TSTP Solution File: SEU141+2 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n013.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 10:25:14 EDT 2022
% Result : Theorem 28.43s 28.64s
% Output : CNFRefutation 28.43s
% 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(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(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
input ).
fof(t4_boole_0,plain,
! [A] :
( set_difference(empty_set,A) = empty_set
| $false ),
inference(orientation,[status(thm)],[t4_boole]) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
input ).
fof(t3_boole_0,plain,
! [A] :
( set_difference(A,empty_set) = A
| $false ),
inference(orientation,[status(thm)],[t3_boole]) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
input ).
fof(t2_tarski_0,plain,
! [A,B] :
( A = B
| ~ ! [C] :
( in(C,A)
<=> in(C,B) ) ),
inference(orientation,[status(thm)],[t2_tarski]) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
input ).
fof(t2_boole_0,plain,
! [A] :
( set_intersection2(A,empty_set) = empty_set
| $false ),
inference(orientation,[status(thm)],[t2_boole]) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
input ).
fof(t1_boole_0,plain,
! [A] :
( set_union2(A,empty_set) = A
| $false ),
inference(orientation,[status(thm)],[t1_boole]) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
input ).
fof(symmetry_r1_xboole_0_0,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(orientation,[status(thm)],[symmetry_r1_xboole_0]) ).
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(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
input ).
fof(irreflexivity_r2_xboole_0_0,plain,
! [A] :
( ~ proper_subset(A,A)
| $false ),
inference(orientation,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
input ).
fof(idempotence_k3_xboole_0_0,plain,
! [A] :
( set_intersection2(A,A) = A
| $false ),
inference(orientation,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
input ).
fof(idempotence_k2_xboole_0_0,plain,
! [A] :
( set_union2(A,A) = A
| $false ),
inference(orientation,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
input ).
fof(fc3_xboole_0_0,plain,
! [A,B] :
( empty(A)
| ~ empty(set_union2(B,A)) ),
inference(orientation,[status(thm)],[fc3_xboole_0]) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
input ).
fof(fc2_xboole_0_0,plain,
! [A,B] :
( empty(A)
| ~ empty(set_union2(A,B)) ),
inference(orientation,[status(thm)],[fc2_xboole_0]) ).
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(dt_k4_xboole_0,axiom,
$true,
input ).
fof(dt_k4_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k4_xboole_0]) ).
fof(dt_k3_xboole_0,axiom,
$true,
input ).
fof(dt_k3_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k3_xboole_0]) ).
fof(dt_k2_xboole_0,axiom,
$true,
input ).
fof(dt_k2_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k2_xboole_0]) ).
fof(dt_k1_xboole_0,axiom,
$true,
input ).
fof(dt_k1_xboole_0_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[dt_k1_xboole_0]) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& A != B ) ),
input ).
fof(d8_xboole_0_0,plain,
! [A,B] :
( proper_subset(A,B)
| ~ ( subset(A,B)
& A != B ) ),
inference(orientation,[status(thm)],[d8_xboole_0]) ).
fof(d8_xboole_0_1,plain,
! [A,B] :
( ~ proper_subset(A,B)
| ( subset(A,B)
& A != B ) ),
inference(orientation,[status(thm)],[d8_xboole_0]) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
input ).
fof(d7_xboole_0_0,plain,
! [A,B] :
( disjoint(A,B)
| set_intersection2(A,B) != empty_set ),
inference(orientation,[status(thm)],[d7_xboole_0]) ).
fof(d7_xboole_0_1,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(orientation,[status(thm)],[d7_xboole_0]) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
input ).
fof(d4_xboole_0_0,plain,
! [A,B,C] :
( C = set_difference(A,B)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(orientation,[status(thm)],[d4_xboole_0]) ).
fof(d4_xboole_0_1,plain,
! [A,B,C] :
( C != set_difference(A,B)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(orientation,[status(thm)],[d4_xboole_0]) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
input ).
fof(d3_xboole_0_0,plain,
! [A,B,C] :
( C = set_intersection2(A,B)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(orientation,[status(thm)],[d3_xboole_0]) ).
fof(d3_xboole_0_1,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(orientation,[status(thm)],[d3_xboole_0]) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
input ).
fof(d3_tarski_0,plain,
! [A,B] :
( subset(A,B)
| ~ ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(orientation,[status(thm)],[d3_tarski]) ).
fof(d3_tarski_1,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(orientation,[status(thm)],[d3_tarski]) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
input ).
fof(d2_xboole_0_0,plain,
! [A,B,C] :
( C = set_union2(A,B)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(orientation,[status(thm)],[d2_xboole_0]) ).
fof(d2_xboole_0_1,plain,
! [A,B,C] :
( C != set_union2(A,B)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(orientation,[status(thm)],[d2_xboole_0]) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
input ).
fof(d1_xboole_0_0,plain,
! [A] :
( A = empty_set
| ~ ! [B] : ~ in(B,A) ),
inference(orientation,[status(thm)],[d1_xboole_0]) ).
fof(d1_xboole_0_1,plain,
! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) ),
inference(orientation,[status(thm)],[d1_xboole_0]) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
input ).
fof(d10_xboole_0_0,plain,
! [A,B] :
( A = B
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[d10_xboole_0]) ).
fof(d10_xboole_0_1,plain,
! [A,B] :
( A != B
| ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[d10_xboole_0]) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
input ).
fof(commutativity_k3_xboole_0_0,plain,
! [A,B] :
( set_intersection2(A,B) = set_intersection2(B,A)
| $false ),
inference(orientation,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
input ).
fof(commutativity_k2_xboole_0_0,plain,
! [A,B] :
( set_union2(A,B) = set_union2(B,A)
| $false ),
inference(orientation,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
input ).
fof(antisymmetry_r2_xboole_0_0,plain,
! [A,B] :
( ~ proper_subset(A,B)
| ~ proper_subset(B,A) ),
inference(orientation,[status(thm)],[antisymmetry_r2_xboole_0]) ).
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(def_lhs_atom1,axiom,
! [B,A] :
( lhs_atom1(B,A)
<=> ~ in(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [A,B] :
( lhs_atom1(B,A)
| ~ in(B,A) ),
inference(fold_definition,[status(thm)],[antisymmetry_r2_hidden_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [B,A] :
( lhs_atom2(B,A)
<=> ~ proper_subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A,B] :
( lhs_atom2(B,A)
| ~ proper_subset(B,A) ),
inference(fold_definition,[status(thm)],[antisymmetry_r2_xboole_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [B,A] :
( lhs_atom3(B,A)
<=> set_union2(A,B) = set_union2(B,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A,B] :
( lhs_atom3(B,A)
| $false ),
inference(fold_definition,[status(thm)],[commutativity_k2_xboole_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [B,A] :
( lhs_atom4(B,A)
<=> set_intersection2(A,B) = set_intersection2(B,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [A,B] :
( lhs_atom4(B,A)
| $false ),
inference(fold_definition,[status(thm)],[commutativity_k3_xboole_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [B,A] :
( lhs_atom5(B,A)
<=> A != B ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [A,B] :
( lhs_atom5(B,A)
| ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[d10_xboole_0_1,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [B,A] :
( lhs_atom6(B,A)
<=> A = B ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [A,B] :
( lhs_atom6(B,A)
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[d10_xboole_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [A] :
( lhs_atom7(A)
<=> A != empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A] :
( lhs_atom7(A)
| ! [B] : ~ in(B,A) ),
inference(fold_definition,[status(thm)],[d1_xboole_0_1,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [A] :
( lhs_atom8(A)
<=> A = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A] :
( lhs_atom8(A)
| ~ ! [B] : ~ in(B,A) ),
inference(fold_definition,[status(thm)],[d1_xboole_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [C,B,A] :
( lhs_atom9(C,B,A)
<=> C != set_union2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [A,B,C] :
( lhs_atom9(C,B,A)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d2_xboole_0_1,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [C,B,A] :
( lhs_atom10(C,B,A)
<=> C = set_union2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [A,B,C] :
( lhs_atom10(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d2_xboole_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [B,A] :
( lhs_atom11(B,A)
<=> ~ subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [A,B] :
( lhs_atom11(B,A)
| ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[d3_tarski_1,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [B,A] :
( lhs_atom12(B,A)
<=> subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [A,B] :
( lhs_atom12(B,A)
| ~ ! [C] :
( in(C,A)
=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[d3_tarski_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [C,B,A] :
( lhs_atom13(C,B,A)
<=> C != set_intersection2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [A,B,C] :
( lhs_atom13(C,B,A)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d3_xboole_0_1,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [C,B,A] :
( lhs_atom14(C,B,A)
<=> C = set_intersection2(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [A,B,C] :
( lhs_atom14(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d3_xboole_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [C,B,A] :
( lhs_atom15(C,B,A)
<=> C != set_difference(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [A,B,C] :
( lhs_atom15(C,B,A)
| ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d4_xboole_0_1,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [C,B,A] :
( lhs_atom16(C,B,A)
<=> C = set_difference(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [A,B,C] :
( lhs_atom16(C,B,A)
| ~ ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
inference(fold_definition,[status(thm)],[d4_xboole_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [B,A] :
( lhs_atom17(B,A)
<=> ~ disjoint(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [A,B] :
( lhs_atom17(B,A)
| set_intersection2(A,B) = empty_set ),
inference(fold_definition,[status(thm)],[d7_xboole_0_1,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [B,A] :
( lhs_atom18(B,A)
<=> disjoint(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [A,B] :
( lhs_atom18(B,A)
| set_intersection2(A,B) != empty_set ),
inference(fold_definition,[status(thm)],[d7_xboole_0_0,def_lhs_atom18]) ).
fof(to_be_clausified_18,plain,
! [A,B] :
( lhs_atom2(B,A)
| ( subset(A,B)
& A != B ) ),
inference(fold_definition,[status(thm)],[d8_xboole_0_1,def_lhs_atom2]) ).
fof(def_lhs_atom19,axiom,
! [B,A] :
( lhs_atom19(B,A)
<=> proper_subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [A,B] :
( lhs_atom19(B,A)
| ~ ( subset(A,B)
& A != B ) ),
inference(fold_definition,[status(thm)],[d8_xboole_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
( lhs_atom20
<=> $true ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[dt_k1_xboole_0_0,def_lhs_atom20]) ).
fof(to_be_clausified_21,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[dt_k2_xboole_0_0,def_lhs_atom20]) ).
fof(to_be_clausified_22,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[dt_k3_xboole_0_0,def_lhs_atom20]) ).
fof(to_be_clausified_23,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[dt_k4_xboole_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
( lhs_atom21
<=> empty(empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
( lhs_atom21
| $false ),
inference(fold_definition,[status(thm)],[fc1_xboole_0_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [A] :
( lhs_atom22(A)
<=> empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [A,B] :
( lhs_atom22(A)
| ~ empty(set_union2(A,B)) ),
inference(fold_definition,[status(thm)],[fc2_xboole_0_0,def_lhs_atom22]) ).
fof(to_be_clausified_26,plain,
! [A,B] :
( lhs_atom22(A)
| ~ empty(set_union2(B,A)) ),
inference(fold_definition,[status(thm)],[fc3_xboole_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [A] :
( lhs_atom23(A)
<=> set_union2(A,A) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [A] :
( lhs_atom23(A)
| $false ),
inference(fold_definition,[status(thm)],[idempotence_k2_xboole_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [A] :
( lhs_atom24(A)
<=> set_intersection2(A,A) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [A] :
( lhs_atom24(A)
| $false ),
inference(fold_definition,[status(thm)],[idempotence_k3_xboole_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [A] :
( lhs_atom25(A)
<=> ~ proper_subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [A] :
( lhs_atom25(A)
| $false ),
inference(fold_definition,[status(thm)],[irreflexivity_r2_xboole_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [A] :
( lhs_atom26(A)
<=> subset(A,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [A] :
( lhs_atom26(A)
| $false ),
inference(fold_definition,[status(thm)],[reflexivity_r1_tarski_0,def_lhs_atom26]) ).
