TSTP Solution File: SET669+3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:08 EDT 2024
% Result : Theorem 2.80s 0.74s
% Output : CNFRefutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 116 ( 15 unt; 0 def)
% Number of atoms : 396 ( 28 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 474 ( 194 ~; 198 |; 30 &)
% ( 14 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 201 ( 196 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ( subset(B,C)
& subset(C,B) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,domain(B,C,D))
& C = range(B,C,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,domain(B,C,D))
& C = range(B,C,D) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f53,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( subset(B,C)
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f54,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ( ilf_type(sk0_1(C,B),set_type)
& member(sk0_1(C,B),B)
& ~ member(sk0_1(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1)
| member(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1)
| ~ member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f88,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f89,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f89]) ).
fof(f99,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( member(B,power_set(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f100,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f99]) ).
fof(f101,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ( ilf_type(sk0_6(C,B),set_type)
& member(sk0_6(C,B),B)
& ~ member(sk0_6(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f101]) ).
fof(f106,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f107,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f109,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f110,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(B,member_type(C))
| member(B,C) )
& ( ilf_type(B,member_type(C))
| ~ member(B,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f110]) ).
fof(f135,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(cnf_transformation,[status(esa)],[f135]) ).
fof(f139,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(cnf_transformation,[status(esa)],[f139]) ).
fof(f141,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f144,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(B,C))
& subset(identity_relation_of(C),D)
& ( ~ subset(C,domain(B,C,D))
| C != range(B,C,D) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f145,plain,
( ilf_type(sk0_12,set_type)
& ilf_type(sk0_13,set_type)
& ilf_type(sk0_14,relation_type(sk0_12,sk0_13))
& subset(identity_relation_of(sk0_13),sk0_14)
& ( ~ subset(sk0_13,domain(sk0_12,sk0_13,sk0_14))
| sk0_13 != range(sk0_12,sk0_13,sk0_14) ) ),
inference(skolemization,[status(esa)],[f144]) ).
fof(f148,plain,
ilf_type(sk0_14,relation_type(sk0_12,sk0_13)),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f149,plain,
subset(identity_relation_of(sk0_13),sk0_14),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f150,plain,
( ~ subset(sk0_13,domain(sk0_12,sk0_13,sk0_14))
| sk0_13 != range(sk0_12,sk0_13,sk0_14) ),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f151,plain,
( spl0_0
<=> subset(sk0_13,domain(sk0_12,sk0_13,sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f153,plain,
( ~ subset(sk0_13,domain(sk0_12,sk0_13,sk0_14))
| spl0_0 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( spl0_1
<=> sk0_13 = range(sk0_12,sk0_13,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f156,plain,
( sk0_13 != range(sk0_12,sk0_13,sk0_14)
| spl0_1 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f150,f151,f154]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(range(X2,X0,X1),subset_type(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f142,f143]) ).
fof(f168,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f143]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| range(X2,X0,X1) = range_of(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f140,f143]) ).
fof(f170,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f143]) ).
fof(f173,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| domain(X2,X0,X1) = domain_of(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f136,f143]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f143]) ).
fof(f187,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f111,f143]) ).
fof(f188,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f143]) ).
fof(f189,plain,
! [X0] : ~ empty(power_set(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f107,f143]) ).
fof(f194,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f102,f143]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f143]) ).
fof(f199,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[f90,f143]) ).
fof(f200,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f143]) ).
fof(f206,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| subset(X1,X0)
| ~ member(sk0_1(X0,X1),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f59,f143]) ).
fof(f207,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_1(X1,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f143]) ).
fof(f208,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| subset(X1,X0)
| member(sk0_1(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f58,f143]) ).
fof(f209,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_1(X1,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f143]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X3,X0))
| ~ subset(identity_relation_of(X1),X2)
| subset(X1,range(X3,X0,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f39,f143]) ).
fof(f226,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ subset(identity_relation_of(X0),X1)
| subset(X0,range(X2,X3,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f143]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X3,X0))
| ~ subset(identity_relation_of(X1),X2)
| subset(X1,domain(X3,X0,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f38,f143]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ subset(identity_relation_of(X0),X1)
| subset(X0,domain(X2,X3,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f143]) ).
fof(f229,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X1 = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f143]) ).
fof(f230,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f143]) ).
fof(f234,plain,
range(sk0_12,sk0_13,sk0_14) = range_of(sk0_14),
inference(resolution,[status(thm)],[f170,f148]) ).
fof(f251,plain,
( spl0_4
<=> ilf_type(sk0_14,relation_type(sk0_12,sk0_13)) ),
introduced(split_symbol_definition) ).
fof(f253,plain,
( ~ ilf_type(sk0_14,relation_type(sk0_12,sk0_13))
| spl0_4 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( spl0_5
<=> ilf_type(range_of(sk0_14),subset_type(sk0_13)) ),
introduced(split_symbol_definition) ).
