X2,X1,X7,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ~ ! [X12] :
( ti(X1,X7) = hAPP(X2,X1,X14,X12)
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X12),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_type__definition_OAbs__cases) ).
fof(fact_15_Abs__triple__cases,axiom,
! [X1,X7] :
~ ! [X12] :
( X7 = hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X12)
=> ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X12),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Abs__triple__cases) ).
fof(help_fequal_1_1_T,axiom,
! [X1,X9,X22] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X9),X22))
| ti(X1,X9) = ti(X1,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
fof(conj_1,conjecture,
! [X6] :
~ ! [X5] : ti(state,X5) = ti(state,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_25_type__definition_ORep__induct,axiom,
! [X2,X1,X10,X8,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X8),X15))
=> ( ! [X11] : hBOOL(hAPP(X2,bool,X10,hAPP(X1,X2,X13,X11)))
=> hBOOL(hAPP(X2,bool,X10,X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_type__definition_ORep__induct) ).
fof(fact_24_type__definition_OAbs__induct,axiom,
! [X2,X1,X7,X10,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ( ! [X12] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X12),X15))
=> hBOOL(hAPP(X1,bool,X10,hAPP(X2,X1,X14,X12))) )
=> hBOOL(hAPP(X1,bool,X10,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_type__definition_OAbs__induct) ).
fof(fact_13_Abs__triple__inject,axiom,
! [X1,X8,X7] :
( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X7),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
=> ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X8),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
=> ( hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X7) = hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X8)
<=> X7 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Abs__triple__inject) ).
fof(fact_12_type__definition__triple,axiom,
! [X1] : hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1)),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),hAPP(fun(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1)),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool)),type_definition(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_2037801986triple(X1)),hoare_244953527triple(X1)),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_type__definition__triple) ).
fof(fact_9_Rep__triple__induct,axiom,
! [X1,X10,X8] :
( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X8),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
=> ( ! [X11] : hBOOL(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool,X10,hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X11)))
=> hBOOL(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool,X10,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Rep__triple__induct) ).
fof(fact_11_Abs__triple__inverse,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X8),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
=> hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X8)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Abs__triple__inverse) ).
fof(fact_10_Rep__triple__cases,axiom,
! [X1,X8] :
( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X8),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
=> ~ ! [X11] : X8 != hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Rep__triple__cases) ).
fof(fact_8_Rep__triple,axiom,
! [X1,X7] : hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X7)),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Rep__triple) ).
fof(fact_14_Abs__triple__induct,axiom,
! [X1,X7,X10] :
( ! [X12] :
( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X12),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
=> hBOOL(hAPP(hoare_509422987triple(X1),bool,X10,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X12))) )
=> hBOOL(hAPP(hoare_509422987triple(X1),bool,X10,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Abs__triple__induct) ).
fof(fact_22_type__definition_ORep__cases,axiom,
! [X2,X1,X8,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X8),X15))
=> ~ ! [X11] : ti(X2,X8) != hAPP(X1,X2,X13,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_type__definition_ORep__cases) ).
fof(fact_16_type__definition_OAbs__inject,axiom,
! [X2,X1,X8,X7,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),X15))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X8),X15))
=> ( hAPP(X2,X1,X14,X7) = hAPP(X2,X1,X14,X8)
<=> ti(X2,X7) = ti(X2,X8) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_type__definition_OAbs__inject) ).
fof(fact_20_type__definition_ORep,axiom,
! [X2,X1,X7,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X13,X7)),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_type__definition_ORep) ).
fof(fact_17_type__definition_OAbs__inverse,axiom,
! [X2,X1,X8,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X8),X15))
=> hAPP(X1,X2,X13,hAPP(X2,X1,X14,X8)) = ti(X2,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_type__definition_OAbs__inverse) ).
fof(fact_18_type__definition_ORep__inject,axiom,
! [X2,X1,X7,X8,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ( hAPP(X1,X2,X13,X7) = hAPP(X1,X2,X13,X8)
<=> ti(X1,X7) = ti(X1,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_type__definition_ORep__inject) ).
fof(fact_19_type__definition_ORep__inverse,axiom,
! [X2,X1,X7,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> hAPP(X2,X1,X14,hAPP(X1,X2,X13,X7)) = ti(X1,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_type__definition_ORep__inverse) ).
fof(fact_30_mem__def,axiom,
! [X1,X7,X15] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X15))
<=> hBOOL(hAPP(X1,bool,X15,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_mem__def) ).
fof(fact_2_Rep__triple__inject,axiom,
! [X1,X7,X8] :
( hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X7) = hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X8)
<=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).
fof(fact_7_Rep__triple__inverse,axiom,
! [X1,X7] : hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X7)) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Rep__triple__inverse) ).
fof(fact_1_equal__triple__def,axiom,
! [X1,X7,X8] :
( hBOOL(hAPP(hoare_509422987triple(X1),bool,hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),equal_equal(hoare_509422987triple(X1)),X7),X8))
<=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).
fof(fact_5_equal__eq,axiom,
! [X1] :
( cl_HOL_Oequal(X1)
=> ! [X7,X8] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),equal_equal(X1),X7),X8))
<=> ti(X1,X7) = ti(X1,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_equal__eq) ).
fof(fact_28_induct__equal__def,axiom,
! [X1,X7,X8] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),induct_equal(X1),X7),X8))
<=> ti(X1,X7) = ti(X1,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_induct__equal__def) ).
fof(fact_29_ext,axiom,
! [X1,X2,X16,X17] :
( ! [X11] : hAPP(X1,X2,X16,X11) = hAPP(X1,X2,X17,X11)
=> ti(fun(X1,X2),X16) = ti(fun(X1,X2),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ext) ).
fof(help_fequal_2_1_T,axiom,
! [X1,X9,X22] :
( ti(X1,X9) != ti(X1,X22)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X9),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res,axiom,
! [X1] : ti(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1)),hoare_244953527triple(X1)) = hoare_244953527triple(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res) ).
fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res,axiom,
! [X1] : ti(fun(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_2037801986triple(X1)) = hoare_2037801986triple(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res) ).
fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res,axiom,
! [X1] : ti(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),hoare_1580379338ep_set(X1)) = hoare_1580379338ep_set(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res) ).
fof(fact_4_equal__refl,axiom,
! [X1] :
( cl_HOL_Oequal(X1)
=> ! [X9] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),equal_equal(X1),X9),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_equal__refl) ).
fof(tsy_c_hAPP_res,axiom,
! [X1,X2,X3,X4] : ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(tsy_c_hAPP_arg1,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,ti(fun(X2,X1),X3),X4) = hAPP(X2,X1,X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(tsy_c_Typedef_Otype__definition_res,axiom,
! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool))),type_definition(X1,X2)) = type_definition(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Typedef_Otype__definition_res) ).
fof(tsy_c_hAPP_arg2,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,X3,ti(X2,X4)) = hAPP(X2,X1,X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(fact_31_Collect__def,axiom,
! [X1,X10] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X10) = ti(fun(X1,bool),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Collect__def) ).
fof(tsy_c_member_res,axiom,
! [X2] : ti(fun(X2,fun(fun(X2,bool),bool)),member(X2)) = member(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).
fof(tsy_c_Set_OCollect_res,axiom,
! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
fof(tsy_c_HOL_Oequal__class_Oequal_res,axiom,
! [X1] :
( cl_HOL_Oequal(X1)
=> ti(fun(X1,fun(X1,bool)),equal_equal(X1)) = equal_equal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oequal__class_Oequal_res) ).
