TSTP Solution File: SET637+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : Thu Aug 31 15:08:50 EDT 2023
% Result : Theorem 3.18s 1.16s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 85 ( 11 unt; 0 def)
% Number of atoms : 239 ( 36 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 261 ( 107 ~; 112 |; 30 &)
% ( 7 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 149 ( 4 sgn; 79 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f5,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f7,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(f9,conjecture,
! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th119) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
inference(negated_conjecture,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
? [X0,X1] :
( intersect(X0,X1)
<~> not_equal(intersection(X0,X1),empty_set) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
=> ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) )
| ~ intersect(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f25,plain,
( ? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) )
=> ( ( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) )
& ( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) )
& ( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f25]) ).
fof(f27,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X0,X1] :
( intersect(X0,X1)
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0,X1] :
( X0 = X1
| member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f41,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f38]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_50,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_51,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_52,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| intersect(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_53,plain,
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_54,plain,
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_55,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f33]) ).
cnf(c_57,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_58,plain,
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_59,plain,
~ not_equal(X0,X0),
inference(cnf_transformation,[],[f46]) ).
cnf(c_60,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f40]) ).
cnf(c_61,plain,
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_62,negated_conjecture,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_63,negated_conjecture,
( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_74,plain,
( ~ intersect(sK2,sK3)
| ~ not_equal(intersection(sK2,sK3),empty_set) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
cnf(c_75,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) ),
inference(renaming,[status(thm)],[c_74]) ).
cnf(c_76,plain,
( intersect(sK2,sK3)
| not_equal(intersection(sK2,sK3),empty_set) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
cnf(c_77,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ),
inference(renaming,[status(thm)],[c_76]) ).
cnf(c_94,plain,
( X0 = X1
| not_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
cnf(c_254,plain,
( intersection(sK2,sK3) != X0
| X1 != empty_set
| ~ intersect(sK2,sK3)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_94,c_75]) ).
cnf(c_255,plain,
( ~ intersect(sK2,sK3)
| intersection(sK2,sK3) = empty_set ),
inference(unflattening,[status(thm)],[c_254]) ).
cnf(c_262,plain,
( intersection(sK2,sK3) != X0
| X0 != empty_set
| intersect(sK2,sK3) ),
inference(resolution_lifted,[status(thm)],[c_59,c_77]) ).
cnf(c_263,plain,
( intersection(sK2,sK3) != empty_set
| intersect(sK2,sK3) ),
inference(unflattening,[status(thm)],[c_262]) ).
cnf(c_274,plain,
( intersect(sK2,sK3)
| intersection(sK2,sK3) != empty_set ),
inference(prop_impl_just,[status(thm)],[c_263]) ).
cnf(c_275,plain,
( intersection(sK2,sK3) != empty_set
| intersect(sK2,sK3) ),
inference(renaming,[status(thm)],[c_274]) ).
cnf(c_276,plain,
( ~ intersect(sK2,sK3)
| intersection(sK2,sK3) = empty_set ),
inference(prop_impl_just,[status(thm)],[c_255]) ).
cnf(c_750,plain,
( ~ intersect(X0,intersection(X1,X2))
| member(sK0(X0,intersection(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_53,c_50]) ).
cnf(c_782,plain,
( ~ member(sK0(X0,X1),X2)
| ~ intersect(X0,X1)
| intersect(X2,X0) ),
inference(superposition,[status(thm)],[c_54,c_52]) ).
cnf(c_795,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X2,X1)) ),
inference(superposition,[status(thm)],[c_60,c_49]) ).
cnf(c_815,plain,
( X0 = empty_set
| member(sK1(X0,empty_set),X0) ),
inference(superposition,[status(thm)],[c_57,c_55]) ).
cnf(c_854,plain,
( intersection(X0,X1) = empty_set
| member(sK1(intersection(X0,X1),empty_set),X0) ),
inference(superposition,[status(thm)],[c_815,c_51]) ).
cnf(c_856,plain,
( ~ member(sK1(X0,empty_set),X1)
| X0 = empty_set
| intersect(X1,X0) ),
inference(superposition,[status(thm)],[c_815,c_52]) ).
