TSTP Solution File: SET143+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET143+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 : Fri May 3 03:00:03 EDT 2024
% Result : Theorem 14.25s 2.64s
% Output : CNFRefutation 14.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 8 unt; 0 def)
% Number of atoms : 141 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 70 ~; 62 |; 16 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 2 sgn 61 !; 9 ?)
% 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(f12,conjecture,
! [X0,X1,X5] : equal_set(intersection(intersection(X0,X1),X5),intersection(X0,intersection(X1,X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI08) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X5] : equal_set(intersection(intersection(X0,X1),X5),intersection(X0,intersection(X1,X5))),
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(f23,plain,
~ ! [X0,X1,X2] : equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2))),
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,X2] : ~ equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2))),
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(f52,plain,
( ? [X0,X1,X2] : ~ equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2)))
=> ~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f29,f52]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
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(f62,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f81,plain,
~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),
inference(cnf_transformation,[],[f53]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_55,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
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_76,negated_conjecture,
~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),
inference(cnf_transformation,[],[f81]) ).
cnf(c_426,plain,
( intersection(intersection(sK3,sK4),sK5) != X0
| intersection(sK3,intersection(sK4,sK5)) != X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_427,plain,
( ~ subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5)))
| ~ subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(unflattening,[status(thm)],[c_426]) ).
cnf(c_1442,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5)))
| subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1498,plain,
( member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2074,plain,
( member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2075,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(intersection(sK3,sK4),sK5))
| subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_2259,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK5) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_2262,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_2886,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK3) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_2887,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_5097,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK4,sK5))
| ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK3)
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_5112,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,sK4))
| ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK5)
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_13682,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK3) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_13683,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK4) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_20253,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),X0)
| ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK3)
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,X0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_20529,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK4) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_20530,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_32716,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK4)
| ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK5)
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_49151,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK3)
| ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK4)
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_20253]) ).
cnf(c_53572,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_49151,c_32716,c_20529,c_20530,c_13682,c_13683,c_5112,c_5097,c_2886,c_2887,c_2262,c_2259,c_2074,c_2075,c_1498,c_1442,c_427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : SET143+4 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n022.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 20:13:42 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 14.25/2.64 % SZS status Started for theBenchmark.p
% 14.25/2.64 % SZS status Theorem for theBenchmark.p
% 14.25/2.64
% 14.25/2.64 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 14.25/2.64
% 14.25/2.64 ------ iProver source info
% 14.25/2.64
% 14.25/2.64 git: date: 2024-05-02 19:28:25 +0000
% 14.25/2.64 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 14.25/2.64 git: non_committed_changes: false
% 14.25/2.64
% 14.25/2.64 ------ Parsing...
% 14.25/2.64 ------ Clausification by vclausify_rel & Parsing by iProver...
% 14.25/2.64
% 14.25/2.64 ------ 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
% 14.25/2.64
% 14.25/2.64 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 14.25/2.64
% 14.25/2.64 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.25/2.64 ------ Proving...
% 14.25/2.64 ------ Problem Properties
% 14.25/2.64
% 14.25/2.64
% 14.25/2.64 clauses 27
% 14.25/2.64 conjectures 0
% 14.25/2.64 EPR 2
% 14.25/2.64 Horn 22
% 14.25/2.64 unary 4
% 14.25/2.64 binary 16
% 14.25/2.64 lits 57
% 14.25/2.64 lits eq 3
% 14.25/2.64 fd_pure 0
% 14.25/2.64 fd_pseudo 0
% 14.25/2.64 fd_cond 0
% 14.25/2.64 fd_pseudo_cond 2
% 14.25/2.64 AC symbols 0
% 14.25/2.64
% 14.25/2.64 ------ Schedule dynamic 5 is on
% 14.25/2.64
% 14.25/2.64 ------ no conjectures: strip conj schedule
% 14.25/2.64
% 14.25/2.64 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 14.25/2.64
% 14.25/2.64
% 14.25/2.64 ------
% 14.25/2.64 Current options:
% 14.25/2.64 ------
% 14.25/2.64
% 14.25/2.64
% 14.25/2.64
% 14.25/2.64
% 14.25/2.64 ------ Proving...
% 14.25/2.64
% 14.25/2.64
% 14.25/2.64 % SZS status Theorem for theBenchmark.p
% 14.25/2.64
% 14.25/2.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.25/2.64
% 14.25/2.65
%------------------------------------------------------------------------------