fof(tsy_c_fequal_res,axiom,
! [X1] : ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
fof(tsy_c_HOL_Oinduct__equal_res,axiom,
! [X1] : ti(fun(X1,fun(X1,bool)),induct_equal(X1)) = induct_equal(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__equal_res) ).
fof(help_ti_idem,axiom,
! [X20,X21] : ti(X20,ti(X20,X21)) = ti(X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [X3] :
( hBOOL(ti(bool,X3))
<=> hBOOL(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(arity_sum___Enum_Oenum,axiom,
! [X18,X19] :
( ( enum(X19)
& enum(X18) )
=> enum(sum_sum(X18,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).
fof(arity_fun___Enum_Oenum,axiom,
! [X18,X19] :
( ( enum(X19)
& enum(X18) )
=> enum(fun(X18,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
fof(arity_fun___HOL_Oequal,axiom,
! [X18,X19] :
( ( cl_HOL_Oequal(X19)
& enum(X18) )
=> cl_HOL_Oequal(fun(X18,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
fof(fact_0_state__not__singleton__def,axiom,
( hBOOL(hoare_1883395792gleton)
<=> ? [X5,X6] : ti(state,X5) != ti(state,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
fof(arity_sum___HOL_Oequal,axiom,
! [X18,X19] : cl_HOL_Oequal(sum_sum(X18,X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).
fof(tsy_c_HOL_Oundefined_res,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(fact_6_eq__equal,axiom,
! [X1] :
( cl_HOL_Oequal(X1)
=> fequal(X1) = equal_equal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_eq__equal) ).
fof(fact_3_equal,axiom,
! [X1] :
( cl_HOL_Oequal(X1)
=> equal_equal(X1) = fequal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_equal) ).
fof(arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal,axiom,
! [X19] : cl_HOL_Oequal(hoare_509422987triple(X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal) ).
fof(fact_21_induct__false__def,axiom,
~ hBOOL(induct_false),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_induct__false__def) ).
fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res,hypothesis,
ti(bool,hoare_1883395792gleton) = hoare_1883395792gleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res) ).
fof(tsy_c_HOL_Oinduct__true_res,axiom,
ti(bool,induct_true) = induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__true_res) ).
fof(tsy_c_HOL_Oinduct__false_res,axiom,
ti(bool,induct_false) = induct_false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__false_res) ).
fof(arity_HOL_Obool___Enum_Oenum,axiom,
enum(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
fof(conj_0,hypothesis,
hBOOL(hoare_1883395792gleton),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_27_induct__true__def,axiom,
hBOOL(induct_true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_induct__true__def) ).
fof(fact_26_induct__trueI,axiom,
hBOOL(induct_true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_induct__trueI) ).
fof(arity_Com_Ostate___HOL_Oequal,axiom,
cl_HOL_Oequal(state),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).
fof(arity_Com_Ocom___HOL_Oequal,axiom,
cl_HOL_Oequal(com),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).
fof(arity_HOL_Obool___HOL_Oequal,axiom,
cl_HOL_Oequal(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
fof(i_0_63,plain,
! [X2,X1,X7,X13,X14,X15] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X13),X14),X15))
=> ~ ! [X12] :
( ti(X1,X7) = hAPP(X2,X1,X14,X12)
=> ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X12),X15)) ) ),
inference(fof_simplification,[status(thm)],[fact_23_type__definition_OAbs__cases]) ).
fof(i_0_64,plain,
! [X1,X7] :
~ ! [X12] :
( X7 = hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X12)
=> ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X12),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))) ),
inference(fof_simplification,[status(thm)],[fact_15_Abs__triple__cases]) ).
fof(i_0_65,plain,
! [X1,X9,X22] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X9),X22))
| ti(X1,X9) = ti(X1,X22) ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_T]) ).
fof(i_0_66,negated_conjecture,
~ ! [X6] :
~ ! [X5] : ti(state,X5) = ti(state,X6),
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(i_0_67,plain,
! [X299,X300,X301,X302,X303,X304,X305] :
( ~ hBOOL(hAPP(fun(X299,bool),bool,hAPP(fun(X299,X300),fun(fun(X299,bool),bool),hAPP(fun(X300,X299),fun(fun(X299,X300),fun(fun(X299,bool),bool)),type_definition(X300,X299),X303),X304),X305))
| ~ hBOOL(hAPP(fun(X299,bool),bool,hAPP(X299,fun(fun(X299,bool),bool),member(X299),X302),X305))
| ~ hBOOL(hAPP(X299,bool,X301,hAPP(X300,X299,X303,esk10_7(X299,X300,X301,X302,X303,X304,X305))))
| hBOOL(hAPP(X299,bool,X301,X302)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25_type__definition_ORep__induct])])]) ).
fof(i_0_68,plain,
! [X291,X292,X293,X294,X295,X296,X297] :
( ( hBOOL(hAPP(fun(X291,bool),bool,hAPP(X291,fun(fun(X291,bool),bool),member(X291),esk9_7(X291,X292,X293,X294,X295,X296,X297)),X297))
| hBOOL(hAPP(X292,bool,X294,X293))
| ~ hBOOL(hAPP(fun(X291,bool),bool,hAPP(fun(X291,X292),fun(fun(X291,bool),bool),hAPP(fun(X292,X291),fun(fun(X291,X292),fun(fun(X291,bool),bool)),type_definition(X292,X291),X295),X296),X297)) )
& ( ~ hBOOL(hAPP(X292,bool,X294,hAPP(X291,X292,X296,esk9_7(X291,X292,X293,X294,X295,X296,X297))))
| hBOOL(hAPP(X292,bool,X294,X293))
| ~ hBOOL(hAPP(fun(X291,bool),bool,hAPP(fun(X291,X292),fun(fun(X291,bool),bool),hAPP(fun(X292,X291),fun(fun(X291,X292),fun(fun(X291,bool),bool)),type_definition(X292,X291),X295),X296),X297)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_24_type__definition_OAbs__induct])])])]) ).
fof(i_0_69,plain,
! [X235,X236,X237] :
( ( hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),hoare_509422987triple(X235),hoare_244953527triple(X235),X237) != hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),hoare_509422987triple(X235),hoare_244953527triple(X235),X236)
| X237 = X236
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),fun(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),X236),hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),collect(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),hoare_1580379338ep_set(X235))))
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),fun(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),X237),hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),collect(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),hoare_1580379338ep_set(X235)))) )
& ( X237 != X236
| hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),hoare_509422987triple(X235),hoare_244953527triple(X235),X237) = hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),hoare_509422987triple(X235),hoare_244953527triple(X235),X236)
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),fun(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),X236),hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),collect(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),hoare_1580379338ep_set(X235))))
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),fun(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),X237),hAPP(fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),fun(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool),bool),collect(fun(node(sum_sum(com,fun(X235,fun(state,bool))),sum_sum(state,X235)),bool)),hoare_1580379338ep_set(X235)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_13_Abs__triple__inject])])]) ).
fof(i_0_70,plain,
! [X234] : hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool),hoare_509422987triple(X234)),fun(fun(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool),bool),bool),hAPP(fun(hoare_509422987triple(X234),fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool)),fun(fun(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool),hoare_509422987triple(X234)),fun(fun(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool),bool),bool)),type_definition(hoare_509422987triple(X234),fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool)),hoare_2037801986triple(X234)),hoare_244953527triple(X234)),hAPP(fun(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool),bool),fun(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool),bool),collect(fun(node(sum_sum(com,fun(X234,fun(state,bool))),sum_sum(state,X234)),bool)),hoare_1580379338ep_set(X234)))),
inference(variable_rename,[status(thm)],[fact_12_type__definition__triple]) ).
