TSTP Solution File: SET694+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET694+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 106.42s 15.27s
% Output : CNFRefutation 106.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 9 unt; 0 def)
% Number of atoms : 147 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 155 ( 67 ~; 66 |; 13 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 2 sgn; 59 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f3,axiom,
! [X2,X0] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f12,conjecture,
! [X0,X1] : subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI22) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
inference(negated_conjecture,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
? [X0,X1] : ~ subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
inference(ennf_transformation,[],[f13]) ).
fof(f26,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,[],[f23]) ).
fof(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,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])],[f27,f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f33]) ).
fof(f48,plain,
( ? [X0,X1] : ~ subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1)))
=> ~ subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
~ subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f25,f48]) ).
fof(f50,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f76,plain,
~ subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),
inference(cnf_transformation,[],[f49]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_53,plain,
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_57,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_59,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_75,negated_conjecture,
~ subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),
inference(cnf_transformation,[],[f76]) ).
cnf(c_100,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
cnf(c_104,plain,
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
cnf(c_105,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_104]) ).
cnf(c_331,plain,
( union(power_set(sK3),power_set(sK4)) != X0
| power_set(union(sK3,sK4)) != X1
| member(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_105,c_75]) ).
cnf(c_332,plain,
member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(power_set(sK3),power_set(sK4))),
inference(unflattening,[status(thm)],[c_331]) ).
cnf(c_336,plain,
( union(power_set(sK3),power_set(sK4)) != X0
| power_set(union(sK3,sK4)) != X1
| ~ member(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_100,c_75]) ).
cnf(c_337,plain,
~ member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(union(sK3,sK4))),
inference(unflattening,[status(thm)],[c_336]) ).
cnf(c_788,plain,
( ~ subset(sK0(X0,power_set(X1)),X1)
| member(sK0(X0,power_set(X1)),power_set(X1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_1058,plain,
( ~ member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(power_set(sK3),power_set(sK4)))
| member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK3))
| member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK4)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_1390,plain,
( ~ member(sK0(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(superposition,[status(thm)],[c_57,c_49]) ).
cnf(c_1392,plain,
( ~ member(sK0(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_49]) ).
cnf(c_2394,plain,
( ~ subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4))
| member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_788]) ).
cnf(c_15352,plain,
( ~ member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(X0))
| subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_15353,plain,
( ~ member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK3))
| subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_15352]) ).
cnf(c_174118,plain,
( ~ member(sK0(X0,X1),X0)
| ~ subset(X0,X2)
| member(sK0(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_191593,plain,
( ~ member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(X0))
| subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_284516,plain,
( ~ member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK4)
| subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1390]) ).
cnf(c_285238,plain,
( ~ member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK3)
| subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_1392]) ).
cnf(c_414825,plain,
( ~ member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))))
| ~ subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),sK4)
| member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK4) ),
inference(instantiation,[status(thm)],[c_174118]) ).
cnf(c_414826,plain,
( ~ member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))))
| ~ subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),sK3)
| member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_174118]) ).
cnf(c_426012,plain,
( member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))))
| subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_437744,plain,
( ~ member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK4))
| subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),sK4) ),
inference(instantiation,[status(thm)],[c_191593]) ).
cnf(c_437745,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_437744,c_426012,c_414826,c_414825,c_285238,c_284516,c_15353,c_2394,c_1058,c_337,c_332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET694+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:00:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 106.42/15.27 % SZS status Started for theBenchmark.p
% 106.42/15.27 % SZS status Theorem for theBenchmark.p
% 106.42/15.27
% 106.42/15.27 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 106.42/15.27
% 106.42/15.27 ------ iProver source info
% 106.42/15.27
% 106.42/15.27 git: date: 2023-05-31 18:12:56 +0000
% 106.42/15.27 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 106.42/15.27 git: non_committed_changes: false
% 106.42/15.27 git: last_make_outside_of_git: false
% 106.42/15.27
% 106.42/15.27 ------ Parsing...
% 106.42/15.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 106.42/15.27
% 106.42/15.27 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 106.42/15.27
% 106.42/15.27 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 106.42/15.27
% 106.42/15.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 106.42/15.27 ------ Proving...
% 106.42/15.27 ------ Problem Properties
% 106.42/15.27
% 106.42/15.27
% 106.42/15.27 clauses 27
% 106.42/15.27 conjectures 1
% 106.42/15.27 EPR 2
% 106.42/15.27 Horn 22
% 106.42/15.27 unary 5
% 106.42/15.27 binary 15
% 106.42/15.27 lits 56
% 106.42/15.27 lits eq 3
% 106.42/15.27 fd_pure 0
% 106.42/15.27 fd_pseudo 0
% 106.42/15.27 fd_cond 0
% 106.42/15.27 fd_pseudo_cond 2
% 106.42/15.27 AC symbols 0
% 106.42/15.27
% 106.42/15.27 ------ Input Options Time Limit: Unbounded
% 106.42/15.27
% 106.42/15.27
% 106.42/15.27 ------
% 106.42/15.27 Current options:
% 106.42/15.27 ------
% 106.42/15.27
% 106.42/15.27
% 106.42/15.27
% 106.42/15.27
% 106.42/15.27 ------ Proving...
% 106.42/15.27
% 106.42/15.27
% 106.42/15.27 % SZS status Theorem for theBenchmark.p
% 106.42/15.27
% 106.42/15.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 106.42/15.27
% 106.42/15.27
%------------------------------------------------------------------------------