fof(to_be_clausified_31,plain,
! [A,B] :
( lhs_atom17(B,A)
| disjoint(B,A) ),
inference(fold_definition,[status(thm)],[symmetry_r1_xboole_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom27,axiom,
! [A] :
( lhs_atom27(A)
<=> set_union2(A,empty_set) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [A] :
( lhs_atom27(A)
| $false ),
inference(fold_definition,[status(thm)],[t1_boole_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [A] :
( lhs_atom28(A)
<=> set_intersection2(A,empty_set) = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [A] :
( lhs_atom28(A)
| $false ),
inference(fold_definition,[status(thm)],[t2_boole_0,def_lhs_atom28]) ).
fof(to_be_clausified_34,plain,
! [A,B] :
( lhs_atom6(B,A)
| ~ ! [C] :
( in(C,A)
<=> in(C,B) ) ),
inference(fold_definition,[status(thm)],[t2_tarski_0,def_lhs_atom6]) ).
fof(def_lhs_atom29,axiom,
! [A] :
( lhs_atom29(A)
<=> set_difference(A,empty_set) = A ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [A] :
( lhs_atom29(A)
| $false ),
inference(fold_definition,[status(thm)],[t3_boole_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [A] :
( lhs_atom30(A)
<=> set_difference(empty_set,A) = empty_set ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [A] :
( lhs_atom30(A)
| $false ),
inference(fold_definition,[status(thm)],[t4_boole_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [A] :
( lhs_atom31(A)
<=> ~ empty(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [A] :
( lhs_atom31(A)
| A = empty_set ),
inference(fold_definition,[status(thm)],[t6_boole_0,def_lhs_atom31]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X1,X2] :
( lhs_atom14(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_1,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_2,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_3,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
<=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_4,axiom,
! [X3,X1,X2] :
( lhs_atom13(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_5,axiom,
! [X3,X1,X2] :
( lhs_atom15(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_6,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_7,axiom,
! [X1,X2] :
( lhs_atom12(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_8,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_9,axiom,
! [X1,X2] :
( lhs_atom22(X2)
| ~ empty(set_union2(X1,X2)) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_10,axiom,
! [X1,X2] :
( lhs_atom22(X2)
| ~ empty(set_union2(X2,X1)) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_11,axiom,
! [X1,X2] :
( lhs_atom11(X1,X2)
| ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_12,axiom,
! [X1,X2] :
( lhs_atom19(X1,X2)
| ~ ( subset(X2,X1)
& X2 != X1 ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_13,axiom,
! [X1,X2] :
( lhs_atom18(X1,X2)
| set_intersection2(X2,X1) != empty_set ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_14,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_15,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_16,axiom,
! [X1,X2] :
( lhs_atom17(X1,X2)
| disjoint(X1,X2) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_17,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ( subset(X2,X1)
& X2 != X1 ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_18,axiom,
! [X1,X2] :
( lhs_atom17(X1,X2)
| set_intersection2(X2,X1) = empty_set ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_19,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_20,axiom,
! [X2] :
( lhs_atom7(X2)
| ! [X1] : ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_21,axiom,
! [X2] :
( lhs_atom8(X2)
| ~ ! [X1] : ~ in(X1,X2) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_22,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_23,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_24,axiom,
! [X2] :
( lhs_atom31(X2)
| X2 = empty_set ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_25,axiom,
! [X2] :
( lhs_atom30(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_26,axiom,
! [X2] :
( lhs_atom29(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_27,axiom,
! [X2] :
( lhs_atom28(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_28,axiom,
! [X2] :
( lhs_atom27(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_29,axiom,
! [X2] :
( lhs_atom26(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_30,axiom,
! [X2] :
( lhs_atom25(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_31,axiom,
! [X2] :
( lhs_atom24(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_32,axiom,
! [X2] :
( lhs_atom23(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_33,axiom,
( lhs_atom21
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_34,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_35,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_36,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_37,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_38,axiom,
! [X3,X1,X2] :
( lhs_atom14(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
c_0_0 ).
fof(c_0_39,plain,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_40,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
c_0_2 ).
fof(c_0_41,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
<=> in(X3,X1) ) ),
c_0_3 ).
fof(c_0_42,axiom,
! [X3,X1,X2] :
( lhs_atom13(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
c_0_4 ).
fof(c_0_43,plain,
! [X3,X1,X2] :
( lhs_atom15(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& ~ in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_44,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
c_0_6 ).
fof(c_0_45,axiom,
! [X1,X2] :
( lhs_atom12(X1,X2)
| ~ ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_7 ).
fof(c_0_46,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_8 ).
fof(c_0_47,plain,
! [X1,X2] :
( lhs_atom22(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_48,plain,
! [X1,X2] :
( lhs_atom22(X2)
| ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_49,axiom,
! [X1,X2] :
( lhs_atom11(X1,X2)
| ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
c_0_11 ).
fof(c_0_50,axiom,
! [X1,X2] :
( lhs_atom19(X1,X2)
| ~ ( subset(X2,X1)
& X2 != X1 ) ),
c_0_12 ).
fof(c_0_51,plain,
! [X1,X2] :
( lhs_atom18(X1,X2)
| set_intersection2(X2,X1) != empty_set ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_52,plain,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_53,plain,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_54,axiom,
! [X1,X2] :
( lhs_atom17(X1,X2)
| disjoint(X1,X2) ),
c_0_16 ).
fof(c_0_55,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ( subset(X2,X1)
& X2 != X1 ) ),
c_0_17 ).
fof(c_0_56,axiom,
! [X1,X2] :
( lhs_atom17(X1,X2)
| set_intersection2(X2,X1) = empty_set ),
c_0_18 ).
fof(c_0_57,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_19 ).
fof(c_0_58,plain,
! [X2] :
( lhs_atom7(X2)
| ! [X1] : ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_59,plain,
! [X2] :
( lhs_atom8(X2)
| ~ ! [X1] : ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_60,plain,
! [X1,X2] : lhs_atom4(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_61,plain,
! [X1,X2] : lhs_atom3(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_62,axiom,
! [X2] :
( lhs_atom31(X2)
| X2 = empty_set ),
c_0_24 ).
fof(c_0_63,plain,
! [X2] : lhs_atom30(X2),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_64,plain,
! [X2] : lhs_atom29(X2),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_65,plain,
! [X2] : lhs_atom28(X2),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_66,plain,
! [X2] : lhs_atom27(X2),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_67,plain,
! [X2] : lhs_atom26(X2),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_68,plain,
! [X2] : lhs_atom25(X2),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_69,plain,
! [X2] : lhs_atom24(X2),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_70,plain,
! [X2] : lhs_atom23(X2),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_71,plain,
lhs_atom21,
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_72,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_73,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_74,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_75,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_76,plain,
! [X5,X6,X7] :
( ( ~ in(esk4_3(X5,X6,X7),X5)
| ~ in(esk4_3(X5,X6,X7),X7)
| ~ in(esk4_3(X5,X6,X7),X6)
| lhs_atom14(X5,X6,X7) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| lhs_atom14(X5,X6,X7) )
& ( in(esk4_3(X5,X6,X7),X6)
| in(esk4_3(X5,X6,X7),X5)
| lhs_atom14(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])]) ).
fof(c_0_77,plain,
! [X5,X6,X7] :
( ( ~ in(esk5_3(X5,X6,X7),X5)
| ~ in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X6)
| lhs_atom16(X5,X6,X7) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| lhs_atom16(X5,X6,X7) )
& ( ~ in(esk5_3(X5,X6,X7),X6)
| in(esk5_3(X5,X6,X7),X5)
| lhs_atom16(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
fof(c_0_78,plain,
! [X5,X6,X7] :
( ( ~ in(esk2_3(X5,X6,X7),X7)
| ~ in(esk2_3(X5,X6,X7),X5)
| lhs_atom10(X5,X6,X7) )
& ( ~ in(esk2_3(X5,X6,X7),X6)
| ~ in(esk2_3(X5,X6,X7),X5)
| lhs_atom10(X5,X6,X7) )
& ( in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X7)
| in(esk2_3(X5,X6,X7),X6)
| lhs_atom10(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
fof(c_0_79,plain,
! [X4,X5] :
( ( ~ in(esk6_2(X4,X5),X5)
| ~ in(esk6_2(X4,X5),X4)
| lhs_atom6(X4,X5) )
& ( in(esk6_2(X4,X5),X5)
| in(esk6_2(X4,X5),X4)
| lhs_atom6(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
fof(c_0_80,plain,
! [X5,X6,X7,X8,X9] :
( ( in(X8,X7)
| ~ in(X8,X5)
| lhs_atom13(X5,X6,X7) )
& ( in(X8,X6)
| ~ in(X8,X5)
| lhs_atom13(X5,X6,X7) )
& ( ~ in(X9,X7)
| ~ in(X9,X6)
| in(X9,X5)
| lhs_atom13(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])]) ).
fof(c_0_81,plain,
! [X5,X6,X7,X8,X9] :
( ( in(X8,X7)
| ~ in(X8,X5)
| lhs_atom15(X5,X6,X7) )
& ( ~ in(X8,X6)
| ~ in(X8,X5)
| lhs_atom15(X5,X6,X7) )
& ( ~ in(X9,X7)
| in(X9,X6)
| in(X9,X5)
| lhs_atom15(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])]) ).
fof(c_0_82,plain,
! [X5,X6,X7,X8,X9] :
( ( ~ in(X8,X5)
| in(X8,X7)
| in(X8,X6)
| lhs_atom9(X5,X6,X7) )
& ( ~ in(X9,X7)
| in(X9,X5)
| lhs_atom9(X5,X6,X7) )
& ( ~ in(X9,X6)
| in(X9,X5)
| lhs_atom9(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])]) ).
fof(c_0_83,plain,
! [X4,X5] :
( ( in(esk3_2(X4,X5),X5)
| lhs_atom12(X4,X5) )
& ( ~ in(esk3_2(X4,X5),X4)
| lhs_atom12(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
fof(c_0_84,plain,
! [X3,X4] :
( lhs_atom6(X3,X4)
| ~ subset(X4,X3)
| ~ subset(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])]) ).
fof(c_0_85,plain,
! [X3,X4] :
( lhs_atom22(X4)
| ~ empty(set_union2(X3,X4)) ),
inference(variable_rename,[status(thm)],[c_0_47]) ).
fof(c_0_86,plain,
! [X3,X4] :
( lhs_atom22(X4)
| ~ empty(set_union2(X4,X3)) ),
inference(variable_rename,[status(thm)],[c_0_48]) ).
fof(c_0_87,plain,
! [X4,X5,X6] :
( lhs_atom11(X4,X5)
| ~ in(X6,X5)
| in(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
fof(c_0_88,plain,
! [X3,X4] :
( lhs_atom19(X3,X4)
| ~ subset(X4,X3)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])]) ).
fof(c_0_89,plain,
! [X3,X4] :
( lhs_atom18(X3,X4)
| set_intersection2(X4,X3) != empty_set ),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_90,plain,
! [X3,X4] :
( lhs_atom2(X3,X4)
| ~ proper_subset(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_52]) ).
fof(c_0_91,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_53]) ).
fof(c_0_92,plain,
! [X3,X4] :
( lhs_atom17(X3,X4)
| disjoint(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_54]) ).
fof(c_0_93,plain,
! [X3,X4] :
( ( subset(X4,X3)
| lhs_atom2(X3,X4) )
& ( X4 != X3
| lhs_atom2(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_55])]) ).
