TSTP Solution File: SET148+3 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SET148+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 02:11:01 EDT 2022
% Result : Theorem 0.23s 0.47s
% Output : CNFRefutation 0.23s
% 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(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
input ).
fof(equal_member_defn_0,plain,
! [B,C] :
( B = C
| ~ ! [D] :
( member(D,B)
<=> member(D,C) ) ),
inference(orientation,[status(thm)],[equal_member_defn]) ).
fof(equal_member_defn_1,plain,
! [B,C] :
( B != C
| ! [D] :
( member(D,B)
<=> member(D,C) ) ),
inference(orientation,[status(thm)],[equal_member_defn]) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
input ).
fof(reflexivity_of_subset_0,plain,
! [B] :
( subset(B,B)
| $false ),
inference(orientation,[status(thm)],[reflexivity_of_subset]) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
input ).
fof(subset_defn_0,plain,
! [B,C] :
( subset(B,C)
| ~ ! [D] :
( member(D,B)
=> member(D,C) ) ),
inference(orientation,[status(thm)],[subset_defn]) ).
fof(subset_defn_1,plain,
! [B,C] :
( ~ subset(B,C)
| ! [D] :
( member(D,B)
=> member(D,C) ) ),
inference(orientation,[status(thm)],[subset_defn]) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
input ).
fof(commutativity_of_intersection_0,plain,
! [B,C] :
( intersection(B,C) = intersection(C,B)
| $false ),
inference(orientation,[status(thm)],[commutativity_of_intersection]) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
input ).
fof(equal_defn_0,plain,
! [B,C] :
( B = C
| ~ ( subset(B,C)
& subset(C,B) ) ),
inference(orientation,[status(thm)],[equal_defn]) ).
fof(equal_defn_1,plain,
! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) ),
inference(orientation,[status(thm)],[equal_defn]) ).
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
input ).
fof(intersection_defn_0,plain,
! [B,C,D] :
( member(D,intersection(B,C))
| ~ ( member(D,B)
& member(D,C) ) ),
inference(orientation,[status(thm)],[intersection_defn]) ).
fof(intersection_defn_1,plain,
! [B,C,D] :
( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) ),
inference(orientation,[status(thm)],[intersection_defn]) ).
fof(subset_intersection,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
input ).
fof(subset_intersection_0,plain,
! [B,C] :
( ~ subset(B,C)
| intersection(B,C) = B ),
inference(orientation,[status(thm)],[subset_intersection]) ).
fof(def_lhs_atom1,axiom,
! [C,B] :
( lhs_atom1(C,B)
<=> ~ subset(B,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [B,C] :
( lhs_atom1(C,B)
| intersection(B,C) = B ),
inference(fold_definition,[status(thm)],[subset_intersection_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [D,C,B] :
( lhs_atom2(D,C,B)
<=> ~ member(D,intersection(B,C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [B,C,D] :
( lhs_atom2(D,C,B)
| ( member(D,B)
& member(D,C) ) ),
inference(fold_definition,[status(thm)],[intersection_defn_1,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [D,C,B] :
( lhs_atom3(D,C,B)
<=> member(D,intersection(B,C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [B,C,D] :
( lhs_atom3(D,C,B)
| ~ ( member(D,B)
& member(D,C) ) ),
inference(fold_definition,[status(thm)],[intersection_defn_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [C,B] :
( lhs_atom4(C,B)
<=> B != C ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [B,C] :
( lhs_atom4(C,B)
| ( subset(B,C)
& subset(C,B) ) ),
inference(fold_definition,[status(thm)],[equal_defn_1,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [C,B] :
( lhs_atom5(C,B)
<=> B = C ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [B,C] :
( lhs_atom5(C,B)
| ~ ( subset(B,C)
& subset(C,B) ) ),
inference(fold_definition,[status(thm)],[equal_defn_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [C,B] :
( lhs_atom6(C,B)
<=> intersection(B,C) = intersection(C,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [B,C] :
( lhs_atom6(C,B)
| $false ),
inference(fold_definition,[status(thm)],[commutativity_of_intersection_0,def_lhs_atom6]) ).
