TSTP Solution File: SEU117+1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 10:25:00 EDT 2022
% Result : Theorem 0.45s 0.64s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
input ).
fof(d5_finsub_1_0,plain,
! [A,B] :
( ~ preboolean(B)
| ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
inference(orientation,[status(thm)],[d5_finsub_1]) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
input ).
fof(t4_subset_0,plain,
! [A,B,C] :
( element(A,C)
| ~ ( in(A,B)
& element(B,powerset(C)) ) ),
inference(orientation,[status(thm)],[t4_subset]) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
input ).
fof(t3_subset_0,plain,
! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ),
inference(orientation,[status(thm)],[t3_subset]) ).
fof(t3_subset_1,plain,
! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) ),
inference(orientation,[status(thm)],[t3_subset]) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
input ).
fof(t1_subset_0,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(orientation,[status(thm)],[t1_subset]) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ),
input ).
fof(rc1_subset_1_0,plain,
! [A] :
( empty(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ),
inference(orientation,[status(thm)],[rc1_subset_1]) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
input ).
fof(fc1_subset_1_0,plain,
! [A] :
( ~ empty(powerset(A))
| $false ),
inference(orientation,[status(thm)],[fc1_subset_1]) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
input ).
fof(rc4_finset_1_0,plain,
! [A] :
( empty(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
inference(orientation,[status(thm)],[rc4_finset_1]) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
input ).
fof(rc3_finset_1_0,plain,
! [A] :
( empty(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
inference(orientation,[status(thm)],[rc3_finset_1]) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
input ).
fof(cc2_finset_1_0,plain,
! [A] :
( ~ finite(A)
| ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
inference(orientation,[status(thm)],[cc2_finset_1]) ).
fof(cc3_finsub_1,axiom,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
input ).
fof(cc3_finsub_1_0,plain,
! [A,B] :
( ~ element(B,finite_subsets(A))
| finite(B) ),
inference(orientation,[status(thm)],[cc3_finsub_1]) ).
fof(cc1_finsub_1,axiom,
! [A] :
( preboolean(A)
=> ( cup_closed(A)
& diff_closed(A) ) ),
input ).
fof(cc1_finsub_1_0,plain,
! [A] :
( ~ preboolean(A)
| ( cup_closed(A)
& diff_closed(A) ) ),
inference(orientation,[status(thm)],[cc1_finsub_1]) ).
fof(fc2_finsub_1,axiom,
! [A] :
( ~ empty(finite_subsets(A))
& cup_closed(finite_subsets(A))
& diff_closed(finite_subsets(A))
& preboolean(finite_subsets(A)) ),
input ).
fof(fc2_finsub_1_0,plain,
! [A] :
( ~ empty(finite_subsets(A))
| $false ),
inference(orientation,[status(thm)],[fc2_finsub_1]) ).
fof(fc2_finsub_1_1,plain,
! [A] :
( cup_closed(finite_subsets(A))
| $false ),
inference(orientation,[status(thm)],[fc2_finsub_1]) ).
fof(fc2_finsub_1_2,plain,
! [A] :
( diff_closed(finite_subsets(A))
| $false ),
inference(orientation,[status(thm)],[fc2_finsub_1]) ).
fof(fc2_finsub_1_3,plain,
! [A] :
( preboolean(finite_subsets(A))
| $false ),
inference(orientation,[status(thm)],[fc2_finsub_1]) ).
fof(fc1_finsub_1,axiom,
! [A] :
( ~ empty(powerset(A))
& cup_closed(powerset(A))
& diff_closed(powerset(A))
& preboolean(powerset(A)) ),
input ).
fof(fc1_finsub_1_0,plain,
! [A] :
( ~ empty(powerset(A))
| $false ),
inference(orientation,[status(thm)],[fc1_finsub_1]) ).
fof(fc1_finsub_1_1,plain,
! [A] :
( cup_closed(powerset(A))
| $false ),
inference(orientation,[status(thm)],[fc1_finsub_1]) ).
fof(fc1_finsub_1_2,plain,
! [A] :
( diff_closed(powerset(A))
| $false ),
inference(orientation,[status(thm)],[fc1_finsub_1]) ).
fof(fc1_finsub_1_3,plain,
! [A] :
( preboolean(powerset(A))
| $false ),
inference(orientation,[status(thm)],[fc1_finsub_1]) ).
fof(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)),
input ).
fof(dt_k5_finsub_1_0,plain,
! [A] :
( preboolean(finite_subsets(A))
| $false ),
inference(orientation,[status(thm)],[dt_k5_finsub_1]) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
input ).
fof(antisymmetry_r2_hidden_0,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(orientation,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
input ).
fof(reflexivity_r1_tarski_0,plain,
! [A] :
( subset(A,A)
| $false ),
inference(orientation,[status(thm)],[reflexivity_r1_tarski]) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
input ).
fof(t6_boole_0,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(orientation,[status(thm)],[t6_boole]) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
input ).
fof(t2_subset_0,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(orientation,[status(thm)],[t2_subset]) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
input ).
fof(cc1_finset_1_0,plain,
! [A] :
( ~ empty(A)
| finite(A) ),
inference(orientation,[status(thm)],[cc1_finset_1]) ).
fof(cc2_finsub_1,axiom,
! [A] :
( ( cup_closed(A)
& diff_closed(A) )
=> preboolean(A) ),
input ).
fof(cc2_finsub_1_0,plain,
! [A] :
( preboolean(A)
| ~ ( cup_closed(A)
& diff_closed(A) ) ),
inference(orientation,[status(thm)],[cc2_finsub_1]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
input ).
fof(fc1_xboole_0_0,plain,
( empty(empty_set)
| $false ),
inference(orientation,[status(thm)],[fc1_xboole_0]) ).
fof(def_lhs_atom1,axiom,
( lhs_atom1
<=> empty(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
( lhs_atom1
| $false ),
inference(fold_definition,[status(thm)],[fc1_xboole_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [A] :
( lhs_atom2(A)
<=> preboolean(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A] :
( lhs_atom2(A)
| ~ ( cup_closed(A)
& diff_closed(A) ) ),
inference(fold_definition,[status(thm)],[cc2_finsub_1_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [A] :
( lhs_atom3(A)
<=> ~ empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A] :
( lhs_atom3(A)
| finite(A) ),
inference(fold_definition,[status(thm)],[cc1_finset_1_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [B,A] :
( lhs_atom4(B,A)
<=> ~ element(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [A,B] :
( lhs_atom4(B,A)
| empty(B)
| in(A,B) ),
inference(fold_definition,[status(thm)],[t2_subset_0,def_lhs_atom4]) ).
fof(to_be_clausified_4,plain,
! [A] :
( lhs_atom3(A)
| A = empty_set ),
inference(fold_definition,[status(thm)],[t6_boole_0,def_lhs_atom3]) ).
fof(def_lhs_atom5,axiom,
! [A] :
( lhs_atom5(A)
<=> subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [A] :
( lhs_atom5(A)
| $false ),
inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [B,A] :
( lhs_atom6(B,A)
<=> ~ in(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A,B] :
( lhs_atom6(B,A)
| ~ in(B,A) ),
inference(fold_definition,[status(thm)],[antisymmetry_r2_hidden_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [A] :
( lhs_atom7(A)
<=> preboolean(finite_subsets(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A] :
( lhs_atom7(A)
| $false ),
inference(fold_definition,[status(thm)],[dt_k5_finsub_1_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [A] :
( lhs_atom8(A)
<=> preboolean(powerset(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [A] :
( lhs_atom8(A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_finsub_1_3,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [A] :
( lhs_atom9(A)
<=> diff_closed(powerset(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [A] :
( lhs_atom9(A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_finsub_1_2,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [A] :
( lhs_atom10(A)
<=> cup_closed(powerset(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [A] :
( lhs_atom10(A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_finsub_1_1,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [A] :
( lhs_atom11(A)
<=> ~ empty(powerset(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [A] :
( lhs_atom11(A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_finsub_1_0,def_lhs_atom11]) ).
fof(to_be_clausified_12,plain,
! [A] :
( lhs_atom7(A)
| $false ),
inference(fold_definition,[status(thm)],[fc2_finsub_1_3,def_lhs_atom7]) ).
fof(def_lhs_atom12,axiom,
! [A] :
( lhs_atom12(A)
<=> diff_closed(finite_subsets(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [A] :
( lhs_atom12(A)
| $false ),
inference(fold_definition,[status(thm)],[fc2_finsub_1_2,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [A] :
( lhs_atom13(A)
<=> cup_closed(finite_subsets(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [A] :
( lhs_atom13(A)
| $false ),
inference(fold_definition,[status(thm)],[fc2_finsub_1_1,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [A] :
( lhs_atom14(A)
<=> ~ empty(finite_subsets(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [A] :
( lhs_atom14(A)
| $false ),
inference(fold_definition,[status(thm)],[fc2_finsub_1_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [A] :
( lhs_atom15(A)
<=> ~ preboolean(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [A] :
( lhs_atom15(A)
| ( cup_closed(A)
& diff_closed(A) ) ),
inference(fold_definition,[status(thm)],[cc1_finsub_1_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [B,A] :
( lhs_atom16(B,A)
<=> ~ element(B,finite_subsets(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [A,B] :
( lhs_atom16(B,A)
| finite(B) ),
inference(fold_definition,[status(thm)],[cc3_finsub_1_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [A] :
( lhs_atom17(A)
<=> ~ finite(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [A] :
( lhs_atom17(A)
| ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
inference(fold_definition,[status(thm)],[cc2_finset_1_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [A] :
( lhs_atom18(A)
<=> empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [A] :
( lhs_atom18(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
inference(fold_definition,[status(thm)],[rc3_finset_1_0,def_lhs_atom18]) ).