fof(i_0_71,plain,
! [X225,X226,X227] :
( ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),fun(fun(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool)),X227),hAPP(fun(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),bool),fun(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),bool),collect(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool)),hoare_1580379338ep_set(X225))))
| ~ hBOOL(hAPP(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),bool,X226,hAPP(hoare_509422987triple(X225),fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),hoare_2037801986triple(X225),esk3_3(X225,X226,X227))))
| hBOOL(hAPP(fun(node(sum_sum(com,fun(X225,fun(state,bool))),sum_sum(state,X225)),bool),bool,X226,X227)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_Rep__triple__induct])])]) ).
fof(i_0_72,plain,
! [X232,X233] :
( ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool),fun(fun(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool)),X233),hAPP(fun(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool),bool),fun(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool),bool),collect(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool)),hoare_1580379338ep_set(X232))))
| hAPP(hoare_509422987triple(X232),fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool),hoare_2037801986triple(X232),hAPP(fun(node(sum_sum(com,fun(X232,fun(state,bool))),sum_sum(state,X232)),bool),hoare_509422987triple(X232),hoare_244953527triple(X232),X233)) = X233 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_Abs__triple__inverse])]) ).
fof(i_0_73,plain,
! [X229,X230] :
( ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool),fun(fun(fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool)),X230),hAPP(fun(fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool),bool),fun(fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool),bool),collect(fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool)),hoare_1580379338ep_set(X229))))
| X230 = hAPP(hoare_509422987triple(X229),fun(node(sum_sum(com,fun(X229,fun(state,bool))),sum_sum(state,X229)),bool),hoare_2037801986triple(X229),esk4_2(X229,X230)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_Rep__triple__cases])])]) ).
fof(i_0_74,plain,
! [X284,X285,X286,X287,X288,X289] :
( ( ti(X285,X286) = hAPP(X284,X285,X288,esk8_6(X284,X285,X286,X287,X288,X289))
| ~ hBOOL(hAPP(fun(X284,bool),bool,hAPP(fun(X284,X285),fun(fun(X284,bool),bool),hAPP(fun(X285,X284),fun(fun(X284,X285),fun(fun(X284,bool),bool)),type_definition(X285,X284),X287),X288),X289)) )
& ( hBOOL(hAPP(fun(X284,bool),bool,hAPP(X284,fun(fun(X284,bool),bool),member(X284),esk8_6(X284,X285,X286,X287,X288,X289)),X289))
| ~ hBOOL(hAPP(fun(X284,bool),bool,hAPP(fun(X284,X285),fun(fun(X284,bool),bool),hAPP(fun(X285,X284),fun(fun(X284,X285),fun(fun(X284,bool),bool)),type_definition(X285,X284),X287),X288),X289)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_63])])])]) ).
fof(i_0_75,plain,
! [X223,X224] : hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool),fun(fun(fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool)),hAPP(hoare_509422987triple(X223),fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool),hoare_2037801986triple(X223),X224)),hAPP(fun(fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool),bool),fun(fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool),bool),collect(fun(node(sum_sum(com,fun(X223,fun(state,bool))),sum_sum(state,X223)),bool)),hoare_1580379338ep_set(X223)))),
inference(variable_rename,[status(thm)],[fact_8_Rep__triple]) ).
fof(i_0_76,plain,
! [X238,X239,X240] :
( ( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool),fun(fun(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool)),esk5_3(X238,X239,X240)),hAPP(fun(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool),bool),fun(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool),bool),collect(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool)),hoare_1580379338ep_set(X238))))
| hBOOL(hAPP(hoare_509422987triple(X238),bool,X240,X239)) )
& ( ~ hBOOL(hAPP(hoare_509422987triple(X238),bool,X240,hAPP(fun(node(sum_sum(com,fun(X238,fun(state,bool))),sum_sum(state,X238)),bool),hoare_509422987triple(X238),hoare_244953527triple(X238),esk5_3(X238,X239,X240))))
| hBOOL(hAPP(hoare_509422987triple(X238),bool,X240,X239)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_Abs__triple__induct])])])]) ).
fof(i_0_77,plain,
! [X242,X243] :
( X243 = hAPP(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool),hoare_509422987triple(X242),hoare_244953527triple(X242),esk6_2(X242,X243))
& hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool),fun(fun(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool)),esk6_2(X242,X243)),hAPP(fun(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool),bool),fun(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool),bool),collect(fun(node(sum_sum(com,fun(X242,fun(state,bool))),sum_sum(state,X242)),bool)),hoare_1580379338ep_set(X242)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_64])])]) ).
fof(i_0_78,plain,
! [X277,X278,X279,X280,X281,X282] :
( ~ hBOOL(hAPP(fun(X277,bool),bool,hAPP(fun(X277,X278),fun(fun(X277,bool),bool),hAPP(fun(X278,X277),fun(fun(X277,X278),fun(fun(X277,bool),bool)),type_definition(X278,X277),X280),X281),X282))
| ~ hBOOL(hAPP(fun(X277,bool),bool,hAPP(X277,fun(fun(X277,bool),bool),member(X277),X279),X282))
| ti(X277,X279) = hAPP(X278,X277,X280,esk7_6(X277,X278,X279,X280,X281,X282)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_type__definition_ORep__cases])])]) ).
fof(i_0_79,plain,
! [X245,X246,X247,X248,X249,X250,X251] :
( ( hAPP(X245,X246,X250,X248) != hAPP(X245,X246,X250,X247)
| ti(X245,X248) = ti(X245,X247)
| ~ hBOOL(hAPP(fun(X245,bool),bool,hAPP(X245,fun(fun(X245,bool),bool),member(X245),X247),X251))
| ~ hBOOL(hAPP(fun(X245,bool),bool,hAPP(X245,fun(fun(X245,bool),bool),member(X245),X248),X251))
| ~ hBOOL(hAPP(fun(X245,bool),bool,hAPP(fun(X245,X246),fun(fun(X245,bool),bool),hAPP(fun(X246,X245),fun(fun(X245,X246),fun(fun(X245,bool),bool)),type_definition(X246,X245),X249),X250),X251)) )
& ( ti(X245,X248) != ti(X245,X247)
| hAPP(X245,X246,X250,X248) = hAPP(X245,X246,X250,X247)
| ~ hBOOL(hAPP(fun(X245,bool),bool,hAPP(X245,fun(fun(X245,bool),bool),member(X245),X247),X251))
| ~ hBOOL(hAPP(fun(X245,bool),bool,hAPP(X245,fun(fun(X245,bool),bool),member(X245),X248),X251))
| ~ hBOOL(hAPP(fun(X245,bool),bool,hAPP(fun(X245,X246),fun(fun(X245,bool),bool),hAPP(fun(X246,X245),fun(fun(X245,X246),fun(fun(X245,bool),bool)),type_definition(X246,X245),X249),X250),X251)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_type__definition_OAbs__inject])])]) ).