fof(c_0_94,plain,
! [X3,X4] :
( lhs_atom17(X3,X4)
| set_intersection2(X4,X3) = empty_set ),
inference(variable_rename,[status(thm)],[c_0_56]) ).
fof(c_0_95,plain,
! [X3,X4] :
( ( subset(X4,X3)
| lhs_atom5(X3,X4) )
& ( subset(X3,X4)
| lhs_atom5(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_57])]) ).
fof(c_0_96,plain,
! [X3,X4] :
( lhs_atom7(X3)
| ~ in(X4,X3) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_58])]) ).
fof(c_0_97,plain,
! [X3] :
( lhs_atom8(X3)
| in(esk1_1(X3),X3) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])]) ).
fof(c_0_98,plain,
! [X3,X4] : lhs_atom4(X3,X4),
inference(variable_rename,[status(thm)],[c_0_60]) ).
fof(c_0_99,plain,
! [X3,X4] : lhs_atom3(X3,X4),
inference(variable_rename,[status(thm)],[c_0_61]) ).
fof(c_0_100,plain,
! [X3] :
( lhs_atom31(X3)
| X3 = empty_set ),
inference(variable_rename,[status(thm)],[c_0_62]) ).
fof(c_0_101,plain,
! [X3] : lhs_atom30(X3),
inference(variable_rename,[status(thm)],[c_0_63]) ).
fof(c_0_102,plain,
! [X3] : lhs_atom29(X3),
inference(variable_rename,[status(thm)],[c_0_64]) ).
fof(c_0_103,plain,
! [X3] : lhs_atom28(X3),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_104,plain,
! [X3] : lhs_atom27(X3),
inference(variable_rename,[status(thm)],[c_0_66]) ).
fof(c_0_105,plain,
! [X3] : lhs_atom26(X3),
inference(variable_rename,[status(thm)],[c_0_67]) ).
fof(c_0_106,plain,
! [X3] : lhs_atom25(X3),
inference(variable_rename,[status(thm)],[c_0_68]) ).
fof(c_0_107,plain,
! [X3] : lhs_atom24(X3),
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_108,plain,
! [X3] : lhs_atom23(X3),
inference(variable_rename,[status(thm)],[c_0_70]) ).
fof(c_0_109,plain,
lhs_atom21,
c_0_71 ).
fof(c_0_110,plain,
lhs_atom20,
c_0_72 ).
fof(c_0_111,plain,
lhs_atom20,
c_0_73 ).
fof(c_0_112,plain,
lhs_atom20,
c_0_74 ).
fof(c_0_113,plain,
lhs_atom20,
c_0_75 ).
cnf(c_0_114,plain,
( lhs_atom14(X1,X2,X3)
| ~ in(esk4_3(X1,X2,X3),X2)
| ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(esk4_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_115,plain,
( lhs_atom16(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X2)
| ~ in(esk5_3(X1,X2,X3),X3)
| ~ in(esk5_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_116,plain,
( lhs_atom10(X1,X2,X3)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_117,plain,
( lhs_atom10(X1,X2,X3)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_118,plain,
( lhs_atom10(X1,X2,X3)
| in(esk2_3(X1,X2,X3),X2)
| in(esk2_3(X1,X2,X3),X3)
| in(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_119,plain,
( lhs_atom16(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_120,plain,
( lhs_atom16(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X1)
| in(esk5_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_121,plain,
( lhs_atom14(X1,X2,X3)
| in(esk4_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_122,plain,
( lhs_atom14(X1,X2,X3)
| in(esk4_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_123,plain,
( lhs_atom6(X1,X2)
| ~ in(esk6_2(X1,X2),X1)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_124,plain,
( lhs_atom13(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_125,plain,
( lhs_atom15(X1,X2,X3)
| in(X4,X1)
| in(X4,X2)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_126,plain,
( lhs_atom9(X1,X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_127,plain,
( lhs_atom15(X1,X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_128,plain,
( lhs_atom6(X1,X2)
| in(esk6_2(X1,X2),X1)
| in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_129,plain,
( lhs_atom15(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_130,plain,
( lhs_atom13(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_131,plain,
( lhs_atom13(X1,X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_132,plain,
( lhs_atom9(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_133,plain,
( lhs_atom9(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_134,plain,
( lhs_atom12(X1,X2)
| ~ in(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_135,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_136,plain,
( lhs_atom12(X1,X2)
| in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_137,plain,
( lhs_atom22(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_138,plain,
( lhs_atom22(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_139,plain,
( in(X1,X2)
| lhs_atom11(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_140,plain,
( X1 = X2
| lhs_atom19(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_141,plain,
( lhs_atom18(X2,X1)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_142,plain,
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_143,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_144,plain,
( disjoint(X1,X2)
| lhs_atom17(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_145,plain,
( lhs_atom2(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_146,plain,
( set_intersection2(X1,X2) = empty_set
| lhs_atom17(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_147,plain,
( lhs_atom5(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_148,plain,
( lhs_atom5(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_149,plain,
( lhs_atom7(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_150,plain,
( in(esk1_1(X1),X1)
| lhs_atom8(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_151,plain,
( lhs_atom2(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_152,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_153,plain,
lhs_atom3(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_154,plain,
( X1 = empty_set
| lhs_atom31(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_155,plain,
lhs_atom30(X1),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_156,plain,
lhs_atom29(X1),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_157,plain,
lhs_atom28(X1),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_158,plain,
lhs_atom27(X1),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_159,plain,
lhs_atom26(X1),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_160,plain,
lhs_atom25(X1),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_161,plain,
lhs_atom24(X1),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_162,plain,
lhs_atom23(X1),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_163,plain,
lhs_atom21,
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_164,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_165,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_166,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_167,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_168,plain,
( lhs_atom14(X1,X2,X3)
| ~ in(esk4_3(X1,X2,X3),X2)
| ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(esk4_3(X1,X2,X3),X1) ),
c_0_114,
[final] ).
cnf(c_0_169,plain,
( lhs_atom16(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X2)
| ~ in(esk5_3(X1,X2,X3),X3)
| ~ in(esk5_3(X1,X2,X3),X1) ),
c_0_115,
[final] ).
cnf(c_0_170,plain,
( lhs_atom10(X1,X2,X3)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X3) ),
c_0_116,
[final] ).
cnf(c_0_171,plain,
( lhs_atom10(X1,X2,X3)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X2) ),
c_0_117,
[final] ).
cnf(c_0_172,plain,
( lhs_atom10(X1,X2,X3)
| in(esk2_3(X1,X2,X3),X2)
| in(esk2_3(X1,X2,X3),X3)
| in(esk2_3(X1,X2,X3),X1) ),
c_0_118,
[final] ).
cnf(c_0_173,plain,
( lhs_atom16(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X1)
| ~ in(esk5_3(X1,X2,X3),X2) ),
c_0_119,
[final] ).
cnf(c_0_174,plain,
( lhs_atom16(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X1)
| in(esk5_3(X1,X2,X3),X3) ),
c_0_120,
[final] ).
cnf(c_0_175,plain,
( lhs_atom14(X1,X2,X3)
| in(esk4_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X3) ),
c_0_121,
[final] ).
cnf(c_0_176,plain,
( lhs_atom14(X1,X2,X3)
| in(esk4_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X2) ),
c_0_122,
[final] ).
cnf(c_0_177,plain,
( lhs_atom6(X1,X2)
| ~ in(esk6_2(X1,X2),X1)
| ~ in(esk6_2(X1,X2),X2) ),
c_0_123,
[final] ).
cnf(c_0_178,plain,
( lhs_atom13(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X3) ),
c_0_124,
[final] ).
cnf(c_0_179,plain,
( lhs_atom15(X1,X2,X3)
| in(X4,X1)
| in(X4,X2)
| ~ in(X4,X3) ),
c_0_125,
[final] ).
cnf(c_0_180,plain,
( lhs_atom9(X1,X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
c_0_126,
[final] ).
cnf(c_0_181,plain,
( lhs_atom15(X1,X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) ),
c_0_127,
[final] ).
cnf(c_0_182,plain,
( lhs_atom6(X1,X2)
| in(esk6_2(X1,X2),X1)
| in(esk6_2(X1,X2),X2) ),
c_0_128,
[final] ).
cnf(c_0_183,plain,
( lhs_atom15(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
c_0_129,
[final] ).
cnf(c_0_184,plain,
( lhs_atom13(X1,X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
c_0_130,
[final] ).
cnf(c_0_185,plain,
( lhs_atom13(X1,X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
c_0_131,
[final] ).
cnf(c_0_186,plain,
( lhs_atom9(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
c_0_132,
[final] ).
cnf(c_0_187,plain,
( lhs_atom9(X1,X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
c_0_133,
[final] ).
cnf(c_0_188,plain,
( lhs_atom12(X1,X2)
| ~ in(esk3_2(X1,X2),X1) ),
c_0_134,
[final] ).
cnf(c_0_189,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_135,
[final] ).
cnf(c_0_190,plain,
( lhs_atom12(X1,X2)
| in(esk3_2(X1,X2),X2) ),
c_0_136,
[final] ).
cnf(c_0_191,plain,
( lhs_atom22(X2)
| ~ empty(set_union2(X1,X2)) ),
c_0_137,
[final] ).
cnf(c_0_192,plain,
( lhs_atom22(X1)
| ~ empty(set_union2(X1,X2)) ),
c_0_138,
[final] ).
cnf(c_0_193,plain,
( in(X1,X2)
| lhs_atom11(X2,X3)
| ~ in(X1,X3) ),
c_0_139,
[final] ).
cnf(c_0_194,plain,
( X1 = X2
| lhs_atom19(X2,X1)
| ~ subset(X1,X2) ),
c_0_140,
[final] ).
cnf(c_0_195,plain,
( lhs_atom18(X2,X1)
| set_intersection2(X1,X2) != empty_set ),
c_0_141,
[final] ).
cnf(c_0_196,plain,
( lhs_atom2(X1,X2)
| ~ proper_subset(X1,X2) ),
c_0_142,
[final] ).
cnf(c_0_197,plain,
( lhs_atom1(X1,X2)
| ~ in(X1,X2) ),
c_0_143,
[final] ).
cnf(c_0_198,plain,
( disjoint(X1,X2)
| lhs_atom17(X1,X2) ),
c_0_144,
[final] ).
cnf(c_0_199,plain,
( lhs_atom2(X1,X2)
| subset(X2,X1) ),
c_0_145,
[final] ).
cnf(c_0_200,plain,
( set_intersection2(X1,X2) = empty_set
| lhs_atom17(X2,X1) ),
c_0_146,
[final] ).
cnf(c_0_201,plain,
( lhs_atom5(X1,X2)
| subset(X2,X1) ),
c_0_147,
[final] ).
cnf(c_0_202,plain,
( lhs_atom5(X1,X2)
| subset(X1,X2) ),
c_0_148,
[final] ).
cnf(c_0_203,plain,
( lhs_atom7(X2)
| ~ in(X1,X2) ),
c_0_149,
[final] ).
cnf(c_0_204,plain,
( in(esk1_1(X1),X1)
| lhs_atom8(X1) ),
c_0_150,
[final] ).
cnf(c_0_205,plain,
( lhs_atom2(X1,X2)
| X2 != X1 ),
c_0_151,
[final] ).
cnf(c_0_206,plain,
lhs_atom4(X1,X2),
c_0_152,
[final] ).
cnf(c_0_207,plain,
lhs_atom3(X1,X2),
c_0_153,
[final] ).
cnf(c_0_208,plain,
( X1 = empty_set
| lhs_atom31(X1) ),
c_0_154,
[final] ).
cnf(c_0_209,plain,
lhs_atom30(X1),
c_0_155,
[final] ).
cnf(c_0_210,plain,
lhs_atom29(X1),
c_0_156,
[final] ).
cnf(c_0_211,plain,
lhs_atom28(X1),
c_0_157,
[final] ).
cnf(c_0_212,plain,
lhs_atom27(X1),
c_0_158,
[final] ).
cnf(c_0_213,plain,
lhs_atom26(X1),
c_0_159,
[final] ).
cnf(c_0_214,plain,
lhs_atom25(X1),
c_0_160,
[final] ).
cnf(c_0_215,plain,
lhs_atom24(X1),
c_0_161,
[final] ).
cnf(c_0_216,plain,
lhs_atom23(X1),
c_0_162,
[final] ).
cnf(c_0_217,plain,
lhs_atom21,
c_0_163,
[final] ).
cnf(c_0_218,plain,
lhs_atom20,
c_0_164,
[final] ).
cnf(c_0_219,plain,
lhs_atom20,
c_0_165,
[final] ).
cnf(c_0_220,plain,
lhs_atom20,
c_0_166,
[final] ).
cnf(c_0_221,plain,
lhs_atom20,
c_0_167,
[final] ).
