TSTP Solution File: SET696+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 15:09:10 EDT 2023
% Result : Theorem 10.21s 2.22s
% Output : CNFRefutation 10.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 10 unt; 0 def)
% Number of atoms : 196 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 218 ( 92 ~; 73 |; 36 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 6 sgn; 91 !; 12 ?)
% 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(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
fof(f12,conjecture,
! [X0,X3] :
( subset(X0,X3)
=> equal_set(intersection(difference(X3,X0),X0),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI28) ).
fof(f13,negated_conjecture,
~ ! [X0,X3] :
( subset(X0,X3)
=> equal_set(intersection(difference(X3,X0),X0),empty_set) ),
inference(negated_conjecture,[],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f17,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f21,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f23,plain,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(intersection(difference(X1,X0),X0),empty_set) ),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f29,plain,
? [X0,X1] :
( ~ equal_set(intersection(difference(X1,X0),X0),empty_set)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f30,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,[],[f25]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f31,f32]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f39]) ).
fof(f44,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f45,f46]) ).
fof(f52,plain,
( ? [X0,X1] :
( ~ equal_set(intersection(difference(X1,X0),X0),empty_set)
& subset(X0,X1) )
=> ( ~ equal_set(intersection(difference(sK4,sK3),sK3),empty_set)
& subset(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
( ~ equal_set(intersection(difference(sK4,sK3),sK3),empty_set)
& subset(sK3,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f52]) ).
fof(f54,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f75,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f82,plain,
~ equal_set(intersection(difference(sK4,sK3),sK3),empty_set),
inference(cnf_transformation,[],[f53]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_56,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_57,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_61,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f66]) ).
cnf(c_63,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_72,plain,
( ~ member(X0,sum(X1))
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_76,negated_conjecture,
~ equal_set(intersection(difference(sK4,sK3),sK3),empty_set),
inference(cnf_transformation,[],[f82]) ).
cnf(c_432,plain,
( intersection(difference(sK4,sK3),sK3) != X0
| X1 != empty_set
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_433,plain,
( ~ subset(intersection(difference(sK4,sK3),sK3),empty_set)
| ~ subset(empty_set,intersection(difference(sK4,sK3),sK3)) ),
inference(unflattening,[status(thm)],[c_432]) ).
cnf(c_1527,plain,
( member(sK0(intersection(difference(sK4,sK3),sK3),empty_set),intersection(difference(sK4,sK3),sK3))
| subset(intersection(difference(sK4,sK3),sK3),empty_set) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1893,plain,
( ~ member(X0,sum(empty_set))
| member(sK1(X0,empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_1894,plain,
~ member(sK1(X0,empty_set),empty_set),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1942,plain,
( ~ member(X0,intersection(difference(X1,X2),X3))
| member(X0,difference(X1,X2)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_2113,plain,
( member(sK0(empty_set,intersection(difference(sK4,sK3),sK3)),empty_set)
| subset(empty_set,intersection(difference(sK4,sK3),sK3)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2147,plain,
( ~ member(sK1(X0,sum(empty_set)),sum(empty_set))
| member(sK1(sK1(X0,sum(empty_set)),empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_1893]) ).
cnf(c_2148,plain,
( ~ member(X0,sum(sum(empty_set)))
| member(sK1(X0,sum(empty_set)),sum(empty_set)) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_2574,plain,
( ~ member(sK0(intersection(difference(sK4,sK3),sK3),empty_set),intersection(difference(sK4,sK3),sK3))
| ~ subset(intersection(difference(sK4,sK3),sK3),X0)
| member(sK0(intersection(difference(sK4,sK3),sK3),empty_set),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_10597,plain,
~ member(sK0(empty_set,intersection(difference(sK4,sK3),sK3)),empty_set),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_13249,plain,
( ~ member(sK0(intersection(difference(sK4,sK3),sK3),empty_set),intersection(difference(sK4,sK3),sK3))
| ~ subset(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set)))
| member(sK0(intersection(difference(sK4,sK3),sK3),empty_set),sum(sum(empty_set))) ),
inference(instantiation,[status(thm)],[c_2574]) ).