fof(to_be_clausified_6,plain,
! [B,C] :
( lhs_atom1(C,B)
| ! [D] :
( member(D,B)
=> member(D,C) ) ),
inference(fold_definition,[status(thm)],[subset_defn_1,def_lhs_atom1]) ).
fof(def_lhs_atom7,axiom,
! [C,B] :
( lhs_atom7(C,B)
<=> subset(B,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [B,C] :
( lhs_atom7(C,B)
| ~ ! [D] :
( member(D,B)
=> member(D,C) ) ),
inference(fold_definition,[status(thm)],[subset_defn_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [B] :
( lhs_atom8(B)
<=> subset(B,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [B] :
( lhs_atom8(B)
| $false ),
inference(fold_definition,[status(thm)],[reflexivity_of_subset_0,def_lhs_atom8]) ).
fof(to_be_clausified_9,plain,
! [B,C] :
( lhs_atom4(C,B)
| ! [D] :
( member(D,B)
<=> member(D,C) ) ),
inference(fold_definition,[status(thm)],[equal_member_defn_1,def_lhs_atom4]) ).
fof(to_be_clausified_10,plain,
! [B,C] :
( lhs_atom5(C,B)
| ~ ! [D] :
( member(D,B)
<=> member(D,C) ) ),
inference(fold_definition,[status(thm)],[equal_member_defn_0,def_lhs_atom5]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
<=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_1,axiom,
! [X3,X1,X2] :
( lhs_atom3(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_2,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_3,axiom,
! [X3,X1,X2] :
( lhs_atom2(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_4,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_5,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ! [X3] :
( member(X3,X2)
<=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_6,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_7,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| intersection(X2,X1) = X2 ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_8,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_9,axiom,
! [X1,X2] :
( lhs_atom6(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_10,axiom,
! [X2] :
( lhs_atom8(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_11,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
<=> member(X3,X1) ) ),
c_0_0 ).
fof(c_0_12,axiom,
! [X3,X1,X2] :
( lhs_atom3(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
c_0_1 ).
fof(c_0_13,axiom,
! [X1,X2] :
( lhs_atom7(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_2 ).
fof(c_0_14,axiom,
! [X3,X1,X2] :
( lhs_atom2(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
c_0_3 ).
fof(c_0_15,axiom,
! [X1,X2] :
( lhs_atom5(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_4 ).
fof(c_0_16,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ! [X3] :
( member(X3,X2)
<=> member(X3,X1) ) ),
c_0_5 ).
fof(c_0_17,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_6 ).
fof(c_0_18,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| intersection(X2,X1) = X2 ),
c_0_7 ).
fof(c_0_19,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_8 ).
fof(c_0_20,plain,
! [X1,X2] : lhs_atom6(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_21,plain,
! [X2] : lhs_atom8(X2),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_22,plain,
! [X4,X5] :
( ( ~ member(esk2_2(X4,X5),X5)
| ~ member(esk2_2(X4,X5),X4)
| lhs_atom5(X4,X5) )
& ( member(esk2_2(X4,X5),X5)
| member(esk2_2(X4,X5),X4)
| lhs_atom5(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_23,plain,
! [X4,X5,X6] :
( lhs_atom3(X4,X5,X6)
| ~ member(X4,X6)
| ~ member(X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_24,plain,
! [X4,X5] :
( ( member(esk1_2(X4,X5),X5)
| lhs_atom7(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X4)
| lhs_atom7(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_25,plain,
! [X4,X5,X6] :
( ( member(X4,X6)
| lhs_atom2(X4,X5,X6) )
& ( member(X4,X5)
| lhs_atom2(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).
