TSTP Solution File: SET811+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% 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 : 300s
% DateTime : Thu Aug 31 15:09:58 EDT 2023
% Result : Theorem 19.66s 3.67s
% Output : CNFRefutation 19.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 75 ( 9 unt; 0 def)
% Number of atoms : 240 ( 2 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 270 ( 105 ~; 90 |; 51 &)
% ( 10 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 132 ( 1 sgn; 91 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( ! [X2] :
( member(X2,X0)
=> subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).
fof(f15,axiom,
! [X2,X4] :
( apply(member_predicate,X2,X4)
<=> member(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_member) ).
fof(f18,axiom,
! [X2,X5,X0,X4] :
( member(X4,initial_segment(X2,X5,X0))
<=> ( apply(X5,X4,X2)
& member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_segment) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> ! [X2] :
( member(X2,X0)
=> equal_set(X2,initial_segment(X2,member_predicate,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV5) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> ! [X2] :
( member(X2,X0)
=> equal_set(X2,initial_segment(X2,member_predicate,X0)) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f31,plain,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( member(X1,X0)
=> subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f34,plain,
! [X0,X1] :
( apply(member_predicate,X0,X1)
<=> member(X0,X1) ),
inference(rectify,[],[f15]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( member(X3,initial_segment(X0,X1,X2))
<=> ( apply(X1,X3,X0)
& member(X3,X2) ) ),
inference(rectify,[],[f18]) ).
fof(f39,plain,
~ ! [X0] :
( member(X0,on)
=> ! [X1] :
( member(X1,X0)
=> equal_set(X1,initial_segment(X1,member_predicate,X0)) ) ),
inference(rectify,[],[f21]) ).
fof(f40,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f42,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f42]) ).
fof(f45,plain,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f53,plain,
? [X0] :
( ? [X1] :
( ~ equal_set(X1,initial_segment(X1,member_predicate,X0))
& member(X1,X0) )
& member(X0,on) ),
inference(ennf_transformation,[],[f39]) ).
fof(f56,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f57,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f57,f58]) ).
fof(f78,plain,
! [X0] :
( ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f79,plain,
! [X0] :
( ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
=> ( ~ subset(sK4(X0),X0)
& member(sK4(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ( member(X0,on)
| ( ~ subset(sK4(X0),X0)
& member(sK4(X0),X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f80,f81]) ).
fof(f95,plain,
! [X0,X1] :
( ( apply(member_predicate,X0,X1)
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ apply(member_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( ( member(X3,initial_segment(X0,X1,X2))
| ~ apply(X1,X3,X0)
| ~ member(X3,X2) )
& ( ( apply(X1,X3,X0)
& member(X3,X2) )
| ~ member(X3,initial_segment(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( ( member(X3,initial_segment(X0,X1,X2))
| ~ apply(X1,X3,X0)
| ~ member(X3,X2) )
& ( ( apply(X1,X3,X0)
& member(X3,X2) )
| ~ member(X3,initial_segment(X0,X1,X2)) ) ),
inference(flattening,[],[f105]) ).
fof(f108,plain,
( ? [X0] :
( ? [X1] :
( ~ equal_set(X1,initial_segment(X1,member_predicate,X0))
& member(X1,X0) )
& member(X0,on) )
=> ( ? [X1] :
( ~ equal_set(X1,initial_segment(X1,member_predicate,sK14))
& member(X1,sK14) )
& member(sK14,on) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ? [X1] :
( ~ equal_set(X1,initial_segment(X1,member_predicate,sK14))
& member(X1,sK14) )
=> ( ~ equal_set(sK15,initial_segment(sK15,member_predicate,sK14))
& member(sK15,sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ~ equal_set(sK15,initial_segment(sK15,member_predicate,sK14))
& member(sK15,sK14)
& member(sK14,on) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f53,f109,f108]) ).
fof(f111,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f112,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f113,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f114,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f140,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ member(X2,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[],[f82]) ).
fof(f153,plain,
! [X0,X1] :
( member(X0,X1)
| ~ apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
! [X0,X1] :
( apply(member_predicate,X0,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f170,plain,
! [X2,X3,X0,X1] :
( apply(X1,X3,X0)
| ~ member(X3,initial_segment(X0,X1,X2)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( member(X3,initial_segment(X0,X1,X2))
| ~ apply(X1,X3,X0)
| ~ member(X3,X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f174,plain,
member(sK14,on),
inference(cnf_transformation,[],[f110]) ).
fof(f175,plain,
member(sK15,sK14),
inference(cnf_transformation,[],[f110]) ).
fof(f176,plain,
~ equal_set(sK15,initial_segment(sK15,member_predicate,sK14)),
inference(cnf_transformation,[],[f110]) ).
cnf(c_49,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_50,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_78,plain,
( ~ member(X0,X1)
| ~ member(X1,on)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_91,plain,
( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_92,plain,
( ~ apply(member_predicate,X0,X1)
| member(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_107,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| member(X1,initial_segment(X2,X0,X3)) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_108,plain,
( ~ member(X0,initial_segment(X1,X2,X3))
| apply(X2,X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_112,negated_conjecture,
~ equal_set(sK15,initial_segment(sK15,member_predicate,sK14)),
inference(cnf_transformation,[],[f176]) ).
cnf(c_113,negated_conjecture,
member(sK15,sK14),
inference(cnf_transformation,[],[f175]) ).
cnf(c_114,negated_conjecture,
member(sK14,on),
inference(cnf_transformation,[],[f174]) ).
cnf(c_1040,plain,
( initial_segment(sK15,member_predicate,sK14) != X1
| X0 != sK15
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_112]) ).
