TSTP Solution File: SET607+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET607+3 : 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 15:08:35 EDT 2023
% Result : Theorem 2.84s 1.17s
% Output : CNFRefutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 155 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 175 ( 69 ~; 80 |; 20 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 7 sgn; 55 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f8,conjecture,
! [X0,X1] : union(X0,X1) = union(X0,difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th79) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : union(X0,X1) = union(X0,difference(X1,X0)),
inference(negated_conjecture,[],[f8]) ).
fof(f11,plain,
? [X0,X1] : union(X0,X1) != union(X0,difference(X1,X0)),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f22,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,[],[f7]) ).
fof(f23,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,[],[f22]) ).
fof(f24,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(f25,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])],[f23,f24]) ).
fof(f26,plain,
( ? [X0,X1] : union(X0,X1) != union(X0,difference(X1,X0))
=> union(sK2,sK3) != union(sK2,difference(sK3,sK2)) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
union(sK2,sK3) != union(sK2,difference(sK3,sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f11,f26]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f33,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f44,plain,
! [X0,X1] :
( X0 = X1
| member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
union(sK2,sK3) != union(sK2,difference(sK3,sK2)),
inference(cnf_transformation,[],[f27]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_50,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_51,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_52,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_54,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_63,plain,
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_64,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_65,negated_conjecture,
union(sK2,difference(sK3,sK2)) != union(sK2,sK3),
inference(cnf_transformation,[],[f46]) ).
cnf(c_718,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2)))
| ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3))
| union(sK2,difference(sK3,sK2)) = union(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_719,plain,
( union(sK2,difference(sK3,sK2)) = union(sK2,sK3)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2)))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_744,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2)))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1084,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1799,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,X0)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2258,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),X0)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(X0,X1))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),X1) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_2260,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),X0)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(X1,X0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_2266,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(X0,X1))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_6542,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2))) ),
inference(instantiation,[status(thm)],[c_1799]) ).
cnf(c_8186,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,difference(sK3,sK2))) ),
inference(instantiation,[status(thm)],[c_2260]) ).
cnf(c_9619,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(X0,sK3)) ),
inference(instantiation,[status(thm)],[c_2260]) ).
cnf(c_9620,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_9619]) ).
cnf(c_10346,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,X0))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),X0) ),
inference(instantiation,[status(thm)],[c_2258]) ).
cnf(c_10347,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2) ),
inference(instantiation,[status(thm)],[c_10346]) ).
cnf(c_18685,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK2)
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),union(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_1799]) ).
cnf(c_20586,plain,
( ~ member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),difference(sK3,sK2))
| member(sK1(union(sK2,difference(sK3,sK2)),union(sK2,sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_2266]) ).
cnf(c_20588,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20586,c_18685,c_10347,c_9620,c_8186,c_6542,c_1084,c_744,c_719,c_718,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET607+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:03:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.84/1.17 % SZS status Started for theBenchmark.p
% 2.84/1.17 % SZS status Theorem for theBenchmark.p
% 2.84/1.17
% 2.84/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.84/1.17
% 2.84/1.17 ------ iProver source info
% 2.84/1.17
% 2.84/1.17 git: date: 2023-05-31 18:12:56 +0000
% 2.84/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.84/1.17 git: non_committed_changes: false
% 2.84/1.17 git: last_make_outside_of_git: false
% 2.84/1.17
% 2.84/1.17 ------ Parsing...
% 2.84/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.84/1.17
% 2.84/1.17 ------ 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
% 2.84/1.17
% 2.84/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.84/1.17
% 2.84/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.84/1.17 ------ Proving...
% 2.84/1.17 ------ Problem Properties
% 2.84/1.17
% 2.84/1.17
% 2.84/1.17 clauses 15
% 2.84/1.17 conjectures 1
% 2.84/1.17 EPR 3
% 2.84/1.17 Horn 11
% 2.84/1.17 unary 3
% 2.84/1.17 binary 6
% 2.84/1.17 lits 33
% 2.84/1.17 lits eq 5
% 2.84/1.17 fd_pure 0
% 2.84/1.17 fd_pseudo 0
% 2.84/1.17 fd_cond 0
% 2.84/1.17 fd_pseudo_cond 3
% 2.84/1.17 AC symbols 0
% 2.84/1.17
% 2.84/1.17 ------ Schedule dynamic 5 is on
% 2.84/1.17
% 2.84/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.84/1.17
% 2.84/1.17
% 2.84/1.17 ------
% 2.84/1.17 Current options:
% 2.84/1.17 ------
% 2.84/1.17
% 2.84/1.17
% 2.84/1.17
% 2.84/1.17
% 2.84/1.17 ------ Proving...
% 2.84/1.17
% 2.84/1.17
% 2.84/1.17 % SZS status Theorem for theBenchmark.p
% 2.84/1.17
% 2.84/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.84/1.18
% 2.84/1.18
%------------------------------------------------------------------------------