fof(c_0_26,plain,
! [X3,X4] :
( lhs_atom5(X3,X4)
| ~ subset(X4,X3)
| ~ subset(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
fof(c_0_27,plain,
! [X4,X5,X6,X7] :
( ( ~ member(X6,X5)
| member(X6,X4)
| lhs_atom4(X4,X5) )
& ( ~ member(X7,X4)
| member(X7,X5)
| lhs_atom4(X4,X5) ) ),
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_16])])])])]) ).
fof(c_0_28,plain,
! [X4,X5,X6] :
( lhs_atom1(X4,X5)
| ~ member(X6,X5)
| member(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_29,plain,
! [X3,X4] :
( lhs_atom1(X3,X4)
| intersection(X4,X3) = X4 ),
inference(variable_rename,[status(thm)],[c_0_18]) ).
fof(c_0_30,plain,
! [X3,X4] :
( ( subset(X4,X3)
| lhs_atom4(X3,X4) )
& ( subset(X3,X4)
| lhs_atom4(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
fof(c_0_31,plain,
! [X3,X4] : lhs_atom6(X3,X4),
inference(variable_rename,[status(thm)],[c_0_20]) ).
fof(c_0_32,plain,
! [X3] : lhs_atom8(X3),
inference(variable_rename,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( lhs_atom5(X1,X2)
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,plain,
( lhs_atom3(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,plain,
( lhs_atom5(X1,X2)
| member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_36,plain,
( lhs_atom7(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,plain,
( lhs_atom2(X1,X2,X3)
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
( lhs_atom2(X1,X2,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
( lhs_atom5(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_40,plain,
( lhs_atom7(X1,X2)
| member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_41,plain,
( lhs_atom4(X1,X2)
| member(X3,X1)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_42,plain,
( lhs_atom4(X1,X2)
| member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_43,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_44,plain,
( intersection(X1,X2) = X1
| lhs_atom1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_45,plain,
( lhs_atom4(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46,plain,
( lhs_atom4(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_47,plain,
lhs_atom6(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_48,plain,
lhs_atom8(X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_49,plain,
( lhs_atom5(X1,X2)
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
c_0_33,
[final] ).
cnf(c_0_50,plain,
( lhs_atom3(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
c_0_34,
[final] ).
cnf(c_0_51,plain,
( lhs_atom5(X1,X2)
| member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2) ),
c_0_35,
[final] ).
cnf(c_0_52,plain,
( lhs_atom7(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
c_0_36,
[final] ).
cnf(c_0_53,plain,
( lhs_atom2(X1,X2,X3)
| member(X1,X3) ),
c_0_37,
[final] ).
cnf(c_0_54,plain,
( lhs_atom2(X1,X2,X3)
| member(X1,X2) ),
c_0_38,
[final] ).
cnf(c_0_55,plain,
( lhs_atom5(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_39,
[final] ).
cnf(c_0_56,plain,
( lhs_atom7(X1,X2)
| member(esk1_2(X1,X2),X2) ),
c_0_40,
[final] ).
cnf(c_0_57,plain,
( lhs_atom4(X1,X2)
| member(X3,X1)
| ~ member(X3,X2) ),
c_0_41,
[final] ).
cnf(c_0_58,plain,
( lhs_atom4(X1,X2)
| member(X3,X2)
| ~ member(X3,X1) ),
c_0_42,
[final] ).
cnf(c_0_59,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
c_0_43,
[final] ).
cnf(c_0_60,plain,
( intersection(X1,X2) = X1
| lhs_atom1(X2,X1) ),
c_0_44,
[final] ).
cnf(c_0_61,plain,
( lhs_atom4(X1,X2)
| subset(X2,X1) ),
c_0_45,
[final] ).
cnf(c_0_62,plain,
( lhs_atom4(X1,X2)
| subset(X1,X2) ),
c_0_46,
[final] ).
cnf(c_0_63,plain,
lhs_atom6(X1,X2),
c_0_47,
[final] ).
cnf(c_0_64,plain,
lhs_atom8(X1),
c_0_48,
[final] ).