fof(to_be_clausified_20,plain,
! [A] :
( lhs_atom18(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ),
inference(fold_definition,[status(thm)],[rc4_finset_1_0,def_lhs_atom18]) ).
fof(to_be_clausified_21,plain,
! [A] :
( lhs_atom11(A)
| $false ),
inference(fold_definition,[status(thm)],[fc1_subset_1_0,def_lhs_atom11]) ).
fof(to_be_clausified_22,plain,
! [A] :
( lhs_atom18(A)
| ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ),
inference(fold_definition,[status(thm)],[rc1_subset_1_0,def_lhs_atom18]) ).
fof(to_be_clausified_23,plain,
! [A,B] :
( lhs_atom6(B,A)
| element(A,B) ),
inference(fold_definition,[status(thm)],[t1_subset_0,def_lhs_atom6]) ).
fof(def_lhs_atom19,axiom,
! [B,A] :
( lhs_atom19(B,A)
<=> ~ element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [A,B] :
( lhs_atom19(B,A)
| subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_1,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [B,A] :
( lhs_atom20(B,A)
<=> element(A,powerset(B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [A,B] :
( lhs_atom20(B,A)
| ~ subset(A,B) ),
inference(fold_definition,[status(thm)],[t3_subset_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [C,A] :
( lhs_atom21(C,A)
<=> element(A,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [A,B,C] :
( lhs_atom21(C,A)
| ~ ( in(A,B)
& element(B,powerset(C)) ) ),
inference(fold_definition,[status(thm)],[t4_subset_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [B] :
( lhs_atom22(B)
<=> ~ preboolean(B) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [A,B] :
( lhs_atom22(B)
| ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
inference(fold_definition,[status(thm)],[d5_finsub_1_0,def_lhs_atom22]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X2,X1] :
( lhs_atom22(X2)
| ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_1,axiom,
! [X3,X2,X1] :
( lhs_atom21(X3,X1)
| ~ ( in(X1,X2)
& element(X2,powerset(X3)) ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_2,axiom,
! [X1] :
( lhs_atom17(X1)
| ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_3,axiom,
! [X2,X1] :
( lhs_atom20(X2,X1)
| ~ subset(X1,X2) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_4,axiom,
! [X2,X1] :
( lhs_atom6(X2,X1)
| ~ in(X2,X1) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_5,axiom,
! [X2,X1] :
( lhs_atom4(X2,X1)
| empty(X2)
| in(X1,X2) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_6,axiom,
! [X1] :
( lhs_atom18(X1)
| ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_7,axiom,
! [X1] :
( lhs_atom18(X1)
| ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_8,axiom,
! [X1] :
( lhs_atom18(X1)
| ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_9,axiom,
! [X2,X1] :
( lhs_atom19(X2,X1)
| subset(X1,X2) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_10,axiom,
! [X2,X1] :
( lhs_atom6(X2,X1)
| element(X1,X2) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_11,axiom,
! [X2,X1] :
( lhs_atom16(X2,X1)
| finite(X2) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_12,axiom,
! [X1] :
( lhs_atom2(X1)
| ~ ( cup_closed(X1)
& diff_closed(X1) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_13,axiom,
! [X1] :
( lhs_atom15(X1)
| ( cup_closed(X1)
& diff_closed(X1) ) ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_14,axiom,
! [X1] :
( lhs_atom3(X1)
| finite(X1) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_15,axiom,
! [X1] :
( lhs_atom3(X1)
| X1 = empty_set ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_16,axiom,
! [X1] :
( lhs_atom11(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_17,axiom,
! [X1] :
( lhs_atom14(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_18,axiom,
! [X1] :
( lhs_atom13(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_19,axiom,
! [X1] :
( lhs_atom12(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_20,axiom,
! [X1] :
( lhs_atom7(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_21,axiom,
! [X1] :
( lhs_atom11(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_22,axiom,
! [X1] :
( lhs_atom10(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_23,axiom,
! [X1] :
( lhs_atom9(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_24,axiom,
! [X1] :
( lhs_atom8(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_25,axiom,
! [X1] :
( lhs_atom7(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_26,axiom,
! [X1] :
( lhs_atom5(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_27,axiom,
( lhs_atom1
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_28,axiom,
! [X2,X1] :
( lhs_atom22(X2)
| ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
c_0_0 ).
fof(c_0_29,axiom,
! [X3,X2,X1] :
( lhs_atom21(X3,X1)
| ~ ( in(X1,X2)
& element(X2,powerset(X3)) ) ),
c_0_1 ).
fof(c_0_30,axiom,
! [X1] :
( lhs_atom17(X1)
| ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
c_0_2 ).
fof(c_0_31,plain,
! [X2,X1] :
( lhs_atom20(X2,X1)
| ~ subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_32,plain,
! [X2,X1] :
( lhs_atom6(X2,X1)
| ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_33,axiom,
! [X2,X1] :
( lhs_atom4(X2,X1)
| empty(X2)
| in(X1,X2) ),
c_0_5 ).
fof(c_0_34,plain,
! [X1] :
( lhs_atom18(X1)
| ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_35,plain,
! [X1] :
( lhs_atom18(X1)
| ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_36,plain,
! [X1] :
( lhs_atom18(X1)
| ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_37,axiom,
! [X2,X1] :
( lhs_atom19(X2,X1)
| subset(X1,X2) ),
c_0_9 ).
fof(c_0_38,axiom,
! [X2,X1] :
( lhs_atom6(X2,X1)
| element(X1,X2) ),
c_0_10 ).
fof(c_0_39,axiom,
! [X2,X1] :
( lhs_atom16(X2,X1)
| finite(X2) ),
c_0_11 ).
fof(c_0_40,axiom,
! [X1] :
( lhs_atom2(X1)
| ~ ( cup_closed(X1)
& diff_closed(X1) ) ),
c_0_12 ).
fof(c_0_41,axiom,
! [X1] :
( lhs_atom15(X1)
| ( cup_closed(X1)
& diff_closed(X1) ) ),
c_0_13 ).
fof(c_0_42,axiom,
! [X1] :
( lhs_atom3(X1)
| finite(X1) ),
c_0_14 ).
fof(c_0_43,axiom,
! [X1] :
( lhs_atom3(X1)
| X1 = empty_set ),
c_0_15 ).
fof(c_0_44,plain,
! [X1] : lhs_atom11(X1),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_45,plain,
! [X1] : lhs_atom14(X1),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_46,plain,
! [X1] : lhs_atom13(X1),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_47,plain,
! [X1] : lhs_atom12(X1),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_48,plain,
! [X1] : lhs_atom7(X1),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_49,plain,
! [X1] : lhs_atom11(X1),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_50,plain,
! [X1] : lhs_atom10(X1),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_51,plain,
! [X1] : lhs_atom9(X1),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_52,plain,
! [X1] : lhs_atom8(X1),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_53,plain,
! [X1] : lhs_atom7(X1),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_54,plain,
! [X1] : lhs_atom5(X1),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_55,plain,
lhs_atom1,
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_56,plain,
! [X4,X5,X6,X7,X8] :
( ( subset(X6,X5)
| ~ in(X6,X4)
| X4 != finite_subsets(X5)
| lhs_atom22(X4) )
& ( finite(X6)
| ~ in(X6,X4)
| X4 != finite_subsets(X5)
| lhs_atom22(X4) )
& ( ~ subset(X7,X5)
| ~ finite(X7)
| in(X7,X4)
| X4 != finite_subsets(X5)
| lhs_atom22(X4) )
& ( ~ in(esk4_2(X4,X8),X4)
| ~ subset(esk4_2(X4,X8),X8)
| ~ finite(esk4_2(X4,X8))
| X4 = finite_subsets(X8)
| lhs_atom22(X4) )
& ( subset(esk4_2(X4,X8),X8)
| in(esk4_2(X4,X8),X4)
| X4 = finite_subsets(X8)
| lhs_atom22(X4) )
& ( finite(esk4_2(X4,X8))
| in(esk4_2(X4,X8),X4)
| X4 = finite_subsets(X8)
| lhs_atom22(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])])]) ).
fof(c_0_57,plain,
! [X4,X5,X6] :
( lhs_atom21(X4,X6)
| ~ in(X6,X5)
| ~ element(X5,powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
fof(c_0_58,plain,
! [X3,X4] :
( lhs_atom17(X3)
| ~ element(X4,powerset(X3))
| finite(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
fof(c_0_59,plain,
! [X3,X4] :
( lhs_atom20(X3,X4)
| ~ subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
fof(c_0_60,plain,
! [X3,X4] :
( lhs_atom6(X3,X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_32]) ).