cnf(c_890,plain,
( ~ intersect(sK2,sK3)
| intersect(sK3,sK2) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_982,plain,
( ~ intersect(sK3,sK2)
| member(sK0(sK3,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_1090,plain,
( ~ intersect(X0,intersection(X1,X2))
| intersect(X2,X0) ),
inference(superposition,[status(thm)],[c_750,c_782]) ).
cnf(c_1541,plain,
( intersection(X0,X1) = empty_set
| intersect(X0,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_854,c_856]) ).
cnf(c_1608,plain,
( intersection(X0,X1) = empty_set
| intersect(X1,X0) ),
inference(superposition,[status(thm)],[c_1541,c_1090]) ).
cnf(c_1658,plain,
( intersection(X0,X1) = empty_set
| intersect(X0,X1) ),
inference(superposition,[status(thm)],[c_1608,c_61]) ).
cnf(c_1776,plain,
intersect(sK2,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_275,c_1658]) ).
cnf(c_1777,plain,
intersection(sK2,sK3) = empty_set,
inference(backward_subsumption_resolution,[status(thm)],[c_276,c_1658]) ).
cnf(c_1817,plain,
( ~ member(X0,sK2)
| ~ member(X0,sK3)
| member(X0,empty_set) ),
inference(superposition,[status(thm)],[c_1777,c_795]) ).
cnf(c_1833,plain,
( ~ member(X0,sK2)
| ~ member(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1817,c_55]) ).
cnf(c_1915,plain,
( ~ member(sK0(sK3,X0),sK2)
| ~ intersect(sK3,X0) ),
inference(superposition,[status(thm)],[c_54,c_1833]) ).
cnf(c_1960,plain,
( ~ member(sK0(sK3,sK2),sK2)
| ~ intersect(sK3,sK2) ),
inference(instantiation,[status(thm)],[c_1915]) ).
cnf(c_1961,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1960,c_1776,c_982,c_890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 14:24:25 EDT 2023
% 0.12/0.34 % 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
% 3.18/1.16 % SZS status Started for theBenchmark.p
% 3.18/1.16 % SZS status Theorem for theBenchmark.p
% 3.18/1.16
% 3.18/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.18/1.16
% 3.18/1.16 ------ iProver source info
% 3.18/1.16
% 3.18/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.18/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.18/1.16 git: non_committed_changes: false
% 3.18/1.16 git: last_make_outside_of_git: false
% 3.18/1.16
% 3.18/1.16 ------ Parsing...
% 3.18/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.18/1.16
% 3.18/1.16 ------ 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
% 3.18/1.16
% 3.18/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.18/1.16
% 3.18/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.18/1.16 ------ Proving...
% 3.18/1.16 ------ Problem Properties
% 3.18/1.16
% 3.18/1.16
% 3.18/1.16 clauses 13
% 3.18/1.16 conjectures 0
% 3.18/1.16 EPR 3
% 3.18/1.16 Horn 12
% 3.18/1.16 unary 2
% 3.18/1.16 binary 7
% 3.18/1.16 lits 28
% 3.18/1.16 lits eq 5
% 3.18/1.16 fd_pure 0
% 3.18/1.16 fd_pseudo 0
% 3.18/1.16 fd_cond 0
% 3.18/1.16 fd_pseudo_cond 2
% 3.18/1.16 AC symbols 0
% 3.18/1.16
% 3.18/1.16 ------ Schedule dynamic 5 is on
% 3.18/1.16
% 3.18/1.16 ------ no conjectures: strip conj schedule
% 3.18/1.16
% 3.18/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.18/1.16
% 3.18/1.16
% 3.18/1.16 ------
% 3.18/1.16 Current options:
% 3.18/1.16 ------
% 3.18/1.16
% 3.18/1.16
% 3.18/1.16
% 3.18/1.16
% 3.18/1.16 ------ Proving...
% 3.18/1.16
% 3.18/1.16
% 3.18/1.16 % SZS status Theorem for theBenchmark.p
% 3.18/1.16
% 3.18/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.18/1.16
% 3.18/1.16
%------------------------------------------------------------------------------