fof(i_0_80,plain,
! [X271,X272,X273,X274,X275,X276] :
( ~ hBOOL(hAPP(fun(X271,bool),bool,hAPP(fun(X271,X272),fun(fun(X271,bool),bool),hAPP(fun(X272,X271),fun(fun(X271,X272),fun(fun(X271,bool),bool)),type_definition(X272,X271),X274),X275),X276))
| hBOOL(hAPP(fun(X271,bool),bool,hAPP(X271,fun(fun(X271,bool),bool),member(X271),hAPP(X272,X271,X274,X273)),X276)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_20_type__definition_ORep])]) ).
fof(i_0_81,plain,
! [X252,X253,X254,X255,X256,X257] :
( ~ hBOOL(hAPP(fun(X252,bool),bool,hAPP(fun(X252,X253),fun(fun(X252,bool),bool),hAPP(fun(X253,X252),fun(fun(X252,X253),fun(fun(X252,bool),bool)),type_definition(X253,X252),X255),X256),X257))
| ~ hBOOL(hAPP(fun(X252,bool),bool,hAPP(X252,fun(fun(X252,bool),bool),member(X252),X254),X257))
| hAPP(X253,X252,X255,hAPP(X252,X253,X256,X254)) = ti(X252,X254) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_type__definition_OAbs__inverse])]) ).
fof(i_0_82,plain,
! [X258,X259,X260,X261,X262,X263,X264] :
( ( hAPP(X259,X258,X262,X260) != hAPP(X259,X258,X262,X261)
| ti(X259,X260) = ti(X259,X261)
| ~ hBOOL(hAPP(fun(X258,bool),bool,hAPP(fun(X258,X259),fun(fun(X258,bool),bool),hAPP(fun(X259,X258),fun(fun(X258,X259),fun(fun(X258,bool),bool)),type_definition(X259,X258),X262),X263),X264)) )
& ( ti(X259,X260) != ti(X259,X261)
| hAPP(X259,X258,X262,X260) = hAPP(X259,X258,X262,X261)
| ~ hBOOL(hAPP(fun(X258,bool),bool,hAPP(fun(X258,X259),fun(fun(X258,bool),bool),hAPP(fun(X259,X258),fun(fun(X258,X259),fun(fun(X258,bool),bool)),type_definition(X259,X258),X262),X263),X264)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_18_type__definition_ORep__inject])])]) ).
fof(i_0_83,plain,
! [X265,X266,X267,X268,X269,X270] :
( ~ hBOOL(hAPP(fun(X265,bool),bool,hAPP(fun(X265,X266),fun(fun(X265,bool),bool),hAPP(fun(X266,X265),fun(fun(X265,X266),fun(fun(X265,bool),bool)),type_definition(X266,X265),X268),X269),X270))
| hAPP(X265,X266,X269,hAPP(X266,X265,X268,X267)) = ti(X266,X267) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_19_type__definition_ORep__inverse])]) ).
fof(i_0_84,plain,
! [X315,X316,X317] :
( ( ~ hBOOL(hAPP(fun(X315,bool),bool,hAPP(X315,fun(fun(X315,bool),bool),member(X315),X316),X317))
| hBOOL(hAPP(X315,bool,X317,X316)) )
& ( ~ hBOOL(hAPP(X315,bool,X317,X316))
| hBOOL(hAPP(fun(X315,bool),bool,hAPP(X315,fun(fun(X315,bool),bool),member(X315),X316),X317)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_mem__def])]) ).
fof(i_0_85,plain,
! [X211,X212,X213] :
( ( hAPP(hoare_509422987triple(X211),fun(node(sum_sum(com,fun(X211,fun(state,bool))),sum_sum(state,X211)),bool),hoare_2037801986triple(X211),X212) != hAPP(hoare_509422987triple(X211),fun(node(sum_sum(com,fun(X211,fun(state,bool))),sum_sum(state,X211)),bool),hoare_2037801986triple(X211),X213)
| X212 = X213 )
& ( X212 != X213
| hAPP(hoare_509422987triple(X211),fun(node(sum_sum(com,fun(X211,fun(state,bool))),sum_sum(state,X211)),bool),hoare_2037801986triple(X211),X212) = hAPP(hoare_509422987triple(X211),fun(node(sum_sum(com,fun(X211,fun(state,bool))),sum_sum(state,X211)),bool),hoare_2037801986triple(X211),X213) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_Rep__triple__inject])]) ).
fof(i_0_86,plain,
! [X221,X222] : hAPP(fun(node(sum_sum(com,fun(X221,fun(state,bool))),sum_sum(state,X221)),bool),hoare_509422987triple(X221),hoare_244953527triple(X221),hAPP(hoare_509422987triple(X221),fun(node(sum_sum(com,fun(X221,fun(state,bool))),sum_sum(state,X221)),bool),hoare_2037801986triple(X221),X222)) = X222,
inference(variable_rename,[status(thm)],[fact_7_Rep__triple__inverse]) ).
fof(i_0_87,plain,
! [X208,X209,X210] :
( ( ~ hBOOL(hAPP(hoare_509422987triple(X208),bool,hAPP(hoare_509422987triple(X208),fun(hoare_509422987triple(X208),bool),equal_equal(hoare_509422987triple(X208)),X209),X210))
| X209 = X210 )
& ( X209 != X210
| hBOOL(hAPP(hoare_509422987triple(X208),bool,hAPP(hoare_509422987triple(X208),fun(hoare_509422987triple(X208),bool),equal_equal(hoare_509422987triple(X208)),X209),X210)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_equal__triple__def])]) ).
fof(i_0_88,plain,
! [X217,X218,X219] :
( ( ~ hBOOL(hAPP(X217,bool,hAPP(X217,fun(X217,bool),equal_equal(X217),X218),X219))
| ti(X217,X218) = ti(X217,X219)
| ~ cl_HOL_Oequal(X217) )
& ( ti(X217,X218) != ti(X217,X219)
| hBOOL(hAPP(X217,bool,hAPP(X217,fun(X217,bool),equal_equal(X217),X218),X219))
| ~ cl_HOL_Oequal(X217) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_equal__eq])])])]) ).
fof(i_0_89,plain,
! [X331,X332,X333] :
( ~ hBOOL(hAPP(X331,bool,hAPP(X331,fun(X331,bool),fequal(X331),X332),X333))
| ti(X331,X332) = ti(X331,X333) ),
inference(variable_rename,[status(thm)],[i_0_65]) ).
fof(i_0_90,plain,
! [X307,X308,X309] :
( ( ~ hBOOL(hAPP(X307,bool,hAPP(X307,fun(X307,bool),induct_equal(X307),X308),X309))
| ti(X307,X308) = ti(X307,X309) )
& ( ti(X307,X308) != ti(X307,X309)
| hBOOL(hAPP(X307,bool,hAPP(X307,fun(X307,bool),induct_equal(X307),X308),X309)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_induct__equal__def])]) ).
fof(i_0_91,plain,
! [X310,X311,X312,X313] :
( hAPP(X310,X311,X312,esk11_4(X310,X311,X312,X313)) != hAPP(X310,X311,X313,esk11_4(X310,X311,X312,X313))
| ti(fun(X310,X311),X312) = ti(fun(X310,X311),X313) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_ext])])]) ).
fof(i_0_92,plain,
! [X334,X335,X336] :
( ti(X334,X335) != ti(X334,X336)
| hBOOL(hAPP(X334,bool,hAPP(X334,fun(X334,bool),fequal(X334),X335),X336)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_T]) ).