fof(c_0_61,plain,
! [X3,X4] :
( lhs_atom4(X3,X4)
| empty(X3)
| in(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_33]) ).
fof(c_0_62,plain,
! [X3] :
( ( element(esk3_1(X3),powerset(X3))
| lhs_atom18(X3) )
& ( ~ empty(esk3_1(X3))
| lhs_atom18(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_34])])]) ).
fof(c_0_63,plain,
! [X3] :
( ( element(esk2_1(X3),powerset(X3))
| lhs_atom18(X3) )
& ( ~ empty(esk2_1(X3))
| lhs_atom18(X3) )
& ( finite(esk2_1(X3))
| lhs_atom18(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_35])])]) ).
fof(c_0_64,plain,
! [X3] :
( ( element(esk1_1(X3),powerset(X3))
| lhs_atom18(X3) )
& ( ~ empty(esk1_1(X3))
| lhs_atom18(X3) )
& ( finite(esk1_1(X3))
| lhs_atom18(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_36])])]) ).
fof(c_0_65,plain,
! [X3,X4] :
( lhs_atom19(X3,X4)
| subset(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_37]) ).
fof(c_0_66,plain,
! [X3,X4] :
( lhs_atom6(X3,X4)
| element(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
fof(c_0_67,plain,
! [X3,X4] :
( lhs_atom16(X3,X4)
| finite(X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_39])])]) ).
fof(c_0_68,plain,
! [X2] :
( lhs_atom2(X2)
| ~ cup_closed(X2)
| ~ diff_closed(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])]) ).
fof(c_0_69,plain,
! [X2] :
( ( cup_closed(X2)
| lhs_atom15(X2) )
& ( diff_closed(X2)
| lhs_atom15(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_41])]) ).
fof(c_0_70,plain,
! [X2] :
( lhs_atom3(X2)
| finite(X2) ),
inference(variable_rename,[status(thm)],[c_0_42]) ).
fof(c_0_71,plain,
! [X2] :
( lhs_atom3(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[c_0_43]) ).
fof(c_0_72,plain,
! [X2] : lhs_atom11(X2),
inference(variable_rename,[status(thm)],[c_0_44]) ).
fof(c_0_73,plain,
! [X2] : lhs_atom14(X2),
inference(variable_rename,[status(thm)],[c_0_45]) ).
fof(c_0_74,plain,
! [X2] : lhs_atom13(X2),
inference(variable_rename,[status(thm)],[c_0_46]) ).
fof(c_0_75,plain,
! [X2] : lhs_atom12(X2),
inference(variable_rename,[status(thm)],[c_0_47]) ).
fof(c_0_76,plain,
! [X2] : lhs_atom7(X2),
inference(variable_rename,[status(thm)],[c_0_48]) ).
fof(c_0_77,plain,
! [X2] : lhs_atom11(X2),
inference(variable_rename,[status(thm)],[c_0_49]) ).
fof(c_0_78,plain,
! [X2] : lhs_atom10(X2),
inference(variable_rename,[status(thm)],[c_0_50]) ).
fof(c_0_79,plain,
! [X2] : lhs_atom9(X2),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_80,plain,
! [X2] : lhs_atom8(X2),
inference(variable_rename,[status(thm)],[c_0_52]) ).
fof(c_0_81,plain,
! [X2] : lhs_atom7(X2),
inference(variable_rename,[status(thm)],[c_0_53]) ).
fof(c_0_82,plain,
! [X2] : lhs_atom5(X2),
inference(variable_rename,[status(thm)],[c_0_54]) ).
fof(c_0_83,plain,
lhs_atom1,
c_0_55 ).
cnf(c_0_84,plain,
( lhs_atom22(X1)
| X1 = finite_subsets(X2)
| ~ finite(esk4_2(X1,X2))
| ~ subset(esk4_2(X1,X2),X2)
| ~ in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_85,plain,
( lhs_atom22(X1)
| X1 = finite_subsets(X2)
| in(esk4_2(X1,X2),X1)
| subset(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_86,plain,
( lhs_atom22(X1)
| X1 = finite_subsets(X2)
| in(esk4_2(X1,X2),X1)
| finite(esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_87,plain,
( lhs_atom21(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_88,plain,
( lhs_atom22(X1)
| in(X3,X1)
| X1 != finite_subsets(X2)
| ~ finite(X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_89,plain,
( lhs_atom22(X1)
| subset(X3,X2)
| X1 != finite_subsets(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_90,plain,
( finite(X1)
| lhs_atom17(X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_91,plain,
( lhs_atom22(X1)
| finite(X3)
| X1 != finite_subsets(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_92,plain,
( lhs_atom20(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_93,plain,
( lhs_atom6(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_94,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_95,plain,
( lhs_atom18(X1)
| element(esk3_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_96,plain,
( lhs_atom18(X1)
| element(esk2_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_97,plain,
( lhs_atom18(X1)
| element(esk1_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_98,plain,
( subset(X1,X2)
| lhs_atom19(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_99,plain,
( element(X1,X2)
| lhs_atom6(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_100,plain,
( lhs_atom18(X1)
| ~ empty(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_101,plain,
( lhs_atom18(X1)
| ~ empty(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_102,plain,
( lhs_atom18(X1)
| ~ empty(esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_103,plain,
( finite(X1)
| lhs_atom16(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_104,plain,
( lhs_atom2(X1)
| ~ diff_closed(X1)
| ~ cup_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_105,plain,
( lhs_atom18(X1)
| finite(esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_106,plain,
( lhs_atom18(X1)
| finite(esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_107,plain,
( lhs_atom15(X1)
| cup_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_108,plain,
( lhs_atom15(X1)
| diff_closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_109,plain,
( finite(X1)
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_110,plain,
( X1 = empty_set
| lhs_atom3(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_111,plain,
lhs_atom11(X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_112,plain,
lhs_atom14(X1),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_113,plain,
lhs_atom13(X1),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_114,plain,
lhs_atom12(X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_115,plain,
lhs_atom7(X1),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_116,plain,
lhs_atom11(X1),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_117,plain,
lhs_atom10(X1),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_118,plain,
lhs_atom9(X1),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_119,plain,
lhs_atom8(X1),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_120,plain,
lhs_atom7(X1),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_121,plain,
lhs_atom5(X1),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_122,plain,
lhs_atom1,
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_123,plain,
( lhs_atom22(X1)
| X1 = finite_subsets(X2)
| ~ finite(esk4_2(X1,X2))
| ~ subset(esk4_2(X1,X2),X2)
| ~ in(esk4_2(X1,X2),X1) ),
c_0_84,
[final] ).
cnf(c_0_124,plain,
( lhs_atom22(X1)
| X1 = finite_subsets(X2)
| in(esk4_2(X1,X2),X1)
| subset(esk4_2(X1,X2),X2) ),
c_0_85,
[final] ).
cnf(c_0_125,plain,
( lhs_atom22(X1)
| X1 = finite_subsets(X2)
| in(esk4_2(X1,X2),X1)
| finite(esk4_2(X1,X2)) ),
c_0_86,
[final] ).
cnf(c_0_126,plain,
( lhs_atom21(X2,X3)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
c_0_87,
[final] ).
cnf(c_0_127,plain,
( lhs_atom22(X1)
| in(X3,X1)
| X1 != finite_subsets(X2)
| ~ finite(X3)
| ~ subset(X3,X2) ),
c_0_88,
[final] ).
cnf(c_0_128,plain,
( lhs_atom22(X1)
| subset(X3,X2)
| X1 != finite_subsets(X2)
| ~ in(X3,X1) ),
c_0_89,
[final] ).
cnf(c_0_129,plain,
( finite(X1)
| lhs_atom17(X2)
| ~ element(X1,powerset(X2)) ),
c_0_90,
[final] ).
cnf(c_0_130,plain,
( lhs_atom22(X1)
| finite(X3)
| X1 != finite_subsets(X2)
| ~ in(X3,X1) ),
c_0_91,
[final] ).
cnf(c_0_131,plain,
( lhs_atom20(X2,X1)
| ~ subset(X1,X2) ),
c_0_92,
[final] ).
cnf(c_0_132,plain,
( lhs_atom6(X1,X2)
| ~ in(X1,X2) ),
c_0_93,
[final] ).
cnf(c_0_133,plain,
( in(X1,X2)
| empty(X2)
| lhs_atom4(X2,X1) ),
c_0_94,
[final] ).
cnf(c_0_134,plain,
( lhs_atom18(X1)
| element(esk3_1(X1),powerset(X1)) ),
c_0_95,
[final] ).
cnf(c_0_135,plain,
( lhs_atom18(X1)
| element(esk2_1(X1),powerset(X1)) ),
c_0_96,
[final] ).
cnf(c_0_136,plain,
( lhs_atom18(X1)
| element(esk1_1(X1),powerset(X1)) ),
c_0_97,
[final] ).
cnf(c_0_137,plain,
( subset(X1,X2)
| lhs_atom19(X2,X1) ),
c_0_98,
[final] ).
cnf(c_0_138,plain,
( element(X1,X2)
| lhs_atom6(X2,X1) ),
c_0_99,
[final] ).
