TSTP Solution File: SET159+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 15:06:53 EDT 2023
% Result : Theorem 17.33s 3.24s
% Output : CNFRefutation 17.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 144 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 154 ( 66 ~; 65 |; 14 &)
% ( 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/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_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,X5] : equal_set(union(union(X0,X1),X5),union(X0,union(X1,X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI09) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X5] : equal_set(union(union(X0,X1),X5),union(X0,union(X1,X5))),
inference(negated_conjecture,[],[f12]) ).
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,X2] : equal_set(union(union(X0,X1),X2),union(X0,union(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(union(union(X0,X1),X2),union(X0,union(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(f37,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(f38,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,[],[f37]) ).
fof(f52,plain,
( ? [X0,X1,X2] : ~ equal_set(union(union(X0,X1),X2),union(X0,union(X1,X2)))
=> ~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(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(f63,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(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_58,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_59,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_60,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_76,negated_conjecture,
~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),
inference(cnf_transformation,[],[f81]) ).
cnf(c_372,plain,
( union(union(sK3,sK4),sK5) != X0
| union(sK3,union(sK4,sK5)) != X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_373,plain,
( ~ subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5)))
| ~ subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
inference(unflattening,[status(thm)],[c_372]) ).
cnf(c_438,plain,
( ~ subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5)))
| ~ subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
inference(prop_impl_just,[status(thm)],[c_373]) ).
cnf(c_1363,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(union(sK3,sK4),sK5))
| subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1378,plain,
( member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,union(sK4,sK5)))
| subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1615,plain,
( member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(union(sK3,sK4),sK5))
| subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1616,plain,
( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,union(sK4,sK5)))
| subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1688,plain,
( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(union(sK3,sK4),sK5))
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,sK4))
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK5) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_1826,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,union(sK4,sK5)))
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK4,sK5))
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK3) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_3681,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK5)
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(union(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_3682,plain,
( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK4,sK5))
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,union(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_3683,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,sK4))
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(union(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_3684,plain,
( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK3)
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,union(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_5518,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(X0,sK5))
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),X0)
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_5547,plain,
( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK5)
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_5548,plain,
( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK4)
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_5569,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK4)
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_5570,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK3)
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_8382,plain,
( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,sK4))
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK3)
| member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK4) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_8430,plain,
~ subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),
inference(global_subsumption_just,[status(thm)],[c_438,c_373,c_1616,c_1615,c_1688,c_3682,c_3684,c_5547,c_5548,c_8382]) ).
cnf(c_15849,plain,
( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK4,sK5))
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK4)
| member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_5518]) ).
cnf(c_15850,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15849,c_8430,c_5570,c_5569,c_3683,c_3681,c_1826,c_1378,c_1363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17 % Problem : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.18 % Command : run_iprover %s %d THM
% 0.16/0.38 % Computer : n014.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sat Aug 26 15:27:02 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.33/3.24 % SZS status Started for theBenchmark.p
% 17.33/3.24 % SZS status Theorem for theBenchmark.p
% 17.33/3.24
% 17.33/3.24 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.33/3.24
% 17.33/3.24 ------ iProver source info
% 17.33/3.24
% 17.33/3.24 git: date: 2023-05-31 18:12:56 +0000
% 17.33/3.24 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.33/3.24 git: non_committed_changes: false
% 17.33/3.24 git: last_make_outside_of_git: false
% 17.33/3.24
% 17.33/3.24 ------ Parsing...
% 17.33/3.24 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.33/3.24
% 17.33/3.24 ------ 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
% 17.33/3.24
% 17.33/3.24 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.33/3.24
% 17.33/3.24 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.33/3.24 ------ Proving...
% 17.33/3.24 ------ Problem Properties
% 17.33/3.24
% 17.33/3.24
% 17.33/3.24 clauses 27
% 17.33/3.24 conjectures 0
% 17.33/3.24 EPR 2
% 17.33/3.24 Horn 22
% 17.33/3.24 unary 4
% 17.33/3.24 binary 16
% 17.33/3.24 lits 57
% 17.33/3.24 lits eq 3
% 17.33/3.24 fd_pure 0
% 17.33/3.24 fd_pseudo 0
% 17.33/3.24 fd_cond 0
% 17.33/3.24 fd_pseudo_cond 2
% 17.33/3.24 AC symbols 0
% 17.33/3.24
% 17.33/3.24 ------ Input Options Time Limit: Unbounded
% 17.33/3.24
% 17.33/3.24
% 17.33/3.24 ------
% 17.33/3.24 Current options:
% 17.33/3.24 ------
% 17.33/3.24
% 17.33/3.24
% 17.33/3.24
% 17.33/3.24
% 17.33/3.24 ------ Proving...
% 17.33/3.24
% 17.33/3.24
% 17.33/3.24 % SZS status Theorem for theBenchmark.p
% 17.33/3.24
% 17.33/3.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.33/3.24
% 17.33/3.25
%------------------------------------------------------------------------------