fof(i_0_93,plain,
! [X183] : ti(fun(fun(node(sum_sum(com,fun(X183,fun(state,bool))),sum_sum(state,X183)),bool),hoare_509422987triple(X183)),hoare_244953527triple(X183)) = hoare_244953527triple(X183),
inference(variable_rename,[status(thm)],[tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res]) ).
fof(i_0_94,plain,
! [X184] : ti(fun(hoare_509422987triple(X184),fun(node(sum_sum(com,fun(X184,fun(state,bool))),sum_sum(state,X184)),bool)),hoare_2037801986triple(X184)) = hoare_2037801986triple(X184),
inference(variable_rename,[status(thm)],[tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res]) ).
fof(i_0_95,plain,
! [X185] : ti(fun(fun(node(sum_sum(com,fun(X185,fun(state,bool))),sum_sum(state,X185)),bool),bool),hoare_1580379338ep_set(X185)) = hoare_1580379338ep_set(X185),
inference(variable_rename,[status(thm)],[tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res]) ).
fof(i_0_96,plain,
! [X215,X216] :
( ~ cl_HOL_Oequal(X215)
| hBOOL(hAPP(X215,bool,hAPP(X215,fun(X215,bool),equal_equal(X215),X216),X216)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_equal__refl])])]) ).
fof(i_0_97,plain,
! [X198,X199,X200,X201] : ti(X198,hAPP(X199,X198,X200,X201)) = hAPP(X199,X198,X200,X201),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
fof(i_0_98,plain,
! [X190,X191,X192,X193] : hAPP(X190,X191,ti(fun(X190,X191),X192),X193) = hAPP(X190,X191,X192,X193),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).
fof(i_0_99,plain,
! [X187,X188] : ti(fun(fun(X187,X188),fun(fun(X188,X187),fun(fun(X188,bool),bool))),type_definition(X187,X188)) = type_definition(X187,X188),
inference(variable_rename,[status(thm)],[tsy_c_Typedef_Otype__definition_res]) ).
fof(i_0_100,plain,
! [X194,X195,X196,X197] : hAPP(X194,X195,X196,ti(X194,X197)) = hAPP(X194,X195,X196,X197),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).
fof(i_0_101,plain,
! [X318,X319] : hAPP(fun(X318,bool),fun(X318,bool),collect(X318),X319) = ti(fun(X318,bool),X319),
inference(variable_rename,[status(thm)],[fact_31_Collect__def]) ).
fof(i_0_102,plain,
! [X203] : ti(fun(X203,fun(fun(X203,bool),bool)),member(X203)) = member(X203),
inference(variable_rename,[status(thm)],[tsy_c_member_res]) ).
fof(i_0_103,plain,
! [X186] : ti(fun(fun(X186,bool),fun(X186,bool)),collect(X186)) = collect(X186),
inference(variable_rename,[status(thm)],[tsy_c_Set_OCollect_res]) ).
fof(i_0_104,plain,
! [X180] :
( ~ cl_HOL_Oequal(X180)
| ti(fun(X180,fun(X180,bool)),equal_equal(X180)) = equal_equal(X180) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_HOL_Oequal__class_Oequal_res])]) ).
fof(i_0_105,plain,
! [X189] : ti(fun(X189,fun(X189,bool)),fequal(X189)) = fequal(X189),
inference(variable_rename,[status(thm)],[tsy_c_fequal_res]) ).
fof(i_0_106,plain,
! [X181] : ti(fun(X181,fun(X181,bool)),induct_equal(X181)) = induct_equal(X181),
inference(variable_rename,[status(thm)],[tsy_c_HOL_Oinduct__equal_res]) ).
fof(i_0_107,plain,
! [X329,X330] : ti(X329,ti(X329,X330)) = ti(X329,X330),
inference(variable_rename,[status(thm)],[help_ti_idem]) ).
fof(i_0_108,hypothesis,
! [X202] :
( ( ~ hBOOL(ti(bool,X202))
| hBOOL(X202) )
& ( ~ hBOOL(X202)
| hBOOL(ti(bool,X202)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1])]) ).
fof(i_0_109,plain,
! [X320,X321] :
( ~ enum(X321)
| ~ enum(X320)
| enum(sum_sum(X320,X321)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum___Enum_Oenum])]) ).
fof(i_0_110,plain,
! [X322,X323] :
( ~ enum(X323)
| ~ enum(X322)
| enum(fun(X322,X323)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Enum_Oenum])]) ).
fof(i_0_111,plain,
! [X324,X325] :
( ~ cl_HOL_Oequal(X325)
| ~ enum(X324)
| cl_HOL_Oequal(fun(X324,X325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___HOL_Oequal])]) ).
fof(i_0_112,plain,
! [X206,X207] :
( ( ~ hBOOL(hoare_1883395792gleton)
| ti(state,esk1_0) != ti(state,esk2_0) )
& ( ti(state,X206) = ti(state,X207)
| hBOOL(hoare_1883395792gleton) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_state__not__singleton__def])])])]) ).
fof(i_0_113,plain,
! [X326,X327] : cl_HOL_Oequal(sum_sum(X326,X327)),
inference(variable_rename,[status(thm)],[arity_sum___HOL_Oequal]) ).
fof(i_0_114,plain,
! [X182] : ti(X182,undefined(X182)) = undefined(X182),
inference(variable_rename,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).
fof(i_0_115,negated_conjecture,
! [X338] : ti(state,X338) = ti(state,esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_66])])]) ).
fof(i_0_116,plain,
! [X220] :
( ~ cl_HOL_Oequal(X220)
| fequal(X220) = equal_equal(X220) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_eq__equal])]) ).
fof(i_0_117,plain,
! [X214] :
( ~ cl_HOL_Oequal(X214)
| equal_equal(X214) = fequal(X214) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_equal])]) ).
fof(i_0_118,plain,
! [X328] : cl_HOL_Oequal(hoare_509422987triple(X328)),
inference(variable_rename,[status(thm)],[arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal]) ).
fof(i_0_119,plain,
~ hBOOL(induct_false),
inference(fof_simplification,[status(thm)],[fact_21_induct__false__def]) ).