cnf(c_13250,plain,
( ~ member(sK0(intersection(difference(sK4,sK3),sK3),empty_set),sum(sum(empty_set)))
| member(sK1(sK0(intersection(difference(sK4,sK3),sK3),empty_set),sum(empty_set)),sum(empty_set)) ),
inference(instantiation,[status(thm)],[c_2148]) ).
cnf(c_26345,plain,
( member(sK0(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))),intersection(difference(sK4,sK3),sK3))
| subset(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_29148,plain,
( ~ member(sK1(sK0(intersection(difference(sK4,sK3),sK3),empty_set),sum(empty_set)),sum(empty_set))
| member(sK1(sK1(sK0(intersection(difference(sK4,sK3),sK3),empty_set),sum(empty_set)),empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_2147]) ).
cnf(c_45543,plain,
( ~ member(sK0(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))),intersection(difference(sK4,sK3),sK3))
| member(sK0(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))),sK3) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_45544,plain,
( ~ member(sK0(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))),intersection(difference(sK4,sK3),sK3))
| member(sK0(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_1942]) ).
cnf(c_49587,plain,
~ member(sK1(sK1(sK0(intersection(difference(sK4,sK3),sK3),empty_set),sum(empty_set)),empty_set),empty_set),
inference(instantiation,[status(thm)],[c_1894]) ).
cnf(c_75645,plain,
( ~ member(sK0(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))),difference(sK4,sK3))
| ~ member(sK0(intersection(difference(sK4,sK3),sK3),sum(sum(empty_set))),sK3) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_75647,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_75645,c_49587,c_45544,c_45543,c_29148,c_26345,c_13250,c_13249,c_10597,c_2113,c_1527,c_433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n022.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 09:12:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.21/2.22 % SZS status Started for theBenchmark.p
% 10.21/2.22 % SZS status Theorem for theBenchmark.p
% 10.21/2.22
% 10.21/2.22 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.21/2.22
% 10.21/2.22 ------ iProver source info
% 10.21/2.22
% 10.21/2.22 git: date: 2023-05-31 18:12:56 +0000
% 10.21/2.22 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.21/2.22 git: non_committed_changes: false
% 10.21/2.22 git: last_make_outside_of_git: false
% 10.21/2.22
% 10.21/2.22 ------ Parsing...
% 10.21/2.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.21/2.22
% 10.21/2.22 ------ 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
% 10.21/2.22
% 10.21/2.22 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.21/2.22
% 10.21/2.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.21/2.22 ------ Proving...
% 10.21/2.22 ------ Problem Properties
% 10.21/2.22
% 10.21/2.22
% 10.21/2.22 clauses 28
% 10.21/2.22 conjectures 1
% 10.21/2.22 EPR 3
% 10.21/2.22 Horn 23
% 10.21/2.22 unary 5
% 10.21/2.22 binary 16
% 10.21/2.22 lits 58
% 10.21/2.22 lits eq 3
% 10.21/2.22 fd_pure 0
% 10.21/2.22 fd_pseudo 0
% 10.21/2.22 fd_cond 0
% 10.21/2.22 fd_pseudo_cond 2
% 10.21/2.22 AC symbols 0
% 10.21/2.22
% 10.21/2.22 ------ Schedule dynamic 5 is on
% 10.21/2.22
% 10.21/2.22 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.21/2.22
% 10.21/2.22
% 10.21/2.22 ------
% 10.21/2.22 Current options:
% 10.21/2.22 ------
% 10.21/2.22
% 10.21/2.22
% 10.21/2.22
% 10.21/2.22
% 10.21/2.22 ------ Proving...
% 10.21/2.22
% 10.21/2.22
% 10.21/2.22 % SZS status Theorem for theBenchmark.p
% 10.21/2.22
% 10.21/2.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.21/2.23
% 10.21/2.23
%------------------------------------------------------------------------------