% End CNF derivation
cnf(c_0_168_0,axiom,
( X1 = set_intersection2(X3,X2)
| ~ in(sk1_esk4_3(X1,X2,X3),X2)
| ~ in(sk1_esk4_3(X1,X2,X3),X3)
| ~ in(sk1_esk4_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_168,def_lhs_atom14]) ).
cnf(c_0_169_0,axiom,
( X1 = set_difference(X3,X2)
| in(sk1_esk5_3(X1,X2,X3),X2)
| ~ in(sk1_esk5_3(X1,X2,X3),X3)
| ~ in(sk1_esk5_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_169,def_lhs_atom16]) ).
cnf(c_0_170_0,axiom,
( X1 = set_union2(X3,X2)
| ~ in(sk1_esk2_3(X1,X2,X3),X1)
| ~ in(sk1_esk2_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_170,def_lhs_atom10]) ).
cnf(c_0_171_0,axiom,
( X1 = set_union2(X3,X2)
| ~ in(sk1_esk2_3(X1,X2,X3),X1)
| ~ in(sk1_esk2_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_171,def_lhs_atom10]) ).
cnf(c_0_172_0,axiom,
( X1 = set_union2(X3,X2)
| in(sk1_esk2_3(X1,X2,X3),X2)
| in(sk1_esk2_3(X1,X2,X3),X3)
| in(sk1_esk2_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_172,def_lhs_atom10]) ).
cnf(c_0_173_0,axiom,
( X1 = set_difference(X3,X2)
| in(sk1_esk5_3(X1,X2,X3),X1)
| ~ in(sk1_esk5_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_173,def_lhs_atom16]) ).
cnf(c_0_174_0,axiom,
( X1 = set_difference(X3,X2)
| in(sk1_esk5_3(X1,X2,X3),X1)
| in(sk1_esk5_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_174,def_lhs_atom16]) ).
cnf(c_0_175_0,axiom,
( X1 = set_intersection2(X3,X2)
| in(sk1_esk4_3(X1,X2,X3),X1)
| in(sk1_esk4_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_175,def_lhs_atom14]) ).
cnf(c_0_176_0,axiom,
( X1 = set_intersection2(X3,X2)
| in(sk1_esk4_3(X1,X2,X3),X1)
| in(sk1_esk4_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_176,def_lhs_atom14]) ).
cnf(c_0_177_0,axiom,
( X2 = X1
| ~ in(sk1_esk6_2(X1,X2),X1)
| ~ in(sk1_esk6_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_177,def_lhs_atom6]) ).
cnf(c_0_178_0,axiom,
( X1 != set_intersection2(X3,X2)
| in(X4,X1)
| ~ in(X4,X2)
| ~ in(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_178,def_lhs_atom13]) ).
cnf(c_0_179_0,axiom,
( X1 != set_difference(X3,X2)
| in(X4,X1)
| in(X4,X2)
| ~ in(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_179,def_lhs_atom15]) ).
cnf(c_0_180_0,axiom,
( X1 != set_union2(X3,X2)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_180,def_lhs_atom9]) ).
cnf(c_0_181_0,axiom,
( X1 != set_difference(X3,X2)
| ~ in(X4,X1)
| ~ in(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_181,def_lhs_atom15]) ).
cnf(c_0_182_0,axiom,
( X2 = X1
| in(sk1_esk6_2(X1,X2),X1)
| in(sk1_esk6_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_182,def_lhs_atom6]) ).
cnf(c_0_183_0,axiom,
( X1 != set_difference(X3,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_183,def_lhs_atom15]) ).
cnf(c_0_184_0,axiom,
( X1 != set_intersection2(X3,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_184,def_lhs_atom13]) ).
cnf(c_0_185_0,axiom,
( X1 != set_intersection2(X3,X2)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_185,def_lhs_atom13]) ).
cnf(c_0_186_0,axiom,
( X1 != set_union2(X3,X2)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_186,def_lhs_atom9]) ).
cnf(c_0_187_0,axiom,
( X1 != set_union2(X3,X2)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_187,def_lhs_atom9]) ).
cnf(c_0_188_0,axiom,
( subset(X2,X1)
| ~ in(sk1_esk3_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_188,def_lhs_atom12]) ).
cnf(c_0_189_0,axiom,
( X2 = X1
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_189,def_lhs_atom6]) ).
cnf(c_0_190_0,axiom,
( subset(X2,X1)
| in(sk1_esk3_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_190,def_lhs_atom12]) ).
cnf(c_0_191_0,axiom,
( empty(X2)
| ~ empty(set_union2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_191,def_lhs_atom22]) ).
cnf(c_0_192_0,axiom,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_192,def_lhs_atom22]) ).
cnf(c_0_193_0,axiom,
( ~ subset(X3,X2)
| in(X1,X2)
| ~ in(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_193,def_lhs_atom11]) ).
cnf(c_0_194_0,axiom,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_194,def_lhs_atom19]) ).
cnf(c_0_195_0,axiom,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(unfold_definition,[status(thm)],[c_0_195,def_lhs_atom18]) ).
cnf(c_0_196_0,axiom,
( ~ proper_subset(X2,X1)
| ~ proper_subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_196,def_lhs_atom2]) ).
cnf(c_0_197_0,axiom,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_197,def_lhs_atom1]) ).
cnf(c_0_198_0,axiom,
( ~ disjoint(X2,X1)
| disjoint(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_198,def_lhs_atom17]) ).
cnf(c_0_199_0,axiom,
( ~ proper_subset(X2,X1)
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_199,def_lhs_atom2]) ).
cnf(c_0_200_0,axiom,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_200,def_lhs_atom17]) ).
cnf(c_0_201_0,axiom,
( X2 != X1
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_201,def_lhs_atom5]) ).
cnf(c_0_202_0,axiom,
( X2 != X1
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_202,def_lhs_atom5]) ).
cnf(c_0_203_0,axiom,
( X2 != empty_set
| ~ in(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_203,def_lhs_atom7]) ).
cnf(c_0_204_0,axiom,
( X1 = empty_set
| in(sk1_esk1_1(X1),X1) ),
inference(unfold_definition,[status(thm)],[c_0_204,def_lhs_atom8]) ).
cnf(c_0_205_0,axiom,
( ~ proper_subset(X2,X1)
| X2 != X1 ),
inference(unfold_definition,[status(thm)],[c_0_205,def_lhs_atom2]) ).
cnf(c_0_208_0,axiom,
( ~ empty(X1)
| X1 = empty_set ),
inference(unfold_definition,[status(thm)],[c_0_208,def_lhs_atom31]) ).
cnf(c_0_206_0,axiom,
set_intersection2(X2,X1) = set_intersection2(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_206,def_lhs_atom4]) ).
cnf(c_0_207_0,axiom,
set_union2(X2,X1) = set_union2(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_207,def_lhs_atom3]) ).
cnf(c_0_209_0,axiom,
set_difference(empty_set,X1) = empty_set,
inference(unfold_definition,[status(thm)],[c_0_209,def_lhs_atom30]) ).
cnf(c_0_210_0,axiom,
set_difference(X1,empty_set) = X1,
inference(unfold_definition,[status(thm)],[c_0_210,def_lhs_atom29]) ).
cnf(c_0_211_0,axiom,
set_intersection2(X1,empty_set) = empty_set,
inference(unfold_definition,[status(thm)],[c_0_211,def_lhs_atom28]) ).
cnf(c_0_212_0,axiom,
set_union2(X1,empty_set) = X1,
inference(unfold_definition,[status(thm)],[c_0_212,def_lhs_atom27]) ).
cnf(c_0_213_0,axiom,
subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_213,def_lhs_atom26]) ).
cnf(c_0_214_0,axiom,
~ proper_subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_214,def_lhs_atom25]) ).
cnf(c_0_215_0,axiom,
set_intersection2(X1,X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_215,def_lhs_atom24]) ).
cnf(c_0_216_0,axiom,
set_union2(X1,X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_216,def_lhs_atom23]) ).
cnf(c_0_217_0,axiom,
empty(empty_set),
inference(unfold_definition,[status(thm)],[c_0_217,def_lhs_atom21]) ).
cnf(c_0_218_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_218,def_lhs_atom20]) ).
cnf(c_0_219_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_219,def_lhs_atom20]) ).
cnf(c_0_220_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_220,def_lhs_atom20]) ).
cnf(c_0_221_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_221,def_lhs_atom20]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('<stdin>',t7_boole) ).
fof(c_0_1_002,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('<stdin>',t8_boole) ).
fof(c_0_2_003,axiom,
? [X1] : ~ empty(X1),
file('<stdin>',rc2_xboole_0) ).
fof(c_0_3_004,axiom,
? [X1] : empty(X1),
file('<stdin>',rc1_xboole_0) ).
fof(c_0_4_005,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
c_0_0 ).
fof(c_0_5_006,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
c_0_1 ).
fof(c_0_6_007,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_7_008,axiom,
? [X1] : empty(X1),
c_0_3 ).
fof(c_0_8_009,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
fof(c_0_9_010,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_5])])])]) ).
fof(c_0_10_011,plain,
~ empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_11_012,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
cnf(c_0_12_013,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_014,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14_015,plain,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15_016,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16_017,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
c_0_12,
[final] ).
cnf(c_0_17_018,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
c_0_13,
[final] ).
cnf(c_0_18_019,plain,
~ empty(esk1_0),
c_0_14,
[final] ).
cnf(c_0_19_020,plain,
empty(esk2_0),
c_0_15,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_16_0,axiom,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_16_1,axiom,
( ~ in(X2,X1)
| ~ empty(X1) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_17_0,axiom,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_17_1,axiom,
( ~ empty(X1)
| X2 = X1
| ~ empty(X2) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_17_2,axiom,
( ~ empty(X2)
| ~ empty(X1)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_18_0,axiom,
~ empty(sk2_esk1_0),
inference(literals_permutation,[status(thm)],[c_0_18]) ).
cnf(c_0_19_0,axiom,
empty(sk2_esk2_0),
inference(literals_permutation,[status(thm)],[c_0_19]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_021,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('<stdin>',t33_xboole_1) ).
fof(c_0_1_022,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('<stdin>',t26_xboole_1) ).
fof(c_0_2_023,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('<stdin>',t4_xboole_0) ).
fof(c_0_3_024,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('<stdin>',t8_xboole_1) ).
fof(c_0_4_025,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('<stdin>',t19_xboole_1) ).
fof(c_0_5_026,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('<stdin>',t3_xboole_0) ).
fof(c_0_6_027,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
file('<stdin>',t45_xboole_1) ).
fof(c_0_7_028,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('<stdin>',t63_xboole_1) ).
fof(c_0_8_029,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('<stdin>',t1_xboole_1) ).