cnf(c_0_139,plain,
( lhs_atom18(X1)
| ~ empty(esk3_1(X1)) ),
c_0_100,
[final] ).
cnf(c_0_140,plain,
( lhs_atom18(X1)
| ~ empty(esk2_1(X1)) ),
c_0_101,
[final] ).
cnf(c_0_141,plain,
( lhs_atom18(X1)
| ~ empty(esk1_1(X1)) ),
c_0_102,
[final] ).
cnf(c_0_142,plain,
( finite(X1)
| lhs_atom16(X1,X2) ),
c_0_103,
[final] ).
cnf(c_0_143,plain,
( lhs_atom2(X1)
| ~ diff_closed(X1)
| ~ cup_closed(X1) ),
c_0_104,
[final] ).
cnf(c_0_144,plain,
( lhs_atom18(X1)
| finite(esk2_1(X1)) ),
c_0_105,
[final] ).
cnf(c_0_145,plain,
( lhs_atom18(X1)
| finite(esk1_1(X1)) ),
c_0_106,
[final] ).
cnf(c_0_146,plain,
( lhs_atom15(X1)
| cup_closed(X1) ),
c_0_107,
[final] ).
cnf(c_0_147,plain,
( lhs_atom15(X1)
| diff_closed(X1) ),
c_0_108,
[final] ).
cnf(c_0_148,plain,
( finite(X1)
| lhs_atom3(X1) ),
c_0_109,
[final] ).
cnf(c_0_149,plain,
( X1 = empty_set
| lhs_atom3(X1) ),
c_0_110,
[final] ).
cnf(c_0_150,plain,
lhs_atom11(X1),
c_0_111,
[final] ).
cnf(c_0_151,plain,
lhs_atom14(X1),
c_0_112,
[final] ).
cnf(c_0_152,plain,
lhs_atom13(X1),
c_0_113,
[final] ).
cnf(c_0_153,plain,
lhs_atom12(X1),
c_0_114,
[final] ).
cnf(c_0_154,plain,
lhs_atom7(X1),
c_0_115,
[final] ).
cnf(c_0_155,plain,
lhs_atom11(X1),
c_0_116,
[final] ).
cnf(c_0_156,plain,
lhs_atom10(X1),
c_0_117,
[final] ).
cnf(c_0_157,plain,
lhs_atom9(X1),
c_0_118,
[final] ).
cnf(c_0_158,plain,
lhs_atom8(X1),
c_0_119,
[final] ).
cnf(c_0_159,plain,
lhs_atom7(X1),
c_0_120,
[final] ).
cnf(c_0_160,plain,
lhs_atom5(X1),
c_0_121,
[final] ).
cnf(c_0_161,plain,
lhs_atom1,
c_0_122,
[final] ).
% End CNF derivation
cnf(c_0_123_0,axiom,
( ~ preboolean(X1)
| X1 = finite_subsets(X2)
| ~ finite(sk1_esk4_2(X1,X2))
| ~ subset(sk1_esk4_2(X1,X2),X2)
| ~ in(sk1_esk4_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_123,def_lhs_atom22]) ).
cnf(c_0_124_0,axiom,
( ~ preboolean(X1)
| X1 = finite_subsets(X2)
| in(sk1_esk4_2(X1,X2),X1)
| subset(sk1_esk4_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_124,def_lhs_atom22]) ).
cnf(c_0_125_0,axiom,
( ~ preboolean(X1)
| X1 = finite_subsets(X2)
| in(sk1_esk4_2(X1,X2),X1)
| finite(sk1_esk4_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_125,def_lhs_atom22]) ).
cnf(c_0_126_0,axiom,
( element(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_126,def_lhs_atom21]) ).
cnf(c_0_127_0,axiom,
( ~ preboolean(X1)
| in(X3,X1)
| X1 != finite_subsets(X2)
| ~ finite(X3)
| ~ subset(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_127,def_lhs_atom22]) ).
cnf(c_0_128_0,axiom,
( ~ preboolean(X1)
| subset(X3,X2)
| X1 != finite_subsets(X2)
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_128,def_lhs_atom22]) ).
cnf(c_0_129_0,axiom,
( ~ finite(X2)
| finite(X1)
| ~ element(X1,powerset(X2)) ),
inference(unfold_definition,[status(thm)],[c_0_129,def_lhs_atom17]) ).
cnf(c_0_130_0,axiom,
( ~ preboolean(X1)
| finite(X3)
| X1 != finite_subsets(X2)
| ~ in(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_130,def_lhs_atom22]) ).
cnf(c_0_131_0,axiom,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_131,def_lhs_atom20]) ).
cnf(c_0_132_0,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_132,def_lhs_atom6]) ).
cnf(c_0_133_0,axiom,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(unfold_definition,[status(thm)],[c_0_133,def_lhs_atom4]) ).
cnf(c_0_134_0,axiom,
( empty(X1)
| element(sk1_esk3_1(X1),powerset(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_134,def_lhs_atom18]) ).
cnf(c_0_135_0,axiom,
( empty(X1)
| element(sk1_esk2_1(X1),powerset(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_135,def_lhs_atom18]) ).
cnf(c_0_136_0,axiom,
( empty(X1)
| element(sk1_esk1_1(X1),powerset(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_136,def_lhs_atom18]) ).
cnf(c_0_137_0,axiom,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_137,def_lhs_atom19]) ).
cnf(c_0_138_0,axiom,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_138,def_lhs_atom6]) ).
cnf(c_0_139_0,axiom,
( empty(X1)
| ~ empty(sk1_esk3_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_139,def_lhs_atom18]) ).
cnf(c_0_140_0,axiom,
( empty(X1)
| ~ empty(sk1_esk2_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_140,def_lhs_atom18]) ).
cnf(c_0_141_0,axiom,
( empty(X1)
| ~ empty(sk1_esk1_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_141,def_lhs_atom18]) ).
cnf(c_0_142_0,axiom,
( ~ element(X1,finite_subsets(X2))
| finite(X1) ),
inference(unfold_definition,[status(thm)],[c_0_142,def_lhs_atom16]) ).
cnf(c_0_143_0,axiom,
( preboolean(X1)
| ~ diff_closed(X1)
| ~ cup_closed(X1) ),
inference(unfold_definition,[status(thm)],[c_0_143,def_lhs_atom2]) ).
cnf(c_0_144_0,axiom,
( empty(X1)
| finite(sk1_esk2_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_144,def_lhs_atom18]) ).
cnf(c_0_145_0,axiom,
( empty(X1)
| finite(sk1_esk1_1(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_145,def_lhs_atom18]) ).
cnf(c_0_146_0,axiom,
( ~ preboolean(X1)
| cup_closed(X1) ),
inference(unfold_definition,[status(thm)],[c_0_146,def_lhs_atom15]) ).
cnf(c_0_147_0,axiom,
( ~ preboolean(X1)
| diff_closed(X1) ),
inference(unfold_definition,[status(thm)],[c_0_147,def_lhs_atom15]) ).
cnf(c_0_148_0,axiom,
( ~ empty(X1)
| finite(X1) ),
inference(unfold_definition,[status(thm)],[c_0_148,def_lhs_atom3]) ).
cnf(c_0_149_0,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_149,def_lhs_atom3]) ).
cnf(c_0_150_0,axiom,
~ empty(powerset(X1)),
inference(unfold_definition,[status(thm)],[c_0_150,def_lhs_atom11]) ).
cnf(c_0_151_0,axiom,
~ empty(finite_subsets(X1)),
inference(unfold_definition,[status(thm)],[c_0_151,def_lhs_atom14]) ).
cnf(c_0_152_0,axiom,
cup_closed(finite_subsets(X1)),
inference(unfold_definition,[status(thm)],[c_0_152,def_lhs_atom13]) ).
cnf(c_0_153_0,axiom,
diff_closed(finite_subsets(X1)),
inference(unfold_definition,[status(thm)],[c_0_153,def_lhs_atom12]) ).
cnf(c_0_154_0,axiom,
preboolean(finite_subsets(X1)),
inference(unfold_definition,[status(thm)],[c_0_154,def_lhs_atom7]) ).
cnf(c_0_155_0,axiom,
~ empty(powerset(X1)),
inference(unfold_definition,[status(thm)],[c_0_155,def_lhs_atom11]) ).
cnf(c_0_156_0,axiom,
cup_closed(powerset(X1)),
inference(unfold_definition,[status(thm)],[c_0_156,def_lhs_atom10]) ).
cnf(c_0_157_0,axiom,
diff_closed(powerset(X1)),
inference(unfold_definition,[status(thm)],[c_0_157,def_lhs_atom9]) ).
cnf(c_0_158_0,axiom,
preboolean(powerset(X1)),
inference(unfold_definition,[status(thm)],[c_0_158,def_lhs_atom8]) ).
cnf(c_0_159_0,axiom,
preboolean(finite_subsets(X1)),
inference(unfold_definition,[status(thm)],[c_0_159,def_lhs_atom7]) ).
cnf(c_0_160_0,axiom,
subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_160,def_lhs_atom5]) ).
cnf(c_0_161_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_161,def_lhs_atom1]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('<stdin>',t5_subset) ).
fof(c_0_1_002,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_2_003,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('<stdin>',rc2_finset_1) ).