% End CNF derivation
cnf(c_0_49_0,axiom,
( X2 = X1
| ~ member(sk1_esk2_2(X1,X2),X1)
| ~ member(sk1_esk2_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_49,def_lhs_atom5]) ).
cnf(c_0_50_0,axiom,
( member(X1,intersection(X3,X2))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_50,def_lhs_atom3]) ).
cnf(c_0_51_0,axiom,
( X2 = X1
| member(sk1_esk2_2(X1,X2),X1)
| member(sk1_esk2_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_51,def_lhs_atom5]) ).
cnf(c_0_52_0,axiom,
( subset(X2,X1)
| ~ member(sk1_esk1_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_52,def_lhs_atom7]) ).
cnf(c_0_53_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_53,def_lhs_atom2]) ).
cnf(c_0_54_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_54,def_lhs_atom2]) ).
cnf(c_0_55_0,axiom,
( X2 = X1
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_55,def_lhs_atom5]) ).
cnf(c_0_56_0,axiom,
( subset(X2,X1)
| member(sk1_esk1_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_56,def_lhs_atom7]) ).
cnf(c_0_57_0,axiom,
( X2 != X1
| member(X3,X1)
| ~ member(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_57,def_lhs_atom4]) ).
cnf(c_0_58_0,axiom,
( X2 != X1
| member(X3,X2)
| ~ member(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_58,def_lhs_atom4]) ).
cnf(c_0_59_0,axiom,
( ~ subset(X3,X2)
| member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_59,def_lhs_atom1]) ).
cnf(c_0_60_0,axiom,
( ~ subset(X1,X2)
| intersection(X1,X2) = X1 ),
inference(unfold_definition,[status(thm)],[c_0_60,def_lhs_atom1]) ).
cnf(c_0_61_0,axiom,
( X2 != X1
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_61,def_lhs_atom4]) ).
cnf(c_0_62_0,axiom,
( X2 != X1
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_62,def_lhs_atom4]) ).
cnf(c_0_63_0,axiom,
intersection(X2,X1) = intersection(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_63,def_lhs_atom6]) ).
cnf(c_0_64_0,axiom,
subset(X1,X1),
inference(unfold_definition,[status(thm)],[c_0_64,def_lhs_atom8]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
! [X1] : intersection(X1,X1) = X1,
file('<stdin>',prove_idempotency_of_intersection) ).
fof(c_0_1_002,negated_conjecture,
~ ! [X1] : intersection(X1,X1) = X1,
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_003,negated_conjecture,
intersection(esk1_0,esk1_0) != esk1_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_004,negated_conjecture,
intersection(esk1_0,esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
intersection(esk1_0,esk1_0) != esk1_0,
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_4,plain,
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_3931cf.p',c_0_60_0) ).
cnf(c_24,plain,
( ~ subset(sk3_esk1_0,sk3_esk1_0)
| intersection(sk3_esk1_0,sk3_esk1_0) = sk3_esk1_0 ),
inference(instantiation,[status(thm)],[c_4]) ).
cnf(c_8,plain,
( member(sk1_esk1_2(X0,X1),X1)
| subset(X1,X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_3931cf.p',c_0_56_0) ).
cnf(c_23,plain,
( subset(sk3_esk1_0,sk3_esk1_0)
| member(sk1_esk1_2(sk3_esk1_0,sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_8]) ).
cnf(c_12,plain,
( ~ member(sk1_esk1_2(X0,X1),X0)
| subset(X1,X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_3931cf.p',c_0_52_0) ).
cnf(c_20,plain,
( subset(sk3_esk1_0,sk3_esk1_0)
| ~ member(sk1_esk1_2(sk3_esk1_0,sk3_esk1_0),sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_12]) ).