fof(c_0_9_030,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('<stdin>',t48_xboole_1) ).
fof(c_0_10_031,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('<stdin>',t40_xboole_1) ).
fof(c_0_11_032,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('<stdin>',t39_xboole_1) ).
fof(c_0_12_033,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
file('<stdin>',t60_xboole_1) ).
fof(c_0_13_034,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('<stdin>',t7_xboole_1) ).
fof(c_0_14_035,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('<stdin>',t36_xboole_1) ).
fof(c_0_15_036,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('<stdin>',t17_xboole_1) ).
fof(c_0_16_037,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('<stdin>',t28_xboole_1) ).
fof(c_0_17_038,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('<stdin>',t12_xboole_1) ).
fof(c_0_18_039,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',t37_xboole_1) ).
fof(c_0_19_040,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('<stdin>',l32_xboole_1) ).
fof(c_0_20_041,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('<stdin>',t83_xboole_1) ).
fof(c_0_21_042,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('<stdin>',t3_xboole_1) ).
fof(c_0_22_043,lemma,
! [X1] : subset(empty_set,X1),
file('<stdin>',t2_xboole_1) ).
fof(c_0_23_044,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
c_0_0 ).
fof(c_0_24_045,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
c_0_1 ).
fof(c_0_25_046,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_26_047,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
c_0_3 ).
fof(c_0_27_048,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
c_0_4 ).
fof(c_0_28_049,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_29_050,lemma,
! [X1,X2] :
( subset(X1,X2)
=> X2 = set_union2(X1,set_difference(X2,X1)) ),
c_0_6 ).
fof(c_0_30_051,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
c_0_7 ).
fof(c_0_31_052,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
c_0_8 ).
fof(c_0_32_053,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_9 ).
fof(c_0_33_054,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_10 ).
fof(c_0_34_055,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_11 ).
fof(c_0_35_056,lemma,
! [X1,X2] :
~ ( subset(X1,X2)
& proper_subset(X2,X1) ),
c_0_12 ).
fof(c_0_36_057,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
c_0_13 ).
fof(c_0_37_058,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
c_0_14 ).
fof(c_0_38_059,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
c_0_15 ).
fof(c_0_39_060,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
c_0_16 ).
fof(c_0_40_061,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
c_0_17 ).
fof(c_0_41_062,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_18 ).
fof(c_0_42_063,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
c_0_19 ).
fof(c_0_43_064,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[c_0_20]) ).
fof(c_0_44_065,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
c_0_21 ).
fof(c_0_45_066,lemma,
! [X1] : subset(empty_set,X1),
c_0_22 ).
fof(c_0_46_067,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_difference(X4,X6),set_difference(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_47_068,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_intersection2(X4,X6),set_intersection2(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_48_069,lemma,
! [X4,X5,X7,X8,X9] :
( ( disjoint(X4,X5)
| in(esk2_2(X4,X5),set_intersection2(X4,X5)) )
& ( ~ in(X9,set_intersection2(X7,X8))
| ~ disjoint(X7,X8) ) ),
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_25])])])])]) ).
fof(c_0_49_070,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X6,X5)
| subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_50_071,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X4,X6)
| subset(X4,set_intersection2(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
fof(c_0_51_072,lemma,
! [X4,X5,X7,X8,X9] :
( ( in(esk1_2(X4,X5),X4)
| disjoint(X4,X5) )
& ( in(esk1_2(X4,X5),X5)
| disjoint(X4,X5) )
& ( ~ in(X9,X7)
| ~ in(X9,X8)
| ~ disjoint(X7,X8) ) ),
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_52_073,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| X4 = set_union2(X3,set_difference(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
fof(c_0_53_074,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ disjoint(X5,X6)
| disjoint(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).
fof(c_0_54_075,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
fof(c_0_55_076,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_32]) ).
fof(c_0_56_077,lemma,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[c_0_33]) ).
fof(c_0_57_078,lemma,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_34]) ).
fof(c_0_58_079,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| ~ proper_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
fof(c_0_59_080,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_36]) ).
fof(c_0_60_081,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_37]) ).
fof(c_0_61_082,lemma,
! [X3,X4] : subset(set_intersection2(X3,X4),X3),
inference(variable_rename,[status(thm)],[c_0_38]) ).
fof(c_0_62_083,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
fof(c_0_63_084,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])]) ).
fof(c_0_64_085,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
fof(c_0_65_086,lemma,
! [X3,X4,X5,X6] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X5,X6)
| set_difference(X5,X6) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
fof(c_0_66_087,negated_conjecture,
( ( ~ disjoint(esk3_0,esk4_0)
| set_difference(esk3_0,esk4_0) != esk3_0 )
& ( disjoint(esk3_0,esk4_0)
| set_difference(esk3_0,esk4_0) = esk3_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
fof(c_0_67_088,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])]) ).
fof(c_0_68_089,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[c_0_45]) ).
cnf(c_0_69_090,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_70_091,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_71_092,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_72_093,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_73_094,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_74_095,lemma,
( in(esk2_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_75_096,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_76_097,lemma,
( X1 = set_union2(X2,set_difference(X1,X2))
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_77_098,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_78_099,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_79_100,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_80_101,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_81_102,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_82_103,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_83_104,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_84_105,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_85_106,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_86_107,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_87_108,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_88_109,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_89_110,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_90_111,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_91_112,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_92_113,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_93_114,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_94_115,negated_conjecture,
( set_difference(esk3_0,esk4_0) != esk3_0
| ~ disjoint(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_95_116,negated_conjecture,
( set_difference(esk3_0,esk4_0) = esk3_0
| disjoint(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_96_117,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_97_118,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_98_119,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
c_0_69,
[final] ).
cnf(c_0_99_120,lemma,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
| ~ subset(X1,X3) ),
c_0_70,
[final] ).
cnf(c_0_100_121,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
c_0_71,
[final] ).
cnf(c_0_101_122,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
c_0_72,
[final] ).
cnf(c_0_102_123,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
c_0_73,
[final] ).
cnf(c_0_103_124,lemma,
( in(esk2_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
c_0_74,
[final] ).
cnf(c_0_104_125,lemma,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
c_0_75,
[final] ).
cnf(c_0_105_126,lemma,
( set_union2(X2,set_difference(X1,X2)) = X1
| ~ subset(X2,X1) ),
c_0_76,
[final] ).
cnf(c_0_106_127,lemma,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
c_0_77,
[final] ).
cnf(c_0_107_128,lemma,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
c_0_78,
[final] ).
cnf(c_0_108_129,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X1) ),
c_0_79,
[final] ).
cnf(c_0_109_130,lemma,
( disjoint(X1,X2)
| in(esk1_2(X1,X2),X2) ),
c_0_80,
[final] ).
cnf(c_0_110_131,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
c_0_81,
[final] ).
cnf(c_0_111_132,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
c_0_82,
[final] ).
cnf(c_0_112_133,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
c_0_83,
[final] ).
cnf(c_0_113_134,lemma,
( ~ proper_subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_84,
[final] ).
cnf(c_0_114_135,lemma,
subset(X1,set_union2(X1,X2)),
c_0_85,
[final] ).
cnf(c_0_115_136,lemma,
subset(set_difference(X1,X2),X1),
c_0_86,
[final] ).
cnf(c_0_116_137,lemma,
subset(set_intersection2(X1,X2),X1),
c_0_87,
[final] ).
cnf(c_0_117_138,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
c_0_88,
[final] ).
cnf(c_0_118_139,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
c_0_89,
[final] ).
cnf(c_0_119_140,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_90,
[final] ).
cnf(c_0_120_141,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_91,
[final] ).
cnf(c_0_121_142,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
c_0_92,
[final] ).
cnf(c_0_122_143,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
c_0_93,
[final] ).
cnf(c_0_123_144,negated_conjecture,
( set_difference(esk3_0,esk4_0) != esk3_0
| ~ disjoint(esk3_0,esk4_0) ),
c_0_94,
[final] ).
cnf(c_0_124_145,negated_conjecture,
( set_difference(esk3_0,esk4_0) = esk3_0
| disjoint(esk3_0,esk4_0) ),
c_0_95,
[final] ).
cnf(c_0_125_146,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
c_0_96,
[final] ).
cnf(c_0_126_147,lemma,
subset(empty_set,X1),
c_0_97,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_84,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_111) ).
cnf(c_173,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(copy,[status(esa)],[c_84]) ).
cnf(c_214,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(copy,[status(esa)],[c_173]) ).
cnf(c_225,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(copy,[status(esa)],[c_214]) ).
cnf(c_261,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(copy,[status(esa)],[c_225]) ).
cnf(c_504,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(copy,[status(esa)],[c_261]) ).
cnf(c_27,plain,
( subset(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_201_0) ).
cnf(c_408,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(copy,[status(esa)],[c_27]) ).
cnf(c_1036,plain,
subset(set_difference(set_union2(X0,X1),X1),set_difference(X0,X1)),
inference(resolution,[status(thm)],[c_504,c_408]) ).
cnf(c_1037,plain,
subset(set_difference(set_union2(X0,X1),X1),set_difference(X0,X1)),
inference(rewriting,[status(thm)],[c_1036]) ).
cnf(c_35,plain,
( ~ in(X0,X1)
| in(X0,X2)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_193_0) ).
cnf(c_424,plain,
( ~ in(X0,X1)
| in(X0,X2)
| ~ subset(X1,X2) ),
inference(copy,[status(esa)],[c_35]) ).
cnf(c_3517,plain,
( ~ in(X0,set_difference(set_union2(X1,X2),X2))
| in(X0,set_difference(X1,X2)) ),
inference(resolution,[status(thm)],[c_1037,c_424]) ).
cnf(c_3518,plain,
( ~ in(X0,set_difference(set_union2(X1,X2),X2))
| in(X0,set_difference(X1,X2)) ),
inference(rewriting,[status(thm)],[c_3517]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,X3)
| X3 != set_difference(X1,X2) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_179_0) ).
cnf(c_452,plain,
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,X3)
| X3 != set_difference(X1,X2) ),
inference(copy,[status(esa)],[c_49]) ).
cnf(c_1042,plain,
( in(X0,set_difference(set_union2(X1,X2),X2))
| ~ in(X0,X1)
| in(X0,X2) ),
inference(resolution,[status(thm)],[c_504,c_452]) ).
cnf(c_1043,plain,
( in(X0,set_difference(set_union2(X1,X2),X2))
| ~ in(X0,X1)
| in(X0,X2) ),
inference(rewriting,[status(thm)],[c_1042]) ).
cnf(c_38754,plain,
( in(X0,set_difference(X1,X2))
| ~ in(X0,X1)
| in(X0,X2) ),
inference(resolution,[status(thm)],[c_3518,c_1043]) ).
cnf(c_38755,plain,
( in(X0,set_difference(X1,X2))
| ~ in(X0,X1)
| in(X0,X2) ),
inference(rewriting,[status(thm)],[c_38754]) ).
cnf(c_75,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_118) ).
cnf(c_159,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_75]) ).
cnf(c_207,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_159]) ).
cnf(c_232,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_207]) ).
cnf(c_254,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_232]) ).
cnf(c_490,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(copy,[status(esa)],[c_254]) ).
cnf(c_47,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| X2 != set_difference(X3,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_181_0) ).
cnf(c_448,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| X2 != set_difference(X3,X1) ),
inference(copy,[status(esa)],[c_47]) ).
cnf(c_872,plain,
( ~ in(X0,set_union2(X1,set_difference(X2,X3)))
| ~ in(X0,X3)
| ~ subset(X1,set_difference(X2,X3)) ),
inference(resolution,[status(thm)],[c_490,c_448]) ).