fof(c_0_3_004,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('<stdin>',rc2_subset_1) ).
fof(c_0_4_005,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('<stdin>',existence_m1_subset_1) ).
fof(c_0_5_006,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_6_007,axiom,
? [X1] :
( ~ empty(X1)
& cup_closed(X1)
& cap_closed(X1)
& diff_closed(X1)
& preboolean(X1) ),
file('<stdin>',rc1_finsub_1) ).
fof(c_0_7_008,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('<stdin>',rc1_finset_1) ).
fof(c_0_8_009,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_9_010,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_10_011,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
c_0_0 ).
fof(c_0_11_012,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_1 ).
fof(c_0_12_013,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
c_0_2 ).
fof(c_0_13_014,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
c_0_3 ).
fof(c_0_14_015,axiom,
! [X1] :
? [X2] : element(X2,X1),
c_0_4 ).
fof(c_0_15_016,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_5 ).
fof(c_0_16_017,plain,
? [X1] :
( ~ empty(X1)
& cup_closed(X1)
& cap_closed(X1)
& diff_closed(X1)
& preboolean(X1) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_17_018,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_18_019,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_19_020,axiom,
? [X1] : empty(X1),
c_0_9 ).
fof(c_0_20_021,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_21_022,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_22_023,plain,
! [X3] :
( element(esk4_1(X3),powerset(X3))
& empty(esk4_1(X3))
& relation(esk4_1(X3))
& function(esk4_1(X3))
& one_to_one(esk4_1(X3))
& epsilon_transitive(esk4_1(X3))
& epsilon_connected(esk4_1(X3))
& ordinal(esk4_1(X3))
& natural(esk4_1(X3))
& finite(esk4_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).
fof(c_0_23_024,plain,
! [X3] :
( element(esk3_1(X3),powerset(X3))
& empty(esk3_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_13])]) ).
fof(c_0_24_025,plain,
! [X3] : element(esk7_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).
fof(c_0_25_026,plain,
! [X3,X4] :
( ~ empty(X3)
| X3 = X4
| ~ empty(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_26_027,plain,
( ~ empty(esk6_0)
& cup_closed(esk6_0)
& cap_closed(esk6_0)
& diff_closed(esk6_0)
& preboolean(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).
fof(c_0_27_028,plain,
( ~ empty(esk5_0)
& finite(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
fof(c_0_28_029,plain,
~ empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_18])]) ).
fof(c_0_29_030,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
cnf(c_0_30_031,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31_032,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32_033,plain,
element(esk4_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33_034,plain,
element(esk3_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34_035,plain,
element(esk7_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35_036,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36_037,plain,
empty(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_37_038,plain,
relation(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_38_039,plain,
function(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_39_040,plain,
one_to_one(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_40_041,plain,
epsilon_transitive(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_41_042,plain,
epsilon_connected(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42_043,plain,
ordinal(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43_044,plain,
natural(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_44_045,plain,
finite(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_45_046,plain,
empty(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_46_047,plain,
~ empty(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_47_048,plain,
~ empty(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_48_049,plain,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_49_050,plain,
cup_closed(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_50_051,plain,
cap_closed(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_51_052,plain,
diff_closed(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_52_053,plain,
preboolean(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_53_054,plain,
finite(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_54_055,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_55_056,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
c_0_30,
[final] ).
cnf(c_0_56_057,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_31,
[final] ).
cnf(c_0_57_058,plain,
element(esk4_1(X1),powerset(X1)),
c_0_32,
[final] ).
cnf(c_0_58_059,plain,
element(esk3_1(X1),powerset(X1)),
c_0_33,
[final] ).
cnf(c_0_59_060,plain,
element(esk7_1(X1),X1),
c_0_34,
[final] ).
cnf(c_0_60_061,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_35,
[final] ).
cnf(c_0_61_062,plain,
empty(esk4_1(X1)),
c_0_36,
[final] ).
cnf(c_0_62_063,plain,
relation(esk4_1(X1)),
c_0_37,
[final] ).
cnf(c_0_63_064,plain,
function(esk4_1(X1)),
c_0_38,
[final] ).
cnf(c_0_64_065,plain,
one_to_one(esk4_1(X1)),
c_0_39,
[final] ).
cnf(c_0_65_066,plain,
epsilon_transitive(esk4_1(X1)),
c_0_40,
[final] ).
cnf(c_0_66_067,plain,
epsilon_connected(esk4_1(X1)),
c_0_41,
[final] ).
cnf(c_0_67_068,plain,
ordinal(esk4_1(X1)),
c_0_42,
[final] ).
cnf(c_0_68_069,plain,
natural(esk4_1(X1)),
c_0_43,
[final] ).
cnf(c_0_69_070,plain,
finite(esk4_1(X1)),
c_0_44,
[final] ).
cnf(c_0_70_071,plain,
empty(esk3_1(X1)),
c_0_45,
[final] ).
cnf(c_0_71_072,plain,
~ empty(esk6_0),
c_0_46,
[final] ).
cnf(c_0_72_073,plain,
~ empty(esk5_0),
c_0_47,
[final] ).
cnf(c_0_73_074,plain,
~ empty(esk1_0),
c_0_48,
[final] ).
cnf(c_0_74_075,plain,
cup_closed(esk6_0),
c_0_49,
[final] ).
cnf(c_0_75_076,plain,
cap_closed(esk6_0),
c_0_50,
[final] ).
cnf(c_0_76_077,plain,
diff_closed(esk6_0),
c_0_51,
[final] ).
cnf(c_0_77_078,plain,
preboolean(esk6_0),
c_0_52,
[final] ).
cnf(c_0_78_079,plain,
finite(esk5_0),
c_0_53,
[final] ).
cnf(c_0_79_080,plain,
empty(esk2_0),
c_0_54,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_55_0,axiom,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_55_1,axiom,
( ~ element(X2,powerset(X1))
| ~ empty(X1)
| ~ in(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_55_2,axiom,
( ~ in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_55]) ).
cnf(c_0_56_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_56_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_56]) ).
cnf(c_0_60_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_60_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_60_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_60]) ).
cnf(c_0_71_0,axiom,
~ empty(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_71]) ).
cnf(c_0_72_0,axiom,
~ empty(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_72]) ).
cnf(c_0_73_0,axiom,
~ empty(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_73]) ).
cnf(c_0_57_0,axiom,
element(sk2_esk4_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_57]) ).
cnf(c_0_58_0,axiom,
element(sk2_esk3_1(X1),powerset(X1)),
inference(literals_permutation,[status(thm)],[c_0_58]) ).
cnf(c_0_59_0,axiom,
element(sk2_esk7_1(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_59]) ).
cnf(c_0_61_0,axiom,
empty(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_61]) ).
cnf(c_0_62_0,axiom,
relation(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_62]) ).
cnf(c_0_63_0,axiom,
function(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_63]) ).
cnf(c_0_64_0,axiom,
one_to_one(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_64]) ).
cnf(c_0_65_0,axiom,
epsilon_transitive(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_65]) ).
cnf(c_0_66_0,axiom,
epsilon_connected(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_66]) ).
cnf(c_0_67_0,axiom,
ordinal(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_67]) ).
cnf(c_0_68_0,axiom,
natural(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_68]) ).
cnf(c_0_69_0,axiom,
finite(sk2_esk4_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_69]) ).
cnf(c_0_70_0,axiom,
empty(sk2_esk3_1(X1)),
inference(literals_permutation,[status(thm)],[c_0_70]) ).
cnf(c_0_74_0,axiom,
cup_closed(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_74]) ).
cnf(c_0_75_0,axiom,
cap_closed(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_75]) ).
cnf(c_0_76_0,axiom,
diff_closed(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_76]) ).
cnf(c_0_77_0,axiom,
preboolean(sk2_esk6_0),
inference(literals_permutation,[status(thm)],[c_0_77]) ).
cnf(c_0_78_0,axiom,
finite(sk2_esk5_0),
inference(literals_permutation,[status(thm)],[c_0_78]) ).
cnf(c_0_79_0,axiom,
empty(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_79]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_081,conjecture,
! [X1,X2] :
( element(X2,finite_subsets(X1))
=> element(X2,powerset(X1)) ),
file('<stdin>',t32_finsub_1) ).
fof(c_0_1_082,negated_conjecture,
~ ! [X1,X2] :
( element(X2,finite_subsets(X1))
=> element(X2,powerset(X1)) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_083,negated_conjecture,
( element(esk2_0,finite_subsets(esk1_0))
& ~ element(esk2_0,powerset(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_084,negated_conjecture,
~ element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_085,negated_conjecture,
element(esk2_0,finite_subsets(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_086,negated_conjecture,
~ element(esk2_0,powerset(esk1_0)),
c_0_3,
[final] ).
cnf(c_0_6_087,negated_conjecture,
element(esk2_0,finite_subsets(esk1_0)),
c_0_4,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_32,plain,
preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p',c_0_159_0) ).
cnf(c_164,plain,
preboolean(finite_subsets(X0)),
inference(copy,[status(esa)],[c_32]) ).
cnf(c_6200,plain,
preboolean(finite_subsets(sk3_esk1_0)),
inference(instantiation,[status(thm)],[c_164]) ).