cnf(i_0_120,plain,
( hBOOL(hAPP(X1,bool,X7,X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X5))
| ~ hBOOL(hAPP(X1,bool,X7,hAPP(X2,X1,X3,esk10_7(X1,X2,X7,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_121,plain,
( hBOOL(hAPP(X1,bool,X2,X5))
| ~ hBOOL(hAPP(X1,bool,X2,hAPP(X3,X1,X4,esk9_7(X3,X1,X5,X2,X6,X4,X7))))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),hAPP(fun(X1,X3),fun(fun(X3,X1),fun(fun(X3,bool),bool)),type_definition(X1,X3),X6),X4),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_122,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk9_7(X1,X2,X3,X4,X5,X6,X7)),X7))
| hBOOL(hAPP(X2,bool,X4,X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X5),X6),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_123,plain,
( X2 = X3
| hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X2) != hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X3)
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X3),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X2),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_124,plain,
hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1)),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),hAPP(fun(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1)),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool)),type_definition(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_2037801986triple(X1)),hoare_244953527triple(X1)),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_125,plain,
( hBOOL(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool,X3,X2))
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X2),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
| ~ hBOOL(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool,X3,hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),esk3_3(X1,X3,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_126,plain,
( hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),X2)) = X2
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X2),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_127,plain,
( X2 = hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),esk4_2(X1,X2))
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X2),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_128,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk8_6(X1,X2,X3,X4,X5,X6)),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_129,plain,
hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X2)),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_130,plain,
( hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),esk5_3(X1,X2,X3)),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
| hBOOL(hAPP(hoare_509422987triple(X1),bool,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_131,plain,
hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),esk6_2(X1,X2)),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1)))),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_132,plain,
( ti(X1,X6) = hAPP(X2,X1,X3,esk7_6(X1,X2,X6,X3,X4,X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_133,plain,
( ti(X1,X2) = hAPP(X3,X1,X4,esk8_6(X3,X1,X2,X5,X4,X6))
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),hAPP(fun(X1,X3),fun(fun(X3,X1),fun(fun(X3,bool),bool)),type_definition(X1,X3),X5),X4),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_134,plain,
( ti(X1,X4) = ti(X1,X5)
| hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X7),X3),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_135,plain,
( hAPP(X1,X4,X5,X2) = hAPP(X1,X4,X5,X3)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),hAPP(fun(X4,X1),fun(fun(X1,X4),fun(fun(X1,bool),bool)),type_definition(X4,X1),X7),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_136,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X6)),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_137,plain,
( hAPP(X2,X1,X3,hAPP(X1,X2,X4,X6)) = ti(X1,X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X3),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_138,plain,
( ti(X1,X4) = ti(X1,X5)
| hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X3),X6),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_139,plain,
( hAPP(X1,X2,X4,hAPP(X2,X1,X3,X6)) = ti(X2,X6)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_140,plain,
( hAPP(X1,X4,X5,X2) = hAPP(X1,X4,X5,X3)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),hAPP(fun(X1,X4),fun(fun(X4,X1),fun(fun(X4,bool),bool)),type_definition(X1,X4),X5),X6),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_141,plain,
( hBOOL(hAPP(hoare_509422987triple(X1),bool,X2,X3))
| ~ hBOOL(hAPP(hoare_509422987triple(X1),bool,X2,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk5_3(X1,X3,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_142,plain,
( hBOOL(hAPP(X1,bool,X3,X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_143,plain,
( X2 = X3
| hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X2) != hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_144,plain,
hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_145,plain,
( X2 = X3
| ~ hBOOL(hAPP(hoare_509422987triple(X1),bool,hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),equal_equal(hoare_509422987triple(X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_146,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_147,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),equal_equal(X1),X2),X3))
| ~ cl_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_148,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_149,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),induct_equal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_150,plain,
( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
| hAPP(X1,X2,X3,esk11_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk11_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_151,plain,
( hBOOL(hAPP(hoare_509422987triple(X3),bool,hAPP(hoare_509422987triple(X3),fun(hoare_509422987triple(X3),bool),equal_equal(hoare_509422987triple(X3)),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_152,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),equal_equal(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ cl_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_153,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_154,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),induct_equal(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_155,plain,
ti(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1)),hoare_244953527triple(X1)) = hoare_244953527triple(X1),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_156,plain,
ti(fun(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_2037801986triple(X1)) = hoare_2037801986triple(X1),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_157,plain,
ti(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),hoare_1580379338ep_set(X1)) = hoare_1580379338ep_set(X1),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_158,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),equal_equal(X1),X2),X2))
| ~ cl_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_159,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_160,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_161,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_162,plain,
ti(fun(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool))),type_definition(X1,X2)) = type_definition(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_163,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_164,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_165,plain,
ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_166,plain,
ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_167,plain,
( ti(fun(X1,fun(X1,bool)),equal_equal(X1)) = equal_equal(X1)
| ~ cl_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_168,plain,
ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_169,plain,
ti(fun(X1,fun(X1,bool)),induct_equal(X1)) = induct_equal(X1),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_170,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_171,hypothesis,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_172,plain,
( enum(sum_sum(X2,X1))
| ~ enum(X1)
| ~ enum(X2) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_173,plain,
( enum(fun(X2,X1))
| ~ enum(X1)
| ~ enum(X2) ),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_174,plain,
( cl_HOL_Oequal(fun(X2,X1))
| ~ cl_HOL_Oequal(X1)
| ~ enum(X2) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_175,plain,
( ~ hBOOL(hoare_1883395792gleton)
| ti(state,esk1_0) != ti(state,esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_176,hypothesis,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_177,plain,
cl_HOL_Oequal(sum_sum(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_178,plain,
( ti(state,X1) = ti(state,X2)
| hBOOL(hoare_1883395792gleton) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_179,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_180,negated_conjecture,
ti(state,X1) = ti(state,esk12_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_181,plain,
( fequal(X1) = equal_equal(X1)
| ~ cl_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_182,plain,
( equal_equal(X1) = fequal(X1)
| ~ cl_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_183,hypothesis,
ti(bool,hoare_1883395792gleton) = hoare_1883395792gleton,
inference(split_conjunct,[status(thm)],[tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res]),
[final] ).
cnf(i_0_184,plain,
ti(bool,induct_true) = induct_true,
inference(split_conjunct,[status(thm)],[tsy_c_HOL_Oinduct__true_res]),
[final] ).
cnf(i_0_185,plain,
ti(bool,induct_false) = induct_false,
inference(split_conjunct,[status(thm)],[tsy_c_HOL_Oinduct__false_res]),
[final] ).
cnf(i_0_186,plain,
cl_HOL_Oequal(hoare_509422987triple(X1)),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_187,plain,
~ hBOOL(induct_false),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_188,plain,
enum(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Enum_Oenum]),
[final] ).
cnf(i_0_189,hypothesis,
hBOOL(hoare_1883395792gleton),
inference(split_conjunct,[status(thm)],[conj_0]),
[final] ).
cnf(i_0_190,plain,
hBOOL(induct_true),
inference(split_conjunct,[status(thm)],[fact_27_induct__true__def]),
[final] ).
cnf(i_0_191,plain,
hBOOL(induct_true),
inference(split_conjunct,[status(thm)],[fact_26_induct__trueI]),
[final] ).
cnf(i_0_192,plain,
cl_HOL_Oequal(state),
inference(split_conjunct,[status(thm)],[arity_Com_Ostate___HOL_Oequal]),
[final] ).
cnf(i_0_193,plain,
cl_HOL_Oequal(com),
inference(split_conjunct,[status(thm)],[arity_Com_Ocom___HOL_Oequal]),
[final] ).
cnf(i_0_194,plain,
cl_HOL_Oequal(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___HOL_Oequal]),
[final] ).
cnf(i_0_195,axiom,
X1 = X1 ).
cnf(i_0_196,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_197,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_198,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_199,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_200,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_201,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_202,axiom,
( X1 != X2
| hoare_244953527triple(X1) = hoare_244953527triple(X2) ) ).
cnf(i_0_203,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_204,axiom,
( X1 != X2
| hoare_1580379338ep_set(X1) = hoare_1580379338ep_set(X2) ) ).
cnf(i_0_205,axiom,
( X1 != X2
| hoare_2037801986triple(X1) = hoare_2037801986triple(X2) ) ).
cnf(i_0_206,axiom,
( X1 != X2
| ti(X1,X3) = ti(X2,X3) ) ).
cnf(i_0_207,axiom,
( X1 != X2
| ti(X3,X1) = ti(X3,X2) ) ).
cnf(i_0_208,axiom,
( X1 != X2
| equal_equal(X1) = equal_equal(X2) ) ).
cnf(i_0_209,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_210,axiom,
( X1 != X2
| induct_equal(X1) = induct_equal(X2) ) ).