cnf(c_873,plain,
( ~ in(X0,set_union2(X1,set_difference(X2,X3)))
| ~ in(X0,X3)
| ~ subset(X1,set_difference(X2,X3)) ),
inference(rewriting,[status(thm)],[c_872]) ).
cnf(c_86,plain,
subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_114) ).
cnf(c_177,plain,
subset(X0,set_union2(X0,X1)),
inference(copy,[status(esa)],[c_86]) ).
cnf(c_216,plain,
subset(X0,set_union2(X0,X1)),
inference(copy,[status(esa)],[c_177]) ).
cnf(c_223,plain,
subset(X0,set_union2(X0,X1)),
inference(copy,[status(esa)],[c_216]) ).
cnf(c_263,plain,
subset(X0,set_union2(X0,X1)),
inference(copy,[status(esa)],[c_223]) ).
cnf(c_508,plain,
subset(X0,set_union2(X0,X1)),
inference(copy,[status(esa)],[c_263]) ).
cnf(c_668,plain,
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c_508,c_424]) ).
cnf(c_669,plain,
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(rewriting,[status(thm)],[c_668]) ).
cnf(c_12312,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,set_difference(X3,X1)) ),
inference(resolution,[status(thm)],[c_873,c_669]) ).
cnf(c_12313,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,set_difference(X3,X1)) ),
inference(rewriting,[status(thm)],[c_12312]) ).
cnf(c_81,negated_conjecture,
( disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) = sk3_esk3_0 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_124) ).
cnf(c_187,negated_conjecture,
( disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) = sk3_esk3_0 ),
inference(copy,[status(esa)],[c_81]) ).
cnf(c_211,negated_conjecture,
( disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) = sk3_esk3_0 ),
inference(copy,[status(esa)],[c_187]) ).
cnf(c_228,negated_conjecture,
( disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) = sk3_esk3_0 ),
inference(copy,[status(esa)],[c_211]) ).
cnf(c_258,negated_conjecture,
( disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) = sk3_esk3_0 ),
inference(copy,[status(esa)],[c_228]) ).
cnf(c_498,negated_conjecture,
( disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) = sk3_esk3_0 ),
inference(copy,[status(esa)],[c_258]) ).
cnf(c_26,plain,
( subset(X0,X1)
| X1 != X0 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_202_0) ).
cnf(c_406,plain,
( subset(X0,X1)
| X1 != X0 ),
inference(copy,[status(esa)],[c_26]) ).
cnf(c_532,plain,
( subset(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0))
| disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_498,c_406]) ).
cnf(c_533,plain,
( subset(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0))
| disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_532]) ).
cnf(c_19552,plain,
( ~ in(X0,sk3_esk3_0)
| ~ in(X0,sk3_esk4_0)
| disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_12313,c_533]) ).
cnf(c_19553,plain,
( ~ in(X0,sk3_esk3_0)
| ~ in(X0,sk3_esk4_0)
| disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_19552]) ).
cnf(c_67,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_104) ).
cnf(c_143,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_67]) ).
cnf(c_199,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_143]) ).
cnf(c_240,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_199]) ).
cnf(c_247,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_240]) ).
cnf(c_476,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(copy,[status(esa)],[c_247]) ).
cnf(c_911015,plain,
( ~ in(X0,sk3_esk3_0)
| ~ in(X0,sk3_esk4_0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19553,c_476]) ).
cnf(c_911016,plain,
( ~ in(X0,sk3_esk3_0)
| ~ in(X0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_911015]) ).
cnf(c_72,plain,
( in(sk3_esk1_2(X0,X1),X1)
| disjoint(X0,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_109) ).
cnf(c_153,plain,
( in(sk3_esk1_2(X0,X1),X1)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_72]) ).
cnf(c_204,plain,
( in(sk3_esk1_2(X0,X1),X1)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_153]) ).
cnf(c_235,plain,
( in(sk3_esk1_2(X0,X1),X1)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_204]) ).
cnf(c_252,plain,
( in(sk3_esk1_2(X0,X1),X1)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_235]) ).
cnf(c_486,plain,
( in(sk3_esk1_2(X0,X1),X1)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_252]) ).
cnf(c_911081,plain,
( ~ in(sk3_esk1_2(X0,sk3_esk4_0),sk3_esk3_0)
| disjoint(X0,sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_911016,c_486]) ).
cnf(c_911082,plain,
( ~ in(sk3_esk1_2(X0,sk3_esk4_0),sk3_esk3_0)
| disjoint(X0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_911081]) ).
cnf(c_71,plain,
( in(sk3_esk1_2(X0,X1),X0)
| disjoint(X0,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_108) ).
cnf(c_151,plain,
( in(sk3_esk1_2(X0,X1),X0)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_71]) ).
cnf(c_203,plain,
( in(sk3_esk1_2(X0,X1),X0)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_151]) ).
cnf(c_236,plain,
( in(sk3_esk1_2(X0,X1),X0)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_203]) ).
cnf(c_251,plain,
( in(sk3_esk1_2(X0,X1),X0)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_236]) ).
cnf(c_484,plain,
( in(sk3_esk1_2(X0,X1),X0)
| disjoint(X0,X1) ),
inference(copy,[status(esa)],[c_251]) ).
cnf(c_911891,plain,
disjoint(sk3_esk3_0,sk3_esk4_0),
inference(resolution,[status(thm)],[c_911082,c_484]) ).
cnf(c_911892,plain,
disjoint(sk3_esk3_0,sk3_esk4_0),
inference(rewriting,[status(thm)],[c_911891]) ).
cnf(c_87,plain,
subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_115) ).
cnf(c_179,plain,
subset(set_difference(X0,X1),X0),
inference(copy,[status(esa)],[c_87]) ).
cnf(c_217,plain,
subset(set_difference(X0,X1),X0),
inference(copy,[status(esa)],[c_179]) ).
cnf(c_222,plain,
subset(set_difference(X0,X1),X0),
inference(copy,[status(esa)],[c_217]) ).
cnf(c_264,plain,
subset(set_difference(X0,X1),X0),
inference(copy,[status(esa)],[c_222]) ).
cnf(c_510,plain,
subset(set_difference(X0,X1),X0),
inference(copy,[status(esa)],[c_264]) ).
cnf(c_674,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(resolution,[status(thm)],[c_510,c_424]) ).
cnf(c_675,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(rewriting,[status(thm)],[c_674]) ).
cnf(c_80,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) != sk3_esk3_0 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_123) ).
cnf(c_185,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) != sk3_esk3_0 ),
inference(copy,[status(esa)],[c_80]) ).
cnf(c_210,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) != sk3_esk3_0 ),
inference(copy,[status(esa)],[c_185]) ).
cnf(c_229,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) != sk3_esk3_0 ),
inference(copy,[status(esa)],[c_210]) ).
cnf(c_257,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) != sk3_esk3_0 ),
inference(copy,[status(esa)],[c_229]) ).
cnf(c_496,negated_conjecture,
( ~ disjoint(sk3_esk3_0,sk3_esk4_0)
| set_difference(sk3_esk3_0,sk3_esk4_0) != sk3_esk3_0 ),
inference(copy,[status(esa)],[c_257]) ).
cnf(c_51,plain,
( ~ in(sk1_esk6_2(X0,X1),X1)
| ~ in(sk1_esk6_2(X0,X1),X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_177_0) ).
cnf(c_456,plain,
( ~ in(sk1_esk6_2(X0,X1),X1)
| ~ in(sk1_esk6_2(X0,X1),X0)
| X1 = X0 ),
inference(copy,[status(esa)],[c_51]) ).
cnf(c_540,plain,
( ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0))
| ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_496,c_456]) ).
cnf(c_543,plain,
( ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0))
| ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_540]) ).
cnf(c_739,plain,
( ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0))
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_675,c_543]) ).
cnf(c_741,plain,
( ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0))
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_739]) ).
cnf(c_913193,plain,
~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0)),
inference(backward_subsumption_resolution,[status(thm)],[c_911892,c_741]) ).
cnf(c_913202,plain,
~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0)),
inference(rewriting,[status(thm)],[c_913193]) ).
cnf(c_1099416,plain,
( ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_38755,c_913202]) ).
cnf(c_1099417,plain,
( ~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_1099416]) ).
cnf(c_46,plain,
( in(sk1_esk6_2(X0,X1),X1)
| in(sk1_esk6_2(X0,X1),X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p',c_0_182_0) ).
cnf(c_446,plain,
( in(sk1_esk6_2(X0,X1),X1)
| in(sk1_esk6_2(X0,X1),X0)
| X1 = X0 ),
inference(copy,[status(esa)],[c_46]) ).
cnf(c_541,plain,
( in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0))
| in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(resolution,[status(thm)],[c_496,c_446]) ).
cnf(c_542,plain,
( in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),set_difference(sk3_esk3_0,sk3_esk4_0))
| in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_541]) ).
cnf(c_737,plain,
( in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_675,c_542]) ).
cnf(c_740,plain,
( in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0)
| ~ disjoint(sk3_esk3_0,sk3_esk4_0) ),
inference(rewriting,[status(thm)],[c_737]) ).
cnf(c_913191,plain,
in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0),
inference(backward_subsumption_resolution,[status(thm)],[c_911892,c_740]) ).
cnf(c_913204,plain,
in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0),
inference(rewriting,[status(thm)],[c_913191]) ).
cnf(c_1100734,plain,
in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk4_0),
inference(forward_subsumption_resolution,[status(thm)],[c_1099417,c_913204]) ).
cnf(c_1100735,plain,
in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk4_0),
inference(rewriting,[status(thm)],[c_1100734]) ).
cnf(c_1100755,plain,
~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0),
inference(resolution,[status(thm)],[c_1100735,c_911016]) ).
cnf(c_1100756,plain,
~ in(sk1_esk6_2(sk3_esk3_0,set_difference(sk3_esk3_0,sk3_esk4_0)),sk3_esk3_0),
inference(rewriting,[status(thm)],[c_1100755]) ).
cnf(c_1100790,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1100756,c_913204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : iprover_modulo %s %d
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 01:50:59 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % Running in mono-core mode
% 0.22/0.44 % Orienting using strategy Equiv(ClausalAll)
% 0.22/0.44 % FOF problem with conjecture
% 0.22/0.44 % 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_a7b3be.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_272f1c.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_383588 | grep -v "SZS"
% 0.22/0.47
% 0.22/0.47 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.22/0.47
% 0.22/0.47 %
% 0.22/0.47 % ------ iProver source info
% 0.22/0.47
% 0.22/0.47 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.22/0.47 % git: non_committed_changes: true
% 0.22/0.47 % git: last_make_outside_of_git: true
% 0.22/0.47
% 0.22/0.47 %
% 0.22/0.47 % ------ Input Options
% 0.22/0.47
% 0.22/0.47 % --out_options all
% 0.22/0.47 % --tptp_safe_out true
% 0.22/0.47 % --problem_path ""
% 0.22/0.47 % --include_path ""
% 0.22/0.47 % --clausifier .//eprover
% 0.22/0.47 % --clausifier_options --tstp-format
% 0.22/0.47 % --stdin false
% 0.22/0.47 % --dbg_backtrace false
% 0.22/0.47 % --dbg_dump_prop_clauses false
% 0.22/0.47 % --dbg_dump_prop_clauses_file -
% 0.22/0.47 % --dbg_out_stat false
% 0.22/0.47
% 0.22/0.47 % ------ General Options
% 0.22/0.47
% 0.22/0.47 % --fof false
% 0.22/0.47 % --time_out_real 150.
% 0.22/0.47 % --time_out_prep_mult 0.2
% 0.22/0.47 % --time_out_virtual -1.