fof(f255,plain,
( ilf_type(range_of(sk0_14),subset_type(sk0_13))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( ~ ilf_type(sk0_14,relation_type(sk0_12,sk0_13))
| ilf_type(range_of(sk0_14),subset_type(sk0_13)) ),
inference(paramodulation,[status(thm)],[f234,f168]) ).
fof(f258,plain,
( ~ spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f257,f251,f254]) ).
fof(f259,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f148]) ).
fof(f260,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f273,plain,
domain(sk0_12,sk0_13,sk0_14) = domain_of(sk0_14),
inference(resolution,[status(thm)],[f174,f148]) ).
fof(f274,plain,
( ~ subset(sk0_13,domain_of(sk0_14))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f273,f153]) ).
fof(f310,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| empty(power_set(X1))
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f200,f188]) ).
fof(f311,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f189]) ).
fof(f327,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(resolution,[status(thm)],[f195,f143]) ).
fof(f388,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(sk0_1(X1,X2),X0)
| subset(X2,X1) ),
inference(resolution,[status(thm)],[f327,f207]) ).
fof(f444,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| subset(X3,range(X1,X2,X0)) ),
inference(resolution,[status(thm)],[f226,f143]) ).
fof(f445,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| subset(X3,domain(X1,X2,X0)) ),
inference(resolution,[status(thm)],[f228,f143]) ).
fof(f482,plain,
( sk0_13 != range_of(sk0_14)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f234,f156]) ).
fof(f668,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f388,f209]) ).
fof(f669,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f668]) ).
fof(f683,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f669,f311]) ).
fof(f698,plain,
( subset(range_of(sk0_14),sk0_13)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f683,f255]) ).
fof(f908,plain,
( spl0_54
<=> subset(sk0_13,range_of(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f910,plain,
( ~ subset(sk0_13,range_of(sk0_14))
| spl0_54 ),
inference(component_clause,[status(thm)],[f908]) ).
fof(f911,plain,
( spl0_55
<=> sk0_13 = range_of(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f912,plain,
( sk0_13 = range_of(sk0_14)
| ~ spl0_55 ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f914,plain,
( ~ subset(sk0_13,range_of(sk0_14))
| sk0_13 = range_of(sk0_14)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f698,f230]) ).
fof(f915,plain,
( ~ spl0_54
| spl0_55
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f914,f908,f911,f254]) ).
fof(f916,plain,
( $false
| spl0_1
| ~ spl0_55 ),
inference(forward_subsumption_resolution,[status(thm)],[f912,f482]) ).
fof(f917,plain,
( spl0_1
| ~ spl0_55 ),
inference(contradiction_clause,[status(thm)],[f916]) ).
fof(f1255,plain,
! [X0,X1] :
( ~ ilf_type(sk0_14,relation_type(X0,X1))
| subset(sk0_13,range(X0,X1,sk0_14)) ),
inference(resolution,[status(thm)],[f444,f149]) ).
fof(f1258,plain,
! [X0,X1] :
( ~ ilf_type(sk0_14,relation_type(X0,X1))
| subset(sk0_13,domain(X0,X1,sk0_14)) ),
inference(resolution,[status(thm)],[f445,f149]) ).
fof(f1613,plain,
subset(sk0_13,range(sk0_12,sk0_13,sk0_14)),
inference(resolution,[status(thm)],[f1255,f148]) ).
fof(f1614,plain,
subset(sk0_13,range_of(sk0_14)),
inference(forward_demodulation,[status(thm)],[f234,f1613]) ).
fof(f1615,plain,
( $false
| spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f1614,f910]) ).
fof(f1616,plain,
spl0_54,
inference(contradiction_clause,[status(thm)],[f1615]) ).
fof(f1622,plain,
subset(sk0_13,domain(sk0_12,sk0_13,sk0_14)),
inference(resolution,[status(thm)],[f1258,f148]) ).
fof(f1623,plain,
subset(sk0_13,domain_of(sk0_14)),
inference(forward_demodulation,[status(thm)],[f273,f1622]) ).
fof(f1624,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1623,f274]) ).
fof(f1625,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f1624]) ).
fof(f1626,plain,
$false,
inference(sat_refutation,[status(thm)],[f157,f258,f260,f915,f917,f1616,f1625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8042.1875MB
% 0.10/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Apr 29 21:56:24 EDT 2024
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V3.6.0
% 2.80/0.74 % Refutation found
% 2.80/0.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.80/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.02/0.85 % Elapsed time: 0.501781 seconds
% 3.02/0.86 % CPU time: 3.115292 seconds
% 3.02/0.86 % Total memory used: 89.407 MB
% 3.02/0.86 % Net memory used: 88.348 MB
%------------------------------------------------------------------------------