cnf(c_16,negated_conjecture,
intersection(sk3_esk1_0,sk3_esk1_0) != sk3_esk1_0,
file('/export/starexec/sandbox2/tmp/iprover_modulo_3931cf.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_24,c_23,c_20,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SET148+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.15 % Command : iprover_modulo %s %d
% 0.15/0.37 % Computer : n027.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sat Jul 9 22:27:17 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.38 % Running in mono-core mode
% 0.23/0.44 % Orienting using strategy Equiv(ClausalAll)
% 0.23/0.44 % FOF problem with conjecture
% 0.23/0.44 % 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_37b86a.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_3931cf.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_38defb | grep -v "SZS"
% 0.23/0.46
% 0.23/0.46 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.23/0.46
% 0.23/0.46 %
% 0.23/0.46 % ------ iProver source info
% 0.23/0.46
% 0.23/0.46 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.23/0.46 % git: non_committed_changes: true
% 0.23/0.46 % git: last_make_outside_of_git: true
% 0.23/0.46
% 0.23/0.46 %
% 0.23/0.46 % ------ Input Options
% 0.23/0.46
% 0.23/0.46 % --out_options all
% 0.23/0.46 % --tptp_safe_out true
% 0.23/0.46 % --problem_path ""
% 0.23/0.46 % --include_path ""
% 0.23/0.46 % --clausifier .//eprover
% 0.23/0.46 % --clausifier_options --tstp-format
% 0.23/0.46 % --stdin false
% 0.23/0.46 % --dbg_backtrace false
% 0.23/0.46 % --dbg_dump_prop_clauses false
% 0.23/0.46 % --dbg_dump_prop_clauses_file -
% 0.23/0.46 % --dbg_out_stat false
% 0.23/0.46
% 0.23/0.46 % ------ General Options
% 0.23/0.46
% 0.23/0.46 % --fof false
% 0.23/0.46 % --time_out_real 150.
% 0.23/0.46 % --time_out_prep_mult 0.2
% 0.23/0.46 % --time_out_virtual -1.
% 0.23/0.46 % --schedule none
% 0.23/0.46 % --ground_splitting input
% 0.23/0.46 % --splitting_nvd 16
% 0.23/0.46 % --non_eq_to_eq false
% 0.23/0.46 % --prep_gs_sim true
% 0.23/0.46 % --prep_unflatten false
% 0.23/0.46 % --prep_res_sim true
% 0.23/0.46 % --prep_upred true
% 0.23/0.46 % --res_sim_input true
% 0.23/0.46 % --clause_weak_htbl true
% 0.23/0.46 % --gc_record_bc_elim false
% 0.23/0.46 % --symbol_type_check false
% 0.23/0.46 % --clausify_out false
% 0.23/0.46 % --large_theory_mode false
% 0.23/0.46 % --prep_sem_filter none
% 0.23/0.46 % --prep_sem_filter_out false
% 0.23/0.46 % --preprocessed_out false
% 0.23/0.46 % --sub_typing false
% 0.23/0.46 % --brand_transform false
% 0.23/0.46 % --pure_diseq_elim true
% 0.23/0.46 % --min_unsat_core false
% 0.23/0.46 % --pred_elim true
% 0.23/0.46 % --add_important_lit false
% 0.23/0.46 % --soft_assumptions false
% 0.23/0.46 % --reset_solvers false
% 0.23/0.46 % --bc_imp_inh []
% 0.23/0.46 % --conj_cone_tolerance 1.5
% 0.23/0.46 % --prolific_symb_bound 500
% 0.23/0.46 % --lt_threshold 2000
% 0.23/0.46
% 0.23/0.46 % ------ SAT Options
% 0.23/0.46
% 0.23/0.46 % --sat_mode false
% 0.23/0.46 % --sat_fm_restart_options ""
% 0.23/0.46 % --sat_gr_def false
% 0.23/0.46 % --sat_epr_types true
% 0.23/0.46 % --sat_non_cyclic_types false
% 0.23/0.46 % --sat_finite_models false
% 0.23/0.46 % --sat_fm_lemmas false
% 0.23/0.46 % --sat_fm_prep false
% 0.23/0.46 % --sat_fm_uc_incr true
% 0.23/0.46 % --sat_out_model small
% 0.23/0.46 % --sat_out_clauses false
% 0.23/0.46
% 0.23/0.46 % ------ QBF Options
% 0.23/0.46
% 0.23/0.46 % --qbf_mode false