cnf(c_63,plain,
( ~ in(X0,X1)
| X1 != finite_subsets(X2)
| subset(X0,X2)
| ~ preboolean(X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p',c_0_128_0) ).
cnf(c_195,plain,
( ~ in(X0,X1)
| X1 != finite_subsets(X2)
| subset(X0,X2)
| ~ preboolean(X1) ),
inference(copy,[status(esa)],[c_63]) ).
cnf(c_5870,plain,
( ~ in(sk3_esk2_0,X0)
| ~ preboolean(X0)
| subset(sk3_esk2_0,sk3_esk1_0)
| X0 != finite_subsets(sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_195]) ).
cnf(c_6012,plain,
( ~ in(sk3_esk2_0,finite_subsets(sk3_esk1_0))
| ~ preboolean(finite_subsets(sk3_esk1_0))
| subset(sk3_esk2_0,sk3_esk1_0)
| finite_subsets(sk3_esk1_0) != finite_subsets(sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_5870]) ).
cnf(c_6199,plain,
( ~ in(sk3_esk2_0,finite_subsets(sk3_esk1_0))
| ~ preboolean(finite_subsets(sk3_esk1_0))
| subset(sk3_esk2_0,sk3_esk1_0) ),
inference(equality_resolution_simp,[status(esa)],[c_6012]) ).
cnf(c_40,plain,
~ empty(finite_subsets(X0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p',c_0_151_0) ).
cnf(c_172,plain,
~ empty(finite_subsets(X0)),
inference(copy,[status(esa)],[c_40]) ).
cnf(c_5880,plain,
~ empty(finite_subsets(sk3_esk1_0)),
inference(instantiation,[status(thm)],[c_172]) ).
cnf(c_58,plain,
( empty(X0)
| in(X1,X0)
| ~ element(X1,X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p',c_0_133_0) ).
cnf(c_190,plain,
( empty(X0)
| in(X1,X0)
| ~ element(X1,X0) ),
inference(copy,[status(esa)],[c_58]) ).
cnf(c_5807,plain,
( empty(finite_subsets(sk3_esk1_0))
| ~ element(sk3_esk2_0,finite_subsets(sk3_esk1_0))
| in(sk3_esk2_0,finite_subsets(sk3_esk1_0)) ),
inference(instantiation,[status(thm)],[c_190]) ).
cnf(c_60,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p',c_0_131_0) ).
cnf(c_192,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(copy,[status(esa)],[c_60]) ).
cnf(c_5795,plain,
( element(sk3_esk2_0,powerset(sk3_esk1_0))
| ~ subset(sk3_esk2_0,sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_192]) ).
cnf(c_69,negated_conjecture,
~ element(sk3_esk2_0,powerset(sk3_esk1_0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p',c_0_5) ).
cnf(c_70,negated_conjecture,
element(sk3_esk2_0,finite_subsets(sk3_esk1_0)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p',c_0_6) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_6200,c_6199,c_5880,c_5807,c_5795,c_69,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : iprover_modulo %s %d
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 05:23:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running in mono-core mode
% 0.19/0.40 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.40 % FOF problem with conjecture
% 0.19/0.40 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_6138d0.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_ed7aef.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_7e04e0 | grep -v "SZS"
% 0.19/0.43
% 0.19/0.43 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ iProver source info
% 0.19/0.43
% 0.19/0.43 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.43 % git: non_committed_changes: true
% 0.19/0.43 % git: last_make_outside_of_git: true
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ Input Options
% 0.19/0.43
% 0.19/0.43 % --out_options all
% 0.19/0.43 % --tptp_safe_out true
% 0.19/0.43 % --problem_path ""
% 0.19/0.43 % --include_path ""
% 0.19/0.43 % --clausifier .//eprover
% 0.19/0.43 % --clausifier_options --tstp-format
% 0.19/0.43 % --stdin false
% 0.19/0.43 % --dbg_backtrace false
% 0.19/0.43 % --dbg_dump_prop_clauses false
% 0.19/0.43 % --dbg_dump_prop_clauses_file -
% 0.19/0.43 % --dbg_out_stat false
% 0.19/0.43
% 0.19/0.43 % ------ General Options
% 0.19/0.43
% 0.19/0.43 % --fof false
% 0.19/0.43 % --time_out_real 150.
% 0.19/0.43 % --time_out_prep_mult 0.2
% 0.19/0.43 % --time_out_virtual -1.
% 0.19/0.43 % --schedule none
% 0.19/0.43 % --ground_splitting input
% 0.19/0.43 % --splitting_nvd 16
% 0.19/0.43 % --non_eq_to_eq false
% 0.19/0.43 % --prep_gs_sim true
% 0.19/0.43 % --prep_unflatten false
% 0.19/0.43 % --prep_res_sim true
% 0.19/0.43 % --prep_upred true
% 0.19/0.43 % --res_sim_input true
% 0.19/0.43 % --clause_weak_htbl true
% 0.19/0.43 % --gc_record_bc_elim false
% 0.19/0.43 % --symbol_type_check false
% 0.19/0.43 % --clausify_out false
% 0.19/0.43 % --large_theory_mode false
% 0.19/0.43 % --prep_sem_filter none
% 0.19/0.43 % --prep_sem_filter_out false
% 0.19/0.43 % --preprocessed_out false
% 0.19/0.43 % --sub_typing false
% 0.19/0.43 % --brand_transform false
% 0.19/0.43 % --pure_diseq_elim true
% 0.19/0.43 % --min_unsat_core false
% 0.19/0.43 % --pred_elim true
% 0.19/0.43 % --add_important_lit false
% 0.19/0.43 % --soft_assumptions false
% 0.19/0.43 % --reset_solvers false
% 0.19/0.43 % --bc_imp_inh []
% 0.19/0.43 % --conj_cone_tolerance 1.5
% 0.19/0.43 % --prolific_symb_bound 500
% 0.19/0.43 % --lt_threshold 2000
% 0.19/0.43
% 0.19/0.43 % ------ SAT Options
% 0.19/0.43
% 0.19/0.43 % --sat_mode false
% 0.19/0.43 % --sat_fm_restart_options ""
% 0.19/0.43 % --sat_gr_def false
% 0.19/0.43 % --sat_epr_types true
% 0.19/0.43 % --sat_non_cyclic_types false
% 0.19/0.43 % --sat_finite_models false
% 0.19/0.43 % --sat_fm_lemmas false
% 0.19/0.43 % --sat_fm_prep false
% 0.19/0.43 % --sat_fm_uc_incr true
% 0.19/0.43 % --sat_out_model small
% 0.19/0.43 % --sat_out_clauses false
% 0.19/0.43
% 0.19/0.43 % ------ QBF Options
% 0.19/0.43
% 0.19/0.43 % --qbf_mode false
% 0.19/0.43 % --qbf_elim_univ true
% 0.19/0.43 % --qbf_sk_in true
% 0.19/0.43 % --qbf_pred_elim true
% 0.19/0.43 % --qbf_split 32
% 0.19/0.43
% 0.19/0.43 % ------ BMC1 Options
% 0.19/0.43
% 0.19/0.43 % --bmc1_incremental false
% 0.19/0.43 % --bmc1_axioms reachable_all
% 0.19/0.43 % --bmc1_min_bound 0
% 0.19/0.43 % --bmc1_max_bound -1
% 0.19/0.43 % --bmc1_max_bound_default -1
% 0.19/0.43 % --bmc1_symbol_reachability true
% 0.19/0.43 % --bmc1_property_lemmas false
% 0.19/0.43 % --bmc1_k_induction false
% 0.19/0.43 % --bmc1_non_equiv_states false
% 0.19/0.43 % --bmc1_deadlock false
% 0.19/0.43 % --bmc1_ucm false
% 0.19/0.43 % --bmc1_add_unsat_core none
% 0.19/0.43 % --bmc1_unsat_core_children false
% 0.19/0.43 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.43 % --bmc1_out_stat full
% 0.19/0.43 % --bmc1_ground_init false
% 0.19/0.43 % --bmc1_pre_inst_next_state false
% 0.19/0.43 % --bmc1_pre_inst_state false
% 0.19/0.43 % --bmc1_pre_inst_reach_state false
% 0.19/0.43 % --bmc1_out_unsat_core false
% 0.19/0.43 % --bmc1_aig_witness_out false
% 0.19/0.43 % --bmc1_verbose false
% 0.19/0.43 % --bmc1_dump_clauses_tptp false
% 0.19/0.44 % --bmc1_dump_unsat_core_tptp false
% 0.19/0.44 % --bmc1_dump_file -
% 0.19/0.44 % --bmc1_ucm_expand_uc_limit 128
% 0.19/0.44 % --bmc1_ucm_n_expand_iterations 6
% 0.19/0.44 % --bmc1_ucm_extend_mode 1
% 0.19/0.44 % --bmc1_ucm_init_mode 2
% 0.19/0.44 % --bmc1_ucm_cone_mode none
% 0.19/0.44 % --bmc1_ucm_reduced_relation_type 0
% 0.19/0.44 % --bmc1_ucm_relax_model 4
% 0.19/0.44 % --bmc1_ucm_full_tr_after_sat true
% 0.19/0.44 % --bmc1_ucm_expand_neg_assumptions false
% 0.19/0.44 % --bmc1_ucm_layered_model none
% 0.19/0.44 % --bmc1_ucm_max_lemma_size 10
% 0.19/0.44
% 0.19/0.44 % ------ AIG Options
% 0.19/0.44
% 0.19/0.44 % --aig_mode false
% 0.19/0.44
% 0.19/0.44 % ------ Instantiation Options
% 0.19/0.44
% 0.19/0.44 % --instantiation_flag true
% 0.19/0.44 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.19/0.44 % --inst_solver_per_active 750
% 0.19/0.44 % --inst_solver_calls_frac 0.5
% 0.19/0.44 % --inst_passive_queue_type priority_queues
% 0.19/0.44 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.19/0.44 % --inst_passive_queues_freq [25;2]
% 0.19/0.44 % --inst_dismatching true
% 0.19/0.44 % --inst_eager_unprocessed_to_passive true
% 0.19/0.44 % --inst_prop_sim_given true
% 0.19/0.44 % --inst_prop_sim_new false
% 0.19/0.44 % --inst_orphan_elimination true
% 0.19/0.44 % --inst_learning_loop_flag true
% 0.19/0.44 % --inst_learning_start 3000
% 0.19/0.44 % --inst_learning_factor 2
% 0.19/0.44 % --inst_start_prop_sim_after_learn 3
% 0.19/0.44 % --inst_sel_renew solver
% 0.19/0.44 % --inst_lit_activity_flag true
% 0.19/0.44 % --inst_out_proof true
% 0.19/0.44
% 0.19/0.44 % ------ Resolution Options
% 0.19/0.44
% 0.19/0.44 % --resolution_flag true
% 0.19/0.44 % --res_lit_sel kbo_max
% 0.19/0.44 % --res_to_prop_solver none
% 0.19/0.44 % --res_prop_simpl_new false
% 0.19/0.44 % --res_prop_simpl_given false
% 0.19/0.44 % --res_passive_queue_type priority_queues
% 0.19/0.44 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.19/0.44 % --res_passive_queues_freq [15;5]
% 0.19/0.44 % --res_forward_subs full
% 0.19/0.44 % --res_backward_subs full
% 0.19/0.44 % --res_forward_subs_resolution true
% 0.19/0.44 % --res_backward_subs_resolution true
% 0.19/0.44 % --res_orphan_elimination false
% 0.19/0.44 % --res_time_limit 1000.