cnf(i_0_211,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_212,axiom,
( X1 != X2
| type_definition(X1,X3) = type_definition(X2,X3) ) ).
cnf(i_0_213,axiom,
( X1 != X2
| type_definition(X3,X1) = type_definition(X3,X2) ) ).
cnf(i_0_214,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_215,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_216,axiom,
( X1 != X2
| ~ cl_HOL_Oequal(X1)
| cl_HOL_Oequal(X2) ) ).
cnf(i_0_217,axiom,
( X1 != X2
| ~ enum(X1)
| enum(X2) ) ).
cnf(i_0_195_001,axiom,
X1 = X1 ).
cnf(i_0_196_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_197_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_198_004,axiom,
( X1 != X2
| hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).
cnf(i_0_199_005,axiom,
( X1 != X2
| hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).
cnf(i_0_200_006,axiom,
( X1 != X2
| hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).
cnf(i_0_201_007,axiom,
( X1 != X2
| hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).
cnf(i_0_202_008,axiom,
( X1 != X2
| hoare_244953527triple(X1) = hoare_244953527triple(X2) ) ).
cnf(i_0_203_009,axiom,
( X1 != X2
| collect(X1) = collect(X2) ) ).
cnf(i_0_204_010,axiom,
( X1 != X2
| hoare_1580379338ep_set(X1) = hoare_1580379338ep_set(X2) ) ).
cnf(i_0_205_011,axiom,
( X1 != X2
| hoare_2037801986triple(X1) = hoare_2037801986triple(X2) ) ).
cnf(i_0_206_012,axiom,
( X1 != X2
| ti(X1,X3) = ti(X2,X3) ) ).
cnf(i_0_207_013,axiom,
( X1 != X2
| ti(X3,X1) = ti(X3,X2) ) ).
cnf(i_0_208_014,axiom,
( X1 != X2
| equal_equal(X1) = equal_equal(X2) ) ).
cnf(i_0_209_015,axiom,
( X1 != X2
| fequal(X1) = fequal(X2) ) ).
cnf(i_0_210_016,axiom,
( X1 != X2
| induct_equal(X1) = induct_equal(X2) ) ).
cnf(i_0_211_017,axiom,
( X1 != X2
| undefined(X1) = undefined(X2) ) ).
cnf(i_0_212_018,axiom,
( X1 != X2
| type_definition(X1,X3) = type_definition(X2,X3) ) ).
cnf(i_0_213_019,axiom,
( X1 != X2
| type_definition(X3,X1) = type_definition(X3,X2) ) ).
cnf(i_0_214_020,axiom,
( X1 != X2
| member(X1) = member(X2) ) ).
cnf(i_0_215_021,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_216_022,axiom,
( X1 != X2
| ~ cl_HOL_Oequal(X1)
| cl_HOL_Oequal(X2) ) ).
cnf(i_0_217_023,axiom,
( X1 != X2
| ~ enum(X1)
| enum(X2) ) ).
cnf(i_0_218,plain,
( X1 = X1
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),fun(fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool)),X1),hAPP(fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),collect(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool)),hoare_1580379338ep_set(X2))))
| ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),fun(fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool)),X1),hAPP(fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),fun(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),bool),collect(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool)),hoare_1580379338ep_set(X2)))) ),
inference(equality_inference,[],[123]) ).
cnf(i_0_219,plain,
( ti(X1,X2) = ti(X1,X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),hAPP(fun(X4,X1),fun(fun(X1,X4),fun(fun(X1,bool),bool)),type_definition(X4,X1),X5),X6),X3)) ),
inference(equality_inference,[],[134]) ).
cnf(i_0_220,plain,
( hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X5))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(fun(X1,bool),bool)),type_definition(X2,X1),X6),X3),X5)) ),
inference(equality_inference,[],[135]) ).
cnf(i_0_221,plain,
( ti(X1,X2) = ti(X1,X2)
| ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),hAPP(fun(X1,X3),fun(fun(X3,X1),fun(fun(X3,bool),bool)),type_definition(X1,X3),X4),X5),X6)) ),
inference(equality_inference,[],[138]) ).
cnf(i_0_222,plain,
( hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(fun(X2,bool),bool)),type_definition(X1,X2),X3),X5),X6)) ),
inference(equality_inference,[],[140]) ).
cnf(i_0_223,plain,
X1 = X1,
inference(equality_inference,[],[143]) ).
cnf(i_0_224,plain,
ti(fun(X1,X2),X3) = ti(fun(X1,X2),X3),
inference(equality_inference,[],[150]) ).
cnf(i_0_225,plain,
hBOOL(hAPP(hoare_509422987triple(X1),bool,hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),equal_equal(hoare_509422987triple(X1)),X2),X2)),
inference(equality_inference,[],[151]) ).
cnf(i_0_226,plain,
( ~ cl_HOL_Oequal(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),equal_equal(X1),X2),X2)) ),
inference(equality_inference,[],[152]) ).
cnf(i_0_227,plain,
hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
inference(equality_inference,[],[153]) ).
cnf(i_0_228,plain,
hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),induct_equal(X1),X2),X2)),
inference(equality_inference,[],[154]) ).
cnf(i_0_229,plain,
ti(state,esk1_0) != ti(state,esk2_0),
inference(scs_inference,[],[i_0_189,i_0_175]) ).
cnf(i_0_230,plain,
ti(state,esk12_0) = ti(state,X1),
inference(scs_inference,[],[i_0_180,i_0_196]) ).
cnf(i_0_231,plain,
esk6_2(X1,X2) = hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),esk4_2(X1,esk6_2(X1,X2))),
inference(scs_inference,[],[i_0_180,i_0_131,i_0_196,i_0_127]) ).
cnf(i_0_232,plain,
( ~ hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),fun(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),X2),hAPP(fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),fun(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),bool),collect(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool)),hoare_1580379338ep_set(X1))))
| X2 = hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),esk4_2(X1,X2)) ),
inference(rename_variables,[],[i_0_127]) ).
cnf(i_0_233,plain,
ti(hoare_509422987triple(X1),X2) = X2,
inference(scs_inference,[],[i_0_180,i_0_163,i_0_131,i_0_196,i_0_127,i_0_143]) ).
cnf(i_0_234,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(rename_variables,[],[i_0_163]) ).
cnf(i_0_235,plain,
( hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X2) != hAPP(hoare_509422987triple(X1),fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_2037801986triple(X1),X3)
| X2 = X3 ),
inference(rename_variables,[],[i_0_143]) ).
cnf(i_0_236,plain,
ti(X1,ti(X1,undefined(X1))) = undefined(X1),
inference(scs_inference,[],[i_0_180,i_0_179,i_0_170,i_0_163,i_0_131,i_0_196,i_0_127,i_0_143,i_0_197]) ).
cnf(i_0_237,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(rename_variables,[],[i_0_179]) ).
cnf(i_0_238,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_239,plain,
hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2) != induct_false,
inference(scs_inference,[],[i_0_180,i_0_227,i_0_187,i_0_179,i_0_170,i_0_163,i_0_131,i_0_196,i_0_127,i_0_143,i_0_197,i_0_215]) ).
cnf(i_0_240,plain,
cl_HOL_Oequal(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,state))),
inference(scs_inference,[],[i_0_180,i_0_227,i_0_187,i_0_192,i_0_179,i_0_170,i_0_163,i_0_159,i_0_131,i_0_196,i_0_127,i_0_143,i_0_197,i_0_215,i_0_216]) ).