% 0.22/0.47 % --schedule none
% 0.22/0.47 % --ground_splitting input
% 0.22/0.47 % --splitting_nvd 16
% 0.22/0.47 % --non_eq_to_eq false
% 0.22/0.47 % --prep_gs_sim true
% 0.22/0.47 % --prep_unflatten false
% 0.22/0.47 % --prep_res_sim true
% 0.22/0.47 % --prep_upred true
% 0.22/0.47 % --res_sim_input true
% 0.22/0.47 % --clause_weak_htbl true
% 0.22/0.47 % --gc_record_bc_elim false
% 0.22/0.47 % --symbol_type_check false
% 0.22/0.47 % --clausify_out false
% 0.22/0.47 % --large_theory_mode false
% 0.22/0.47 % --prep_sem_filter none
% 0.22/0.47 % --prep_sem_filter_out false
% 0.22/0.47 % --preprocessed_out false
% 0.22/0.47 % --sub_typing false
% 0.22/0.47 % --brand_transform false
% 0.22/0.47 % --pure_diseq_elim true
% 0.22/0.47 % --min_unsat_core false
% 0.22/0.47 % --pred_elim true
% 0.22/0.47 % --add_important_lit false
% 0.22/0.47 % --soft_assumptions false
% 0.22/0.47 % --reset_solvers false
% 0.22/0.47 % --bc_imp_inh []
% 0.22/0.47 % --conj_cone_tolerance 1.5
% 0.22/0.47 % --prolific_symb_bound 500
% 0.22/0.47 % --lt_threshold 2000
% 0.22/0.47
% 0.22/0.47 % ------ SAT Options
% 0.22/0.47
% 0.22/0.47 % --sat_mode false
% 0.22/0.47 % --sat_fm_restart_options ""
% 0.22/0.47 % --sat_gr_def false
% 0.22/0.47 % --sat_epr_types true
% 0.22/0.47 % --sat_non_cyclic_types false
% 0.22/0.47 % --sat_finite_models false
% 0.22/0.47 % --sat_fm_lemmas false
% 0.22/0.47 % --sat_fm_prep false
% 0.22/0.47 % --sat_fm_uc_incr true
% 0.22/0.47 % --sat_out_model small
% 0.22/0.47 % --sat_out_clauses false
% 0.22/0.47
% 0.22/0.47 % ------ QBF Options
% 0.22/0.47
% 0.22/0.47 % --qbf_mode false
% 0.22/0.47 % --qbf_elim_univ true
% 0.22/0.47 % --qbf_sk_in true
% 0.22/0.47 % --qbf_pred_elim true
% 0.22/0.47 % --qbf_split 32
% 0.22/0.47
% 0.22/0.47 % ------ BMC1 Options
% 0.22/0.47
% 0.22/0.47 % --bmc1_incremental false
% 0.22/0.47 % --bmc1_axioms reachable_all
% 0.22/0.47 % --bmc1_min_bound 0
% 0.22/0.47 % --bmc1_max_bound -1
% 0.22/0.47 % --bmc1_max_bound_default -1
% 0.22/0.47 % --bmc1_symbol_reachability true
% 0.22/0.47 % --bmc1_property_lemmas false
% 0.22/0.47 % --bmc1_k_induction false
% 0.22/0.47 % --bmc1_non_equiv_states false
% 0.22/0.47 % --bmc1_deadlock false
% 0.22/0.47 % --bmc1_ucm false
% 0.22/0.47 % --bmc1_add_unsat_core none
% 0.22/0.47 % --bmc1_unsat_core_children false
% 0.22/0.47 % --bmc1_unsat_core_extrapolate_axioms false
% 0.22/0.47 % --bmc1_out_stat full
% 0.22/0.47 % --bmc1_ground_init false
% 0.22/0.47 % --bmc1_pre_inst_next_state false
% 0.22/0.47 % --bmc1_pre_inst_state false
% 0.22/0.47 % --bmc1_pre_inst_reach_state false
% 0.22/0.47 % --bmc1_out_unsat_core false
% 0.22/0.47 % --bmc1_aig_witness_out false
% 0.22/0.47 % --bmc1_verbose false
% 0.22/0.47 % --bmc1_dump_clauses_tptp false
% 0.40/0.73 % --bmc1_dump_unsat_core_tptp false
% 0.40/0.73 % --bmc1_dump_file -
% 0.40/0.73 % --bmc1_ucm_expand_uc_limit 128
% 0.40/0.73 % --bmc1_ucm_n_expand_iterations 6
% 0.40/0.73 % --bmc1_ucm_extend_mode 1
% 0.40/0.73 % --bmc1_ucm_init_mode 2
% 0.40/0.73 % --bmc1_ucm_cone_mode none
% 0.40/0.73 % --bmc1_ucm_reduced_relation_type 0
% 0.40/0.73 % --bmc1_ucm_relax_model 4
% 0.40/0.73 % --bmc1_ucm_full_tr_after_sat true
% 0.40/0.73 % --bmc1_ucm_expand_neg_assumptions false
% 0.40/0.73 % --bmc1_ucm_layered_model none
% 0.40/0.73 % --bmc1_ucm_max_lemma_size 10
% 0.40/0.73
% 0.40/0.73 % ------ AIG Options
% 0.40/0.73
% 0.40/0.73 % --aig_mode false
% 0.40/0.73
% 0.40/0.73 % ------ Instantiation Options
% 0.40/0.73
% 0.40/0.73 % --instantiation_flag true
% 0.40/0.73 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.40/0.73 % --inst_solver_per_active 750
% 0.40/0.73 % --inst_solver_calls_frac 0.5
% 0.40/0.73 % --inst_passive_queue_type priority_queues
% 0.40/0.73 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.40/0.73 % --inst_passive_queues_freq [25;2]
% 0.40/0.73 % --inst_dismatching true
% 0.40/0.73 % --inst_eager_unprocessed_to_passive true
% 0.40/0.73 % --inst_prop_sim_given true
% 0.40/0.73 % --inst_prop_sim_new false
% 0.40/0.73 % --inst_orphan_elimination true
% 0.40/0.73 % --inst_learning_loop_flag true
% 0.40/0.73 % --inst_learning_start 3000
% 0.40/0.73 % --inst_learning_factor 2
% 0.40/0.73 % --inst_start_prop_sim_after_learn 3
% 0.40/0.73 % --inst_sel_renew solver
% 0.40/0.73 % --inst_lit_activity_flag true
% 0.40/0.73 % --inst_out_proof true
% 0.40/0.73
% 0.40/0.73 % ------ Resolution Options
% 0.40/0.73
% 0.40/0.73 % --resolution_flag true
% 0.40/0.73 % --res_lit_sel kbo_max
% 0.40/0.73 % --res_to_prop_solver none
% 0.40/0.73 % --res_prop_simpl_new false
% 0.40/0.73 % --res_prop_simpl_given false
% 0.40/0.73 % --res_passive_queue_type priority_queues
% 0.40/0.73 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.40/0.73 % --res_passive_queues_freq [15;5]
% 0.40/0.73 % --res_forward_subs full
% 0.40/0.73 % --res_backward_subs full
% 0.40/0.73 % --res_forward_subs_resolution true
% 0.40/0.73 % --res_backward_subs_resolution true
% 0.40/0.73 % --res_orphan_elimination false
% 0.40/0.73 % --res_time_limit 1000.
% 0.40/0.73 % --res_out_proof true
% 0.40/0.73 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_a7b3be.s
% 0.40/0.73 % --modulo true
% 0.40/0.73
% 0.40/0.73 % ------ Combination Options
% 0.40/0.73
% 0.40/0.73 % --comb_res_mult 1000
% 0.40/0.73 % --comb_inst_mult 300
% 0.40/0.73 % ------
% 0.40/0.73
% 0.40/0.73 % ------ Parsing...% successful
% 0.40/0.73
% 0.40/0.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe_e snvd_s sp: 0 0s snvd_e %
% 0.40/0.73
% 0.40/0.73 % ------ Proving...
% 0.40/0.73 % ------ Problem Properties
% 0.40/0.73
% 0.40/0.73 %
% 0.40/0.73 % EPR false
% 0.40/0.73 % Horn false
% 0.40/0.73 % Has equality true
% 0.40/0.73
% 0.40/0.73 % % ------ Input Options Time Limit: Unbounded
% 0.40/0.73
% 0.40/0.73
% 0.40/0.73 Compiling...
% 0.40/0.73 Loading plugin: done.
% 0.40/0.73 Compiling...
% 0.40/0.73 Loading plugin: done.
% 0.40/0.73 % % ------ Current options:
% 0.40/0.73
% 0.40/0.73 % ------ Input Options
% 0.40/0.73
% 0.40/0.73 % --out_options all
% 0.40/0.73 % --tptp_safe_out true
% 0.40/0.73 % --problem_path ""
% 0.40/0.73 % --include_path ""
% 0.40/0.73 % --clausifier .//eprover
% 0.40/0.73 % --clausifier_options --tstp-format
% 0.40/0.73 % --stdin false
% 0.40/0.73 % --dbg_backtrace false
% 0.40/0.73 % --dbg_dump_prop_clauses false
% 0.40/0.73 % --dbg_dump_prop_clauses_file -
% 0.40/0.73 % --dbg_out_stat false
% 0.40/0.73
% 0.40/0.73 % ------ General Options
% 0.40/0.73
% 0.40/0.73 % --fof false
% 0.40/0.73 % --time_out_real 150.
% 0.40/0.73 % --time_out_prep_mult 0.2
% 0.40/0.73 % --time_out_virtual -1.