% 0.19/0.44 % --res_out_proof true
% 0.19/0.44 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_6138d0.s
% 0.19/0.44 % --modulo true
% 0.19/0.44
% 0.19/0.44 % ------ Combination Options
% 0.19/0.44
% 0.19/0.44 % --comb_res_mult 1000
% 0.19/0.44 % --comb_inst_mult 300
% 0.19/0.44 % ------
% 0.19/0.44
% 0.19/0.44 % ------ Parsing...% successful
% 0.19/0.44
% 0.19/0.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.19/0.44
% 0.19/0.44 % ------ Proving...
% 0.19/0.44 % ------ Problem Properties
% 0.19/0.44
% 0.19/0.44 %
% 0.19/0.44 % EPR false
% 0.19/0.44 % Horn false
% 0.19/0.44 % Has equality true
% 0.19/0.44
% 0.19/0.44 % % ------ Input Options Time Limit: Unbounded
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 % % ------ Current options:
% 0.19/0.44
% 0.19/0.44 % ------ Input Options
% 0.19/0.44
% 0.19/0.44 % --out_options all
% 0.19/0.44 % --tptp_safe_out true
% 0.19/0.44 % --problem_path ""
% 0.19/0.44 % --include_path ""
% 0.19/0.44 % --clausifier .//eprover
% 0.19/0.44 % --clausifier_options --tstp-format
% 0.19/0.44 % --stdin false
% 0.19/0.44 % --dbg_backtrace false
% 0.19/0.44 % --dbg_dump_prop_clauses false
% 0.19/0.44 % --dbg_dump_prop_clauses_file -
% 0.19/0.44 % --dbg_out_stat false
% 0.19/0.44
% 0.19/0.44 % ------ General Options
% 0.19/0.44
% 0.19/0.44 % --fof false
% 0.19/0.44 % --time_out_real 150.
% 0.19/0.44 % --time_out_prep_mult 0.2
% 0.19/0.44 % --time_out_virtual -1.
% 0.19/0.44 % --schedule none
% 0.19/0.44 % --ground_splitting input
% 0.19/0.44 % --splitting_nvd 16
% 0.19/0.44 % --non_eq_to_eq false
% 0.19/0.44 % --prep_gs_sim true
% 0.19/0.44 % --prep_unflatten false
% 0.19/0.44 % --prep_res_sim true
% 0.19/0.44 % --prep_upred true
% 0.19/0.44 % --res_sim_input true
% 0.19/0.44 % --clause_weak_htbl true
% 0.19/0.44 % --gc_record_bc_elim false
% 0.19/0.44 % --symbol_type_check false
% 0.19/0.44 % --clausify_out false
% 0.19/0.44 % --large_theory_mode false
% 0.19/0.44 % --prep_sem_filter none
% 0.19/0.44 % --prep_sem_filter_out false
% 0.19/0.44 % --preprocessed_out false
% 0.19/0.44 % --sub_typing false
% 0.19/0.44 % --brand_transform false
% 0.19/0.44 % --pure_diseq_elim true
% 0.19/0.44 % --min_unsat_core false
% 0.19/0.44 % --pred_elim true
% 0.19/0.44 % --add_important_lit false
% 0.19/0.44 % --soft_assumptions false
% 0.19/0.44 % --reset_solvers false
% 0.19/0.44 % --bc_imp_inh []
% 0.19/0.44 % --conj_cone_tolerance 1.5
% 0.19/0.44 % --prolific_symb_bound 500
% 0.19/0.44 % --lt_threshold 2000
% 0.19/0.44
% 0.19/0.44 % ------ SAT Options
% 0.19/0.44
% 0.19/0.44 % --sat_mode false
% 0.19/0.44 % --sat_fm_restart_options ""
% 0.19/0.44 % --sat_gr_def false
% 0.19/0.44 % --sat_epr_types true
% 0.19/0.44 % --sat_non_cyclic_types false
% 0.19/0.44 % --sat_finite_models false
% 0.19/0.44 % --sat_fm_lemmas false
% 0.19/0.44 % --sat_fm_prep false
% 0.19/0.44 % --sat_fm_uc_incr true
% 0.19/0.44 % --sat_out_model small
% 0.19/0.44 % --sat_out_clauses false
% 0.19/0.44
% 0.19/0.44 % ------ QBF Options
% 0.19/0.44
% 0.19/0.44 % --qbf_mode false
% 0.19/0.44 % --qbf_elim_univ true
% 0.19/0.44 % --qbf_sk_in true
% 0.19/0.44 % --qbf_pred_elim true
% 0.19/0.44 % --qbf_split 32
% 0.19/0.44
% 0.19/0.44 % ------ BMC1 Options
% 0.19/0.44
% 0.19/0.44 % --bmc1_incremental false
% 0.19/0.44 % --bmc1_axioms reachable_all
% 0.19/0.44 % --bmc1_min_bound 0
% 0.19/0.44 % --bmc1_max_bound -1
% 0.19/0.44 % --bmc1_max_bound_default -1
% 0.19/0.44 % --bmc1_symbol_reachability true
% 0.19/0.44 % --bmc1_property_lemmas false
% 0.19/0.44 % --bmc1_k_induction false
% 0.19/0.44 % --bmc1_non_equiv_states false
% 0.19/0.44 % --bmc1_deadlock false
% 0.19/0.44 % --bmc1_ucm false
% 0.19/0.44 % --bmc1_add_unsat_core none
% 0.19/0.44 % --bmc1_unsat_core_children false
% 0.19/0.44 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.44 % --bmc1_out_stat full
% 0.19/0.44 % --bmc1_ground_init false
% 0.19/0.44 % --bmc1_pre_inst_next_state false
% 0.19/0.44 % --bmc1_pre_inst_state false
% 0.19/0.44 % --bmc1_pre_inst_reach_state false
% 0.19/0.44 % --bmc1_out_unsat_core false
% 0.19/0.44 % --bmc1_aig_witness_out false
% 0.19/0.44 % --bmc1_verbose false
% 0.19/0.44 % --bmc1_dump_clauses_tptp false
% 0.19/0.44 % --bmc1_dump_unsat_core_tptp false
% 0.19/0.44 % --bmc1_dump_file -
% 0.19/0.44 % --bmc1_ucm_expand_uc_limit 128
% 0.19/0.44 % --bmc1_ucm_n_expand_iterations 6
% 0.19/0.44 % --bmc1_ucm_extend_mode 1
% 0.19/0.44 % --bmc1_ucm_init_mode 2
% 0.19/0.44 % --bmc1_ucm_cone_mode none
% 0.19/0.44 % --bmc1_ucm_reduced_relation_type 0
% 0.19/0.44 % --bmc1_ucm_relax_model 4
% 0.19/0.44 % --bmc1_ucm_full_tr_after_sat true
% 0.19/0.44 % --bmc1_ucm_expand_neg_assumptions false
% 0.19/0.44 % --bmc1_ucm_layered_model none
% 0.19/0.44 % --bmc1_ucm_max_lemma_size 10
% 0.19/0.44
% 0.19/0.44 % ------ AIG Options
% 0.19/0.44
% 0.19/0.44 % --aig_mode false
% 0.19/0.44
% 0.19/0.44 % ------ Instantiation Options
% 0.19/0.44
% 0.19/0.44 % --instantiation_flag true
% 0.19/0.44 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.19/0.44 % --inst_solver_per_active 750
% 0.19/0.44 % --inst_solver_calls_frac 0.5
% 0.19/0.44 % --inst_passive_queue_type priority_queues
% 0.19/0.44 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.19/0.44 % --inst_passive_queues_freq [25;2]
% 0.19/0.44 % --inst_dismatching true
% 0.19/0.44 % --inst_eager_unprocessed_to_passive true
% 0.19/0.44 % --inst_prop_sim_given true
% 0.45/0.63 % --inst_prop_sim_new false
% 0.45/0.63 % --inst_orphan_elimination true
% 0.45/0.63 % --inst_learning_loop_flag true
% 0.45/0.63 % --inst_learning_start 3000
% 0.45/0.63 % --inst_learning_factor 2
% 0.45/0.63 % --inst_start_prop_sim_after_learn 3
% 0.45/0.63 % --inst_sel_renew solver
% 0.45/0.63 % --inst_lit_activity_flag true
% 0.45/0.63 % --inst_out_proof true
% 0.45/0.63
% 0.45/0.63 % ------ Resolution Options
% 0.45/0.63
% 0.45/0.63 % --resolution_flag true
% 0.45/0.63 % --res_lit_sel kbo_max
% 0.45/0.63 % --res_to_prop_solver none
% 0.45/0.63 % --res_prop_simpl_new false
% 0.45/0.63 % --res_prop_simpl_given false
% 0.45/0.63 % --res_passive_queue_type priority_queues
% 0.45/0.63 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.45/0.63 % --res_passive_queues_freq [15;5]
% 0.45/0.63 % --res_forward_subs full
% 0.45/0.63 % --res_backward_subs full
% 0.45/0.63 % --res_forward_subs_resolution true
% 0.45/0.63 % --res_backward_subs_resolution true
% 0.45/0.63 % --res_orphan_elimination false
% 0.45/0.63 % --res_time_limit 1000.