cnf(i_0_241,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_242,plain,
enum(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,bool))),
inference(scs_inference,[],[i_0_180,i_0_227,i_0_187,i_0_188,i_0_192,i_0_179,i_0_170,i_0_163,i_0_159,i_0_241,i_0_131,i_0_196,i_0_127,i_0_143,i_0_197,i_0_215,i_0_216,i_0_217]) ).
cnf(i_0_243,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_244,plain,
esk1_0 != esk2_0,
inference(scs_inference,[],[i_0_229,i_0_207]) ).
cnf(i_0_245,plain,
undefined(X1) = ti(X1,ti(X1,undefined(X1))),
inference(scs_inference,[],[i_0_236,i_0_229,i_0_207,i_0_196]) ).
cnf(i_0_246,plain,
ti(state,esk12_0) = undefined(state),
inference(scs_inference,[],[i_0_236,i_0_230,i_0_229,i_0_207,i_0_196,i_0_197]) ).
cnf(i_0_247,plain,
ti(X1,ti(X1,undefined(X1))) = undefined(X1),
inference(rename_variables,[],[i_0_236]) ).
cnf(i_0_248,plain,
ti(state,esk12_0) = ti(state,X1),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_249,plain,
hAPP(X1,bool,hAPP(X1,fun(X1,bool),induct_equal(X1),X2),X2) != induct_false,
inference(scs_inference,[],[i_0_236,i_0_228,i_0_230,i_0_229,i_0_187,i_0_207,i_0_196,i_0_197,i_0_215]) ).
cnf(i_0_250,plain,
cl_HOL_Oequal(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,state))))),
inference(scs_inference,[],[i_0_236,i_0_240,i_0_228,i_0_230,i_0_229,i_0_187,i_0_159,i_0_207,i_0_196,i_0_197,i_0_215,i_0_216]) ).
cnf(i_0_251,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_252,plain,
enum(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,bool))))),
inference(scs_inference,[],[i_0_236,i_0_240,i_0_242,i_0_228,i_0_230,i_0_229,i_0_187,i_0_159,i_0_251,i_0_207,i_0_196,i_0_197,i_0_215,i_0_216,i_0_217]) ).
cnf(i_0_253,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_254,plain,
undefined(state) = ti(state,esk12_0),
inference(scs_inference,[],[i_0_246,i_0_196]) ).
cnf(i_0_255,plain,
ti(state,X1) = undefined(state),
inference(scs_inference,[],[i_0_180,i_0_246,i_0_196,i_0_197]) ).
cnf(i_0_256,plain,
hAPP(hoare_509422987triple(X1),bool,hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),equal_equal(hoare_509422987triple(X1)),X2),X2) != induct_false,
inference(scs_inference,[],[i_0_180,i_0_225,i_0_246,i_0_187,i_0_196,i_0_197,i_0_215]) ).
cnf(i_0_257,plain,
cl_HOL_Oequal(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,hAPP(fun(node(sum_sum(com,fun(X3,fun(state,bool))),sum_sum(state,X3)),bool),hoare_509422987triple(X3),hoare_244953527triple(X3),esk6_2(X3,state))))))),
inference(scs_inference,[],[i_0_180,i_0_250,i_0_225,i_0_246,i_0_187,i_0_159,i_0_196,i_0_197,i_0_215,i_0_216]) ).
cnf(i_0_258,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_259,plain,
enum(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,hAPP(fun(node(sum_sum(com,fun(X3,fun(state,bool))),sum_sum(state,X3)),bool),hoare_509422987triple(X3),hoare_244953527triple(X3),esk6_2(X3,bool))))))),
inference(scs_inference,[],[i_0_180,i_0_250,i_0_252,i_0_225,i_0_246,i_0_187,i_0_159,i_0_258,i_0_196,i_0_197,i_0_215,i_0_216,i_0_217]) ).
cnf(i_0_260,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_261,plain,
undefined(state) = ti(state,X1),
inference(scs_inference,[],[i_0_255,i_0_196]) ).
cnf(i_0_262,plain,
hoare_1883395792gleton != induct_false,
inference(scs_inference,[],[i_0_255,i_0_189,i_0_187,i_0_196,i_0_215]) ).
cnf(i_0_263,plain,
cl_HOL_Oequal(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,hAPP(fun(node(sum_sum(com,fun(X3,fun(state,bool))),sum_sum(state,X3)),bool),hoare_509422987triple(X3),hoare_244953527triple(X3),esk6_2(X3,hAPP(fun(node(sum_sum(com,fun(X4,fun(state,bool))),sum_sum(state,X4)),bool),hoare_509422987triple(X4),hoare_244953527triple(X4),esk6_2(X4,state))))))))),
inference(scs_inference,[],[i_0_257,i_0_255,i_0_189,i_0_187,i_0_159,i_0_196,i_0_215,i_0_216]) ).
cnf(i_0_264,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_265,plain,
enum(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,hAPP(fun(node(sum_sum(com,fun(X3,fun(state,bool))),sum_sum(state,X3)),bool),hoare_509422987triple(X3),hoare_244953527triple(X3),esk6_2(X3,hAPP(fun(node(sum_sum(com,fun(X4,fun(state,bool))),sum_sum(state,X4)),bool),hoare_509422987triple(X4),hoare_244953527triple(X4),esk6_2(X4,bool))))))))),
inference(scs_inference,[],[i_0_257,i_0_259,i_0_255,i_0_189,i_0_187,i_0_159,i_0_264,i_0_196,i_0_215,i_0_216,i_0_217]) ).
cnf(i_0_266,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_267,plain,
ti(state,X1) = ti(state,ti(state,undefined(state))),
inference(scs_inference,[],[i_0_245,i_0_257,i_0_259,i_0_255,i_0_189,i_0_187,i_0_159,i_0_264,i_0_196,i_0_215,i_0_216,i_0_217,i_0_197]) ).
cnf(i_0_268,plain,
undefined(X1) = ti(X1,ti(X1,undefined(X1))),
inference(rename_variables,[],[i_0_245]) ).
cnf(i_0_269,plain,
ti(state,ti(state,undefined(state))) = ti(state,X1),
inference(scs_inference,[],[i_0_267,i_0_196]) ).
cnf(i_0_270,plain,
cl_HOL_Oequal(hAPP(fun(node(sum_sum(com,fun(X1,fun(state,bool))),sum_sum(state,X1)),bool),hoare_509422987triple(X1),hoare_244953527triple(X1),esk6_2(X1,com))),
inference(scs_inference,[],[i_0_267,i_0_193,i_0_159,i_0_196,i_0_216]) ).
cnf(i_0_271,plain,
X1 = hAPP(fun(node(sum_sum(com,fun(X2,fun(state,bool))),sum_sum(state,X2)),bool),hoare_509422987triple(X2),hoare_244953527triple(X2),esk6_2(X2,X1)),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_272,plain,
$false,
inference(scs_inference,[],[i_0_267,i_0_261,i_0_255,i_0_193,i_0_229,i_0_159,i_0_196,i_0_216,i_0_197]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW469+5 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 06:53:20 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.43/1.62 % Version : CSE_E---1.7
% 0.43/1.62 % Problem : theBenchmark.p
% 0.43/1.62 % SZS status Theorem for theBenchmark.p
% 0.43/1.62 % SZS output start CNFRefutation
% See solution above
% 0.53/1.76 % Total time : 1.274s
%------------------------------------------------------------------------------