TSTP Solution File: SET578+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 15:08:22 EDT 2023
% Result : Theorem 0.46s 1.16s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 3 unt; 0 def)
% Number of atoms : 223 ( 23 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 264 ( 101 ~; 106 |; 43 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 130 ( 2 sgn; 77 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) )
=> intersection(X1,X2) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th19) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) )
=> intersection(X1,X2) = X0 ),
inference(negated_conjecture,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2] :
( intersection(X1,X2) != X0
& ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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(f12,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,[],[f11]) ).
fof(f15,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,[],[f9]) ).
fof(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,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])],[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,[],[f6]) ).
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,X2] :
( intersection(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X2)
| ~ member(X3,X1) )
& ( ( member(X3,X2)
& member(X3,X1) )
| ~ member(X3,X0) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f24,plain,
? [X0,X1,X2] :
( intersection(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X2)
| ~ member(X3,X1) )
& ( ( member(X3,X2)
& member(X3,X1) )
| ~ member(X3,X0) ) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ? [X0,X1,X2] :
( intersection(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X2)
| ~ member(X3,X1) )
& ( ( member(X3,X2)
& member(X3,X1) )
| ~ member(X3,X0) ) ) )
=> ( sK2 != intersection(sK3,sK4)
& ! [X3] :
( ( member(X3,sK2)
| ~ member(X3,sK4)
| ~ member(X3,sK3) )
& ( ( member(X3,sK4)
& member(X3,sK3) )
| ~ member(X3,sK2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( sK2 != intersection(sK3,sK4)
& ! [X3] :
( ( member(X3,sK2)
| ~ member(X3,sK4)
| ~ member(X3,sK3) )
& ( ( member(X3,sK4)
& member(X3,sK3) )
| ~ member(X3,sK2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f24,f25]) ).
fof(f27,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = X1
| member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X3] :
( member(X3,sK3)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X3] :
( member(X3,sK4)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X3] :
( member(X3,sK2)
| ~ member(X3,sK4)
| ~ member(X3,sK3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
sK2 != intersection(sK3,sK4),
inference(cnf_transformation,[],[f26]) ).
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_56,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_57,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_60,plain,
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_61,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_62,negated_conjecture,
intersection(sK3,sK4) != sK2,
inference(cnf_transformation,[],[f45]) ).
cnf(c_63,negated_conjecture,
( ~ member(X0,sK3)
| ~ member(X0,sK4)
| member(X0,sK2) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_64,negated_conjecture,
( ~ member(X0,sK2)
| member(X0,sK4) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_65,negated_conjecture,
( ~ member(X0,sK2)
| member(X0,sK3) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_572,plain,
( member(sK0(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_50]) ).
cnf(c_582,plain,
( member(sK0(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_51]) ).
cnf(c_694,plain,
( ~ member(sK1(intersection(sK3,sK4),sK2),intersection(sK3,sK4))
| ~ member(sK1(intersection(sK3,sK4),sK2),sK2)
| intersection(sK3,sK4) = sK2 ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_702,plain,
( intersection(sK3,sK4) = sK2
| member(sK1(intersection(sK3,sK4),sK2),intersection(sK3,sK4))
| member(sK1(intersection(sK3,sK4),sK2),sK2) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_797,plain,
( ~ member(sK0(intersection(sK3,sK4),sK2),sK2)
| subset(intersection(sK3,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_799,plain,
( ~ member(sK1(intersection(sK3,sK4),sK2),intersection(sK3,sK4))
| ~ subset(intersection(sK3,sK4),X0)
| member(sK1(intersection(sK3,sK4),sK2),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_800,plain,
( ~ member(sK1(intersection(sK3,sK4),sK2),intersection(sK3,sK4))
| ~ subset(intersection(sK3,sK4),sK2)
| member(sK1(intersection(sK3,sK4),sK2),sK2) ),
inference(instantiation,[status(thm)],[c_799]) ).
cnf(c_915,plain,
( ~ member(sK0(intersection(sK3,X0),X1),sK4)
| member(sK0(intersection(sK3,X0),X1),sK2)
| subset(intersection(sK3,X0),X1) ),
inference(superposition,[status(thm)],[c_582,c_63]) ).
cnf(c_943,plain,
( ~ member(sK1(intersection(sK3,sK4),sK2),sK2)
| member(sK1(intersection(sK3,sK4),sK2),sK3) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_944,plain,
( ~ member(sK1(intersection(sK3,sK4),sK2),sK2)
| member(sK1(intersection(sK3,sK4),sK2),sK4) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_1116,plain,
( ~ member(sK1(intersection(sK3,sK4),sK2),X0)
| ~ member(sK1(intersection(sK3,sK4),sK2),X1)
| member(sK1(intersection(sK3,sK4),sK2),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_2075,plain,
( member(sK0(intersection(sK3,sK4),X0),sK2)
| subset(intersection(sK3,sK4),X0) ),
inference(superposition,[status(thm)],[c_572,c_915]) ).
cnf(c_2095,plain,
( member(sK0(intersection(sK3,sK4),sK2),sK2)
| subset(intersection(sK3,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_2075]) ).
cnf(c_2546,plain,
( ~ member(sK1(intersection(sK3,sK4),sK2),sK3)
| ~ member(sK1(intersection(sK3,sK4),sK2),sK4)
| member(sK1(intersection(sK3,sK4),sK2),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1116]) ).
cnf(c_2547,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2546,c_2095,c_943,c_944,c_800,c_797,c_702,c_694,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 10:37:56 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.46/1.16 % SZS status Started for theBenchmark.p
% 0.46/1.16 % SZS status Theorem for theBenchmark.p
% 0.46/1.16
% 0.46/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.46/1.16
% 0.46/1.16 ------ iProver source info
% 0.46/1.16
% 0.46/1.16 git: date: 2023-05-31 18:12:56 +0000
% 0.46/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.46/1.16 git: non_committed_changes: false
% 0.46/1.16 git: last_make_outside_of_git: false
% 0.46/1.16
% 0.46/1.16 ------ Parsing...
% 0.46/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.46/1.16
% 0.46/1.16 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.46/1.16
% 0.46/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.46/1.16
% 0.46/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.46/1.16 ------ Proving...
% 0.46/1.16 ------ Problem Properties
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 clauses 15
% 0.46/1.16 conjectures 4
% 0.46/1.16 EPR 6
% 0.46/1.16 Horn 13
% 0.46/1.16 unary 3
% 0.46/1.16 binary 6
% 0.46/1.16 lits 33
% 0.46/1.16 lits eq 5
% 0.46/1.16 fd_pure 0
% 0.46/1.16 fd_pseudo 0
% 0.46/1.16 fd_cond 0
% 0.46/1.16 fd_pseudo_cond 3
% 0.46/1.16 AC symbols 0
% 0.46/1.16
% 0.46/1.16 ------ Schedule dynamic 5 is on
% 0.46/1.16
% 0.46/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 ------
% 0.46/1.16 Current options:
% 0.46/1.16 ------
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 ------ Proving...
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 % SZS status Theorem for theBenchmark.p
% 0.46/1.16
% 0.46/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.16
% 0.46/1.16
%------------------------------------------------------------------------------