cnf(c_1041,plain,
( ~ subset(initial_segment(sK15,member_predicate,sK14),sK15)
| ~ subset(sK15,initial_segment(sK15,member_predicate,sK14)) ),
inference(unflattening,[status(thm)],[c_1040]) ).
cnf(c_2572,plain,
( ~ subset(sK15,initial_segment(sK15,member_predicate,sK14))
| ~ subset(initial_segment(sK15,member_predicate,sK14),sK15) ),
inference(prop_impl_just,[status(thm)],[c_1041]) ).
cnf(c_2573,plain,
( ~ subset(initial_segment(sK15,member_predicate,sK14),sK15)
| ~ subset(sK15,initial_segment(sK15,member_predicate,sK14)) ),
inference(renaming,[status(thm)],[c_2572]) ).
cnf(c_6426,plain,
( ~ member(sK1(initial_segment(sK15,member_predicate,sK14),sK15),sK15)
| subset(initial_segment(sK15,member_predicate,sK14),sK15) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_6427,plain,
( member(sK1(initial_segment(sK15,member_predicate,sK14),sK15),initial_segment(sK15,member_predicate,sK14))
| subset(initial_segment(sK15,member_predicate,sK14),sK15) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_6836,plain,
( ~ member(sK14,on)
| subset(sK15,sK14) ),
inference(superposition,[status(thm)],[c_113,c_78]) ).
cnf(c_6846,plain,
subset(sK15,sK14),
inference(forward_subsumption_resolution,[status(thm)],[c_6836,c_114]) ).
cnf(c_7822,plain,
( member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK15)
| subset(sK15,initial_segment(sK15,member_predicate,sK14)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_7823,plain,
( ~ member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),initial_segment(sK15,member_predicate,sK14))
| subset(sK15,initial_segment(sK15,member_predicate,sK14)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_12088,plain,
( ~ member(sK1(initial_segment(sK15,member_predicate,sK14),sK15),initial_segment(sK15,member_predicate,sK14))
| apply(member_predicate,sK1(initial_segment(sK15,member_predicate,sK14),sK15),sK15) ),
inference(instantiation,[status(thm)],[c_108]) ).
cnf(c_16980,plain,
( ~ apply(member_predicate,sK1(initial_segment(sK15,member_predicate,sK14),sK15),sK15)
| member(sK1(initial_segment(sK15,member_predicate,sK14),sK15),sK15) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_18388,plain,
( ~ member(X0,X1)
| ~ subset(X1,sK14)
| member(X0,sK14) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_20374,plain,
( ~ apply(member_predicate,sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK15)
| ~ member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK14)
| member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),initial_segment(sK15,member_predicate,sK14)) ),
inference(instantiation,[status(thm)],[c_107]) ).
cnf(c_35670,plain,
~ subset(sK15,initial_segment(sK15,member_predicate,sK14)),
inference(global_subsumption_just,[status(thm)],[c_2573,c_1041,c_6426,c_6427,c_12088,c_16980]) ).
cnf(c_42096,plain,
( ~ member(X0,sK15)
| apply(member_predicate,X0,sK15) ),
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_88715,plain,
( ~ member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK15)
| apply(member_predicate,sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK15) ),
inference(instantiation,[status(thm)],[c_42096]) ).
cnf(c_116945,plain,
( ~ member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK15)
| ~ subset(sK15,sK14)
| member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK14) ),
inference(instantiation,[status(thm)],[c_18388]) ).
cnf(c_116946,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116945,c_88715,c_35670,c_20374,c_7822,c_7823,c_6846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 12:23:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.66/3.67 % SZS status Started for theBenchmark.p
% 19.66/3.67 % SZS status Theorem for theBenchmark.p
% 19.66/3.67
% 19.66/3.67 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 19.66/3.67
% 19.66/3.67 ------ iProver source info
% 19.66/3.67
% 19.66/3.67 git: date: 2023-05-31 18:12:56 +0000
% 19.66/3.67 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 19.66/3.67 git: non_committed_changes: false
% 19.66/3.67 git: last_make_outside_of_git: false
% 19.66/3.67
% 19.66/3.67 ------ Parsing...
% 19.66/3.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 19.66/3.67
% 19.66/3.67 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 19.66/3.67
% 19.66/3.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 19.66/3.67
% 19.66/3.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 19.66/3.67 ------ Proving...
% 19.66/3.67 ------ Problem Properties
% 19.66/3.67
% 19.66/3.67
% 19.66/3.67 clauses 65
% 19.66/3.67 conjectures 2
% 19.66/3.67 EPR 16
% 19.66/3.67 Horn 46
% 19.66/3.67 unary 6
% 19.66/3.67 binary 33
% 19.66/3.67 lits 160
% 19.66/3.67 lits eq 5
% 19.66/3.67 fd_pure 0
% 19.66/3.67 fd_pseudo 0
% 19.66/3.67 fd_cond 0
% 19.66/3.67 fd_pseudo_cond 3
% 19.66/3.67 AC symbols 0
% 19.66/3.67
% 19.66/3.67 ------ Schedule dynamic 5 is on
% 19.66/3.67
% 19.66/3.67 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 19.66/3.67
% 19.66/3.67
% 19.66/3.67 ------
% 19.66/3.67 Current options:
% 19.66/3.67 ------
% 19.66/3.67
% 19.66/3.67
% 19.66/3.67
% 19.66/3.67
% 19.66/3.67 ------ Proving...
% 19.66/3.67
% 19.66/3.67
% 19.66/3.67 % SZS status Theorem for theBenchmark.p
% 19.66/3.67
% 19.66/3.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.66/3.67
% 19.66/3.67
%------------------------------------------------------------------------------