% 0.23/0.46 % --qbf_elim_univ true
% 0.23/0.46 % --qbf_sk_in true
% 0.23/0.46 % --qbf_pred_elim true
% 0.23/0.46 % --qbf_split 32
% 0.23/0.46
% 0.23/0.46 % ------ BMC1 Options
% 0.23/0.46
% 0.23/0.46 % --bmc1_incremental false
% 0.23/0.46 % --bmc1_axioms reachable_all
% 0.23/0.46 % --bmc1_min_bound 0
% 0.23/0.46 % --bmc1_max_bound -1
% 0.23/0.46 % --bmc1_max_bound_default -1
% 0.23/0.46 % --bmc1_symbol_reachability true
% 0.23/0.46 % --bmc1_property_lemmas false
% 0.23/0.46 % --bmc1_k_induction false
% 0.23/0.46 % --bmc1_non_equiv_states false
% 0.23/0.46 % --bmc1_deadlock false
% 0.23/0.46 % --bmc1_ucm false
% 0.23/0.46 % --bmc1_add_unsat_core none
% 0.23/0.46 % --bmc1_unsat_core_children false
% 0.23/0.46 % --bmc1_unsat_core_extrapolate_axioms false
% 0.23/0.46 % --bmc1_out_stat full
% 0.23/0.46 % --bmc1_ground_init false
% 0.23/0.46 % --bmc1_pre_inst_next_state false
% 0.23/0.46 % --bmc1_pre_inst_state false
% 0.23/0.46 % --bmc1_pre_inst_reach_state false
% 0.23/0.46 % --bmc1_out_unsat_core false
% 0.23/0.46 % --bmc1_aig_witness_out false
% 0.23/0.46 % --bmc1_verbose false
% 0.23/0.46 % --bmc1_dump_clauses_tptp false
% 0.23/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.23/0.46 % --bmc1_dump_file -
% 0.23/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.23/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.23/0.46 % --bmc1_ucm_extend_mode 1
% 0.23/0.46 % --bmc1_ucm_init_mode 2
% 0.23/0.46 % --bmc1_ucm_cone_mode none
% 0.23/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.23/0.46 % --bmc1_ucm_relax_model 4
% 0.23/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.23/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.23/0.46 % --bmc1_ucm_layered_model none
% 0.23/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.23/0.46
% 0.23/0.46 % ------ AIG Options
% 0.23/0.46
% 0.23/0.46 % --aig_mode false
% 0.23/0.46
% 0.23/0.46 % ------ Instantiation Options
% 0.23/0.46
% 0.23/0.46 % --instantiation_flag true
% 0.23/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.23/0.46 % --inst_solver_per_active 750
% 0.23/0.46 % --inst_solver_calls_frac 0.5
% 0.23/0.46 % --inst_passive_queue_type priority_queues
% 0.23/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.23/0.47 % --inst_passive_queues_freq [25;2]
% 0.23/0.47 % --inst_dismatching true
% 0.23/0.47 % --inst_eager_unprocessed_to_passive true
% 0.23/0.47 % --inst_prop_sim_given true
% 0.23/0.47 % --inst_prop_sim_new false
% 0.23/0.47 % --inst_orphan_elimination true
% 0.23/0.47 % --inst_learning_loop_flag true
% 0.23/0.47 % --inst_learning_start 3000
% 0.23/0.47 % --inst_learning_factor 2
% 0.23/0.47 % --inst_start_prop_sim_after_learn 3
% 0.23/0.47 % --inst_sel_renew solver
% 0.23/0.47 % --inst_lit_activity_flag true
% 0.23/0.47 % --inst_out_proof true
% 0.23/0.47
% 0.23/0.47 % ------ Resolution Options
% 0.23/0.47
% 0.23/0.47 % --resolution_flag true
% 0.23/0.47 % --res_lit_sel kbo_max
% 0.23/0.47 % --res_to_prop_solver none
% 0.23/0.47 % --res_prop_simpl_new false
% 0.23/0.47 % --res_prop_simpl_given false
% 0.23/0.47 % --res_passive_queue_type priority_queues
% 0.23/0.47 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.23/0.47 % --res_passive_queues_freq [15;5]
% 0.23/0.47 % --res_forward_subs full
% 0.23/0.47 % --res_backward_subs full
% 0.23/0.47 % --res_forward_subs_resolution true
% 0.23/0.47 % --res_backward_subs_resolution true
% 0.23/0.47 % --res_orphan_elimination false
% 0.23/0.47 % --res_time_limit 1000.