% 0.40/0.73 % --schedule none
% 0.40/0.73 % --ground_splitting input
% 0.40/0.73 % --splitting_nvd 16
% 0.40/0.73 % --non_eq_to_eq false
% 0.40/0.73 % --prep_gs_sim true
% 0.40/0.73 % --prep_unflatten false
% 0.40/0.73 % --prep_res_sim true
% 0.40/0.73 % --prep_upred true
% 0.40/0.73 % --res_sim_input true
% 0.40/0.73 % --clause_weak_htbl true
% 0.40/0.73 % --gc_record_bc_elim false
% 0.40/0.73 % --symbol_type_check false
% 0.40/0.73 % --clausify_out false
% 0.40/0.73 % --large_theory_mode false
% 0.40/0.73 % --prep_sem_filter none
% 0.40/0.73 % --prep_sem_filter_out false
% 0.40/0.73 % --preprocessed_out false
% 0.40/0.73 % --sub_typing false
% 0.40/0.73 % --brand_transform false
% 0.40/0.73 % --pure_diseq_elim true
% 0.40/0.73 % --min_unsat_core false
% 0.40/0.73 % --pred_elim true
% 0.40/0.73 % --add_important_lit false
% 0.40/0.73 % --soft_assumptions false
% 0.40/0.73 % --reset_solvers false
% 0.40/0.73 % --bc_imp_inh []
% 0.40/0.73 % --conj_cone_tolerance 1.5
% 0.40/0.73 % --prolific_symb_bound 500
% 0.40/0.73 % --lt_threshold 2000
% 0.40/0.73
% 0.40/0.73 % ------ SAT Options
% 0.40/0.73
% 0.40/0.73 % --sat_mode false
% 0.40/0.73 % --sat_fm_restart_options ""
% 0.40/0.73 % --sat_gr_def false
% 0.40/0.73 % --sat_epr_types true
% 0.40/0.73 % --sat_non_cyclic_types false
% 0.40/0.73 % --sat_finite_models false
% 0.40/0.73 % --sat_fm_lemmas false
% 0.40/0.73 % --sat_fm_prep false
% 0.40/0.73 % --sat_fm_uc_incr true
% 0.40/0.73 % --sat_out_model small
% 0.40/0.73 % --sat_out_clauses false
% 0.40/0.73
% 0.40/0.73 % ------ QBF Options
% 0.40/0.73
% 0.40/0.73 % --qbf_mode false
% 0.40/0.73 % --qbf_elim_univ true
% 0.40/0.73 % --qbf_sk_in true
% 0.40/0.73 % --qbf_pred_elim true
% 0.40/0.73 % --qbf_split 32
% 0.40/0.73
% 0.40/0.73 % ------ BMC1 Options
% 0.40/0.73
% 0.40/0.73 % --bmc1_incremental false
% 0.40/0.73 % --bmc1_axioms reachable_all
% 0.40/0.73 % --bmc1_min_bound 0
% 0.40/0.73 % --bmc1_max_bound -1
% 0.40/0.73 % --bmc1_max_bound_default -1
% 0.40/0.73 % --bmc1_symbol_reachability true
% 0.40/0.73 % --bmc1_property_lemmas false
% 0.40/0.73 % --bmc1_k_induction false
% 0.40/0.73 % --bmc1_non_equiv_states false
% 0.40/0.73 % --bmc1_deadlock false
% 0.40/0.73 % --bmc1_ucm false
% 0.40/0.73 % --bmc1_add_unsat_core none
% 0.40/0.73 % --bmc1_unsat_core_children false
% 0.40/0.73 % --bmc1_unsat_core_extrapolate_axioms false
% 0.40/0.73 % --bmc1_out_stat full
% 0.40/0.73 % --bmc1_ground_init false
% 0.40/0.73 % --bmc1_pre_inst_next_state false
% 0.40/0.73 % --bmc1_pre_inst_state false
% 0.40/0.73 % --bmc1_pre_inst_reach_state false
% 0.40/0.73 % --bmc1_out_unsat_core false
% 0.40/0.73 % --bmc1_aig_witness_out false
% 0.40/0.73 % --bmc1_verbose false
% 0.40/0.73 % --bmc1_dump_clauses_tptp false
% 0.40/0.73 % --bmc1_dump_unsat_core_tptp false
% 0.40/0.73 % --bmc1_dump_file -
% 0.40/0.73 % --bmc1_ucm_expand_uc_limit 128
% 0.40/0.73 % --bmc1_ucm_n_expand_iterations 6
% 0.40/0.73 % --bmc1_ucm_extend_mode 1
% 0.40/0.73 % --bmc1_ucm_init_mode 2
% 0.40/0.73 % --bmc1_ucm_cone_mode none
% 0.40/0.73 % --bmc1_ucm_reduced_relation_type 0
% 0.40/0.73 % --bmc1_ucm_relax_model 4
% 0.40/0.73 % --bmc1_ucm_full_tr_after_sat true
% 0.40/0.73 % --bmc1_ucm_expand_neg_assumptions false
% 0.40/0.73 % --bmc1_ucm_layered_model none
% 0.40/0.73 % --bmc1_ucm_max_lemma_size 10
% 0.40/0.73
% 0.40/0.73 % ------ AIG Options
% 0.40/0.73
% 0.40/0.73 % --aig_mode false
% 0.40/0.73
% 0.40/0.73 % ------ Instantiation Options
% 0.40/0.73
% 0.40/0.73 % --instantiation_flag true
% 0.40/0.73 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.40/0.73 % --inst_solver_per_active 750
% 0.40/0.73 % --inst_solver_calls_frac 0.5
% 0.40/0.73 % --inst_passive_queue_type priority_queues
% 0.40/0.73 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.40/0.73 % --inst_passive_queues_freq [25;2]
% 0.40/0.73 % --inst_dismatching true
% 28.31/28.64 % --inst_eager_unprocessed_to_passive true
% 28.31/28.64 % --inst_prop_sim_given true
% 28.31/28.64 % --inst_prop_sim_new false
% 28.31/28.64 % --inst_orphan_elimination true
% 28.31/28.64 % --inst_learning_loop_flag true
% 28.31/28.64 % --inst_learning_start 3000
% 28.31/28.64 % --inst_learning_factor 2
% 28.31/28.64 % --inst_start_prop_sim_after_learn 3
% 28.31/28.64 % --inst_sel_renew solver
% 28.31/28.64 % --inst_lit_activity_flag true
% 28.31/28.64 % --inst_out_proof true
% 28.31/28.64
% 28.31/28.64 % ------ Resolution Options
% 28.31/28.64
% 28.31/28.64 % --resolution_flag true
% 28.31/28.64 % --res_lit_sel kbo_max
% 28.31/28.64 % --res_to_prop_solver none
% 28.31/28.64 % --res_prop_simpl_new false
% 28.31/28.64 % --res_prop_simpl_given false
% 28.31/28.64 % --res_passive_queue_type priority_queues
% 28.31/28.64 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 28.31/28.64 % --res_passive_queues_freq [15;5]
% 28.31/28.64 % --res_forward_subs full
% 28.31/28.64 % --res_backward_subs full
% 28.31/28.64 % --res_forward_subs_resolution true
% 28.31/28.64 % --res_backward_subs_resolution true
% 28.31/28.64 % --res_orphan_elimination false
% 28.31/28.64 % --res_time_limit 1000.
% 28.31/28.64 % --res_out_proof true
% 28.31/28.64 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_a7b3be.s
% 28.31/28.64 % --modulo true
% 28.31/28.64
% 28.31/28.64 % ------ Combination Options
% 28.31/28.64
% 28.31/28.64 % --comb_res_mult 1000
% 28.31/28.64 % --comb_inst_mult 300
% 28.31/28.64 % ------
% 28.31/28.64
% 28.31/28.64
% 28.31/28.64
% 28.31/28.64 % ------ Proving...
% 28.31/28.64 %
% 28.31/28.64
% 28.31/28.64
% 28.31/28.64 % Resolution empty clause
% 28.31/28.64
% 28.31/28.64 % ------ Statistics
% 28.31/28.64
% 28.31/28.64 % ------ General
% 28.31/28.64
% 28.31/28.64 % num_of_input_clauses: 90
% 28.31/28.64 % num_of_input_neg_conjectures: 2
% 28.31/28.64 % num_of_splits: 0
% 28.31/28.64 % num_of_split_atoms: 0
% 28.31/28.64 % num_of_sem_filtered_clauses: 0
% 28.31/28.64 % num_of_subtypes: 0
% 28.31/28.64 % monotx_restored_types: 0
% 28.31/28.64 % sat_num_of_epr_types: 0
% 28.31/28.64 % sat_num_of_non_cyclic_types: 0
% 28.31/28.64 % sat_guarded_non_collapsed_types: 0
% 28.31/28.64 % is_epr: 0
% 28.31/28.64 % is_horn: 0
% 28.31/28.64 % has_eq: 1
% 28.31/28.64 % num_pure_diseq_elim: 0
% 28.31/28.64 % simp_replaced_by: 0
% 28.31/28.64 % res_preprocessed: 31
% 28.31/28.64 % prep_upred: 0
% 28.31/28.64 % prep_unflattend: 0
% 28.31/28.64 % pred_elim_cands: 3
% 28.31/28.64 % pred_elim: 1
% 28.31/28.64 % pred_elim_cl: 1
% 28.31/28.64 % pred_elim_cycles: 2
% 28.31/28.64 % forced_gc_time: 0
% 28.31/28.64 % gc_basic_clause_elim: 0
% 28.31/28.64 % parsing_time: 0.004
% 28.31/28.64 % sem_filter_time: 0.
% 28.31/28.64 % pred_elim_time: 0.
% 28.31/28.64 % out_proof_time: 0.001
% 28.31/28.64 % monotx_time: 0.
% 28.31/28.64 % subtype_inf_time: 0.
% 28.31/28.64 % unif_index_cands_time: 0.219
% 28.31/28.64 % unif_index_add_time: 0.019
% 28.31/28.64 % total_time: 28.189
% 28.31/28.64 % num_of_symbols: 46
% 28.31/28.64 % num_of_terms: 664257
% 28.31/28.64
% 28.31/28.64 % ------ Propositional Solver
% 28.31/28.64
% 28.31/28.64 % prop_solver_calls: 12
% 28.31/28.64 % prop_fast_solver_calls: 112
% 28.31/28.64 % prop_num_of_clauses: 5079
% 28.31/28.64 % prop_preprocess_simplified: 5673
% 28.31/28.64 % prop_fo_subsumed: 0
% 28.31/28.64 % prop_solver_time: 0.
% 28.31/28.64 % prop_fast_solver_time: 0.
% 28.31/28.64 % prop_unsat_core_time: 0.
% 28.31/28.64
% 28.31/28.64 % ------ QBF
% 28.31/28.64
% 28.31/28.64 % qbf_q_res: 0
% 28.31/28.64 % qbf_num_tautologies: 0
% 28.31/28.64 % qbf_prep_cycles: 0
% 28.31/28.64
% 28.31/28.64 % ------ BMC1
% 28.31/28.64
% 28.31/28.64 % bmc1_current_bound: -1
% 28.31/28.64 % bmc1_last_solved_bound: -1
% 28.31/28.64 % bmc1_unsat_core_size: -1
% 28.31/28.64 % bmc1_unsat_core_parents_size: -1
% 28.31/28.64 % bmc1_merge_next_fun: 0
% 28.31/28.64 % bmc1_unsat_core_clauses_time: 0.
% 28.31/28.64
% 28.31/28.64 % ------ Instantiation
% 28.31/28.64
% 28.31/28.64 % inst_num_of_clauses: 3051
% 28.31/28.64 % inst_num_in_passive: 1553
% 28.31/28.64 % inst_num_in_active: 970
% 28.31/28.64 % inst_num_in_unprocessed: 506
% 28.31/28.64 % inst_num_of_loops: 1200
% 28.31/28.64 % inst_num_of_learning_restarts: 0
% 28.31/28.64 % inst_num_moves_active_passive: 208
% 28.31/28.64 % inst_lit_activity: 950
% 28.31/28.64 % inst_lit_activity_moves: 0
% 28.31/28.64 % inst_num_tautologies: 20
% 28.31/28.64 % inst_num_prop_implied: 0
% 28.31/28.64 % inst_num_existing_simplified: 0
% 28.31/28.64 % inst_num_eq_res_simplified: 2
% 28.31/28.64 % inst_num_child_elim: 0
% 28.31/28.64 % inst_num_of_dismatching_blockings: 1368
% 28.31/28.64 % inst_num_of_non_proper_insts: 2584
% 28.31/28.64 % inst_num_of_duplicates: 973
% 28.31/28.64 % inst_inst_num_from_inst_to_res: 0
% 28.31/28.64 % inst_dismatching_checking_time: 0.006
% 28.31/28.64
% 28.31/28.64 % ------ Resolution
% 28.31/28.64
% 28.31/28.64 % res_num_of_clauses: 458934
% 28.31/28.64 % res_num_in_passive: 462996
% 28.31/28.64 % res_num_in_active: 2614
% 28.31/28.64 % res_num_of_loops: 4265
% 28.31/28.64 % res_forward_subset_subsumed: 69399
% 28.31/28.64 % res_backward_subset_subsumed: 6860
% 28.31/28.64 % res_forward_subsumed: 682
% 28.31/28.64 % res_backward_subsumed: 817
% 28.31/28.64 % res_forward_subsumption_resolution: 62
% 28.31/28.64 % res_backward_subsumption_resolution: 97
% 28.31/28.64 % res_clause_to_clause_subsumption: 111790
% 28.31/28.64 % res_orphan_elimination: 0
% 28.31/28.64 % res_tautology_del: 820
% 28.31/28.64 % res_num_eq_res_simplified: 0
% 28.31/28.64 % res_num_sel_changes: 0
% 28.31/28.64 % res_moves_from_active_to_pass: 0
% 28.31/28.64
% 28.43/28.64 % Status Unsatisfiable
% 28.43/28.64 % SZS status Theorem
% 28.43/28.64 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------