TSTP Solution File: SET811+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 : Fri May 3 03:01:36 EDT 2024
% Result : Theorem 67.79s 10.30s
% Output : CNFRefutation 67.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 8 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 257 ( 96 ~; 86 |; 51 &)
% ( 10 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 131 ( 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_279,plain,
( ~ subset(initial_segment(sK15,member_predicate,sK14),sK15)
| ~ subset(sK15,initial_segment(sK15,member_predicate,sK14))
| equal_set(sK15,initial_segment(sK15,member_predicate,sK14)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_597,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_598,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_658,plain,
( ~ apply(member_predicate,X0,sK15)
| member(X0,sK15) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_724,plain,
( ~ member(X0,X1)
| ~ subset(X1,sK14)
| member(X0,sK14) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1708,plain,
( ~ member(X0,sK14)
| subset(X0,sK14) ),
inference(resolution,[status(thm)],[c_78,c_114]) ).
cnf(c_1857,plain,
subset(sK15,sK14),
inference(resolution,[status(thm)],[c_1708,c_113]) ).
cnf(c_4347,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_4348,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_22929,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_724]) ).
cnf(c_23679,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_658]) ).
cnf(c_30061,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_71273,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_76197,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_91]) ).
cnf(c_76583,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_76197,c_71273,c_30061,c_23679,c_22929,c_4347,c_4348,c_1857,c_597,c_598,c_279,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 2 20:23:56 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 67.79/10.30 % SZS status Started for theBenchmark.p
% 67.79/10.30 % SZS status Theorem for theBenchmark.p
% 67.79/10.30
% 67.79/10.30 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 67.79/10.30
% 67.79/10.30 ------ iProver source info
% 67.79/10.30
% 67.79/10.30 git: date: 2024-05-02 19:28:25 +0000
% 67.79/10.30 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 67.79/10.30 git: non_committed_changes: false
% 67.79/10.30
% 67.79/10.30 ------ Parsing...
% 67.79/10.30 ------ Clausification by vclausify_rel & Parsing by iProver...
% 67.79/10.30
% 67.79/10.30 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 67.79/10.30
% 67.79/10.30 ------ Preprocessing...
% 67.79/10.30
% 67.79/10.30 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 67.79/10.30 ------ Proving...
% 67.79/10.30 ------ Problem Properties
% 67.79/10.30
% 67.79/10.30
% 67.79/10.30 clauses 66
% 67.79/10.30 conjectures 3
% 67.79/10.30 EPR 17
% 67.79/10.30 Horn 47
% 67.79/10.30 unary 7
% 67.79/10.30 binary 32
% 67.79/10.30 lits 162
% 67.79/10.30 lits eq 5
% 67.79/10.30 fd_pure 0
% 67.79/10.30 fd_pseudo 0
% 67.79/10.30 fd_cond 0
% 67.79/10.30 fd_pseudo_cond 3
% 67.79/10.30 AC symbols 0
% 67.79/10.30
% 67.79/10.30 ------ Input Options Time Limit: Unbounded
% 67.79/10.30
% 67.79/10.30
% 67.79/10.30 ------
% 67.79/10.30 Current options:
% 67.79/10.30 ------
% 67.79/10.30
% 67.79/10.30
% 67.79/10.30
% 67.79/10.30
% 67.79/10.30 ------ Proving...
% 67.79/10.30
% 67.79/10.30
% 67.79/10.30 % SZS status Theorem for theBenchmark.p
% 67.79/10.30
% 67.79/10.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 67.79/10.30
% 67.79/10.31
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