% 0.23/0.47 % --res_out_proof true
% 0.23/0.47 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_37b86a.s
% 0.23/0.47 % --modulo true
% 0.23/0.47
% 0.23/0.47 % ------ Combination Options
% 0.23/0.47
% 0.23/0.47 % --comb_res_mult 1000
% 0.23/0.47 % --comb_inst_mult 300
% 0.23/0.47 % ------
% 0.23/0.47
% 0.23/0.47 % ------ Parsing...% successful
% 0.23/0.47
% 0.23/0.47 %
% 0.23/0.47
% 0.23/0.47
% 0.23/0.47 % ------ Statistics
% 0.23/0.47
% 0.23/0.47 % ------ General
% 0.23/0.47
% 0.23/0.47 % num_of_input_clauses: 17
% 0.23/0.47 % num_of_input_neg_conjectures: 1
% 0.23/0.47 % num_of_splits: 0
% 0.23/0.47 % num_of_split_atoms: 0
% 0.23/0.47 % num_of_sem_filtered_clauses: 0
% 0.23/0.47 % num_of_subtypes: 0
% 0.23/0.47 % monotx_restored_types: 0
% 0.23/0.47 % sat_num_of_epr_types: 0
% 0.23/0.47 % sat_num_of_non_cyclic_types: 0
% 0.23/0.47 % sat_guarded_non_collapsed_types: 0
% 0.23/0.47 % is_epr: 0
% 0.23/0.47 % is_horn: 0
% 0.23/0.47 % has_eq: 0
% 0.23/0.47 % num_pure_diseq_elim: 0
% 0.23/0.47 % simp_replaced_by: 0
% 0.23/0.47 % res_preprocessed: 0
% 0.23/0.47 % prep_upred: 0
% 0.23/0.47 % prep_unflattend: 0
% 0.23/0.47 % pred_elim_cands: 0
% 0.23/0.47 % pred_elim: 0
% 0.23/0.47 % pred_elim_cl: 0
% 0.23/0.47 % pred_elim_cycles: 0
% 0.23/0.47 % forced_gc_time: 0
% 0.23/0.47 % gc_basic_clause_elim: 0
% 0.23/0.47 % parsing_time: 0.
% 0.23/0.47 % sem_filter_time: 0.
% 0.23/0.47 % pred_elim_time: 0.
% 0.23/0.47 % out_proof_time: 0.
% 0.23/0.47 % monotx_time: 0.
% 0.23/0.47 % subtype_inf_time: 0.
% 0.23/0.47 % unif_index_cands_time: 0.
% 0.23/0.47 % unif_index_add_time: 0.