% 0.45/0.63 % --res_out_proof true
% 0.45/0.63 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_6138d0.s
% 0.45/0.63 % --modulo true
% 0.45/0.63
% 0.45/0.63 % ------ Combination Options
% 0.45/0.63
% 0.45/0.63 % --comb_res_mult 1000
% 0.45/0.63 % --comb_inst_mult 300
% 0.45/0.63 % ------
% 0.45/0.63
% 0.45/0.63
% 0.45/0.63
% 0.45/0.63 % ------ Proving...
% 0.45/0.63 %
% 0.45/0.63
% 0.45/0.63
% 0.45/0.63 % ------ Statistics
% 0.45/0.63
% 0.45/0.63 % ------ General
% 0.45/0.63
% 0.45/0.63 % num_of_input_clauses: 71
% 0.45/0.63 % num_of_input_neg_conjectures: 2
% 0.45/0.63 % num_of_splits: 0
% 0.45/0.63 % num_of_split_atoms: 0
% 0.45/0.63 % num_of_sem_filtered_clauses: 0
% 0.45/0.63 % num_of_subtypes: 0
% 0.45/0.63 % monotx_restored_types: 0
% 0.45/0.63 % sat_num_of_epr_types: 0
% 0.45/0.63 % sat_num_of_non_cyclic_types: 0
% 0.45/0.63 % sat_guarded_non_collapsed_types: 0
% 0.45/0.63 % is_epr: 0
% 0.45/0.63 % is_horn: 0
% 0.45/0.63 % has_eq: 1
% 0.45/0.63 % num_pure_diseq_elim: 0
% 0.45/0.63 % simp_replaced_by: 0
% 0.45/0.63 % res_preprocessed: 4
% 0.45/0.63 % prep_upred: 0
% 0.45/0.63 % prep_unflattend: 0
% 0.45/0.63 % pred_elim_cands: 0
% 0.45/0.63 % pred_elim: 0
% 0.45/0.63 % pred_elim_cl: 0
% 0.45/0.63 % pred_elim_cycles: 0
% 0.45/0.63 % forced_gc_time: 0
% 0.45/0.63 % gc_basic_clause_elim: 0
% 0.45/0.63 % parsing_time: 0.002
% 0.45/0.63 % sem_filter_time: 0.
% 0.45/0.63 % pred_elim_time: 0.
% 0.45/0.63 % out_proof_time: 0.
% 0.45/0.63 % monotx_time: 0.
% 0.45/0.63 % subtype_inf_time: 0.
% 0.45/0.63 % unif_index_cands_time: 0.001
% 0.45/0.63 % unif_index_add_time: 0.002
% 0.45/0.63 % total_time: 0.223
% 0.45/0.63 % num_of_symbols: 57
% 0.45/0.63 % num_of_terms: 5001
% 0.45/0.63
% 0.45/0.63 % ------ Propositional Solver
% 0.45/0.63
% 0.45/0.63 % prop_solver_calls: 5
% 0.45/0.63 % prop_fast_solver_calls: 6
% 0.45/0.63 % prop_num_of_clauses: 439
% 0.45/0.63 % prop_preprocess_simplified: 656
% 0.45/0.63 % prop_fo_subsumed: 0
% 0.45/0.63 % prop_solver_time: 0.
% 0.45/0.63 % prop_fast_solver_time: 0.
% 0.45/0.63 % prop_unsat_core_time: 0.
% 0.45/0.63
% 0.45/0.63 % ------ QBF
% 0.45/0.63
% 0.45/0.63 % qbf_q_res: 0
% 0.45/0.63 % qbf_num_tautologies: 0
% 0.45/0.63 % qbf_prep_cycles: 0
% 0.45/0.63
% 0.45/0.63 % ------ BMC1
% 0.45/0.63
% 0.45/0.63 % bmc1_current_bound: -1
% 0.45/0.63 % bmc1_last_solved_bound: -1
% 0.45/0.63 % bmc1_unsat_core_size: -1
% 0.45/0.63 % bmc1_unsat_core_parents_size: -1
% 0.45/0.63 % bmc1_merge_next_fun: 0
% 0.45/0.63 % bmc1_unsat_core_clauses_time: 0.
% 0.45/0.63
% 0.45/0.63 % ------ Instantiation
% 0.45/0.63
% 0.45/0.63 % inst_num_of_clauses: 278
% 0.45/0.63 % inst_num_in_passive: 124
% 0.45/0.63 % inst_num_in_active: 138
% 0.45/0.63 % inst_num_in_unprocessed: 13
% 0.45/0.63 % inst_num_of_loops: 141
% 0.45/0.63 % inst_num_of_learning_restarts: 0
% 0.45/0.64 % inst_num_moves_active_passive: 1
% 0.45/0.64 % inst_lit_activity: 22
% 0.45/0.64 % inst_lit_activity_moves: 0
% 0.45/0.64 % inst_num_tautologies: 0
% 0.45/0.64 % inst_num_prop_implied: 0
% 0.45/0.64 % inst_num_existing_simplified: 0
% 0.45/0.64 % inst_num_eq_res_simplified: 1
% 0.45/0.64 % inst_num_child_elim: 0
% 0.45/0.64 % inst_num_of_dismatching_blockings: 31
% 0.45/0.64 % inst_num_of_non_proper_insts: 195
% 0.45/0.64 % inst_num_of_duplicates: 41
% 0.45/0.64 % inst_inst_num_from_inst_to_res: 0
% 0.45/0.64 % inst_dismatching_checking_time: 0.
% 0.45/0.64
% 0.45/0.64 % ------ Resolution
% 0.45/0.64
% 0.45/0.64 % res_num_of_clauses: 1299
% 0.45/0.64 % res_num_in_passive: 554
% 0.45/0.64 % res_num_in_active: 722
% 0.45/0.64 % res_num_of_loops: 1000
% 0.45/0.64 % res_forward_subset_subsumed: 134
% 0.45/0.64 % res_backward_subset_subsumed: 0
% 0.45/0.64 % res_forward_subsumed: 341
% 0.45/0.64 % res_backward_subsumed: 0
% 0.45/0.64 % res_forward_subsumption_resolution: 1
% 0.45/0.64 % res_backward_subsumption_resolution: 0
% 0.45/0.64 % res_clause_to_clause_subsumption: 810
% 0.45/0.64 % res_orphan_elimination: 0
% 0.45/0.64 % res_tautology_del: 0
% 0.45/0.64 % res_num_eq_res_simplified: 0
% 0.45/0.64 % res_num_sel_changes: 0
% 0.45/0.64 % res_moves_from_active_to_pass: 0
% 0.45/0.64
% 0.45/0.64 % Status Unsatisfiable
% 0.45/0.64 % SZS status Theorem
% 0.45/0.64 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------