% 0.23/0.47 % total_time: 0.013
% 0.23/0.47 % num_of_symbols: 31
% 0.23/0.47 % num_of_terms: 75
% 0.23/0.47
% 0.23/0.47 % ------ Propositional Solver
% 0.23/0.47
% 0.23/0.47 % prop_solver_calls: 0
% 0.23/0.47 % prop_fast_solver_calls: 0
% 0.23/0.47 % prop_num_of_clauses: 27
% 0.23/0.47 % prop_preprocess_simplified: 6
% 0.23/0.47 % prop_fo_subsumed: 0
% 0.23/0.47 % prop_solver_time: 0.
% 0.23/0.47 % prop_fast_solver_time: 0.
% 0.23/0.47 % prop_unsat_core_time: 0.
% 0.23/0.47
% 0.23/0.47 % ------ QBF
% 0.23/0.47
% 0.23/0.47 % qbf_q_res: 0
% 0.23/0.47 % qbf_num_tautologies: 0
% 0.23/0.47 % qbf_prep_cycles: 0
% 0.23/0.47
% 0.23/0.47 % ------ BMC1
% 0.23/0.47
% 0.23/0.47 % bmc1_current_bound: -1
% 0.23/0.47 % bmc1_last_solved_bound: -1
% 0.23/0.47 % bmc1_unsat_core_size: -1
% 0.23/0.47 % bmc1_unsat_core_parents_size: -1
% 0.23/0.47 % bmc1_merge_next_fun: 0
% 0.23/0.47 % bmc1_unsat_core_clauses_time: 0.
% 0.23/0.47
% 0.23/0.47 % ------ Instantiation
% 0.23/0.47
% 0.23/0.47 % inst_num_of_clauses: undef
% 0.23/0.47 % inst_num_in_passive: undef
% 0.23/0.47 % inst_num_in_active: 0
% 0.23/0.47 % inst_num_in_unprocessed: 0
% 0.23/0.47 % inst_num_of_loops: 0
% 0.23/0.47 % inst_num_of_learning_restarts: 0
% 0.23/0.47 % inst_num_moves_active_passive: 0
% 0.23/0.47 % inst_lit_activity: 0
% 0.23/0.47 % inst_lit_activity_moves: 0
% 0.23/0.47 % inst_num_tautologies: 0
% 0.23/0.47 % inst_num_prop_implied: 0
% 0.23/0.47 % inst_num_existing_simplified: 0
% 0.23/0.47 % inst_num_eq_res_simplified: 0
% 0.23/0.47 % inst_num_child_elim: 0
% 0.23/0.47 % inst_num_of_dismatching_blockings: 0
% 0.23/0.47 % inst_num_of_non_proper_insts: 0
% 0.23/0.47 % inst_num_of_duplicates: 0
% 0.23/0.47 % inst_inst_num_from_inst_to_res: 0
% 0.23/0.47 % inst_dismatching_checking_time: 0.
% 0.23/0.47
% 0.23/0.47 % ------ Resolution
% 0.23/0.47
% 0.23/0.47 % res_num_of_clauses: undef
% 0.23/0.47 % res_num_in_passive: undef
% 0.23/0.47 % res_num_in_active: 0
% 0.23/0.47 % res_num_of_loops: 0
% 0.23/0.47 % res_forward_subset_subsumed: 0
% 0.23/0.47 % res_backward_subset_subsumed: 0
% 0.23/0.47 % res_forward_subsumed: 0
% 0.23/0.47 % res_backward_subsumed: 0
% 0.23/0.47 % res_forward_subsumption_resolution: 0
% 0.23/0.47 % res_backward_subsumption_resolution: 0
% 0.23/0.47 % res_clause_to_clause_subsumption: 0
% 0.23/0.47 % res_orphan_elimination: 0
% 0.23/0.47 % res_tautology_del: 0
% 0.23/0.47 % res_num_eq_res_simplified: 0
% 0.23/0.47 % res_num_sel_changes: 0
% 0.23/0.47 % res_moves_from_active_to_pass: 0
% 0.23/0.47
% 0.23/0.47 % Status Unsatisfiable
% 0.23/0.47 % SZS status Theorem
% 0.23/0.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------