TSTP Solution File: SET945+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% 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 15:10:46 EDT 2023
% Result : Theorem 0.49s 1.21s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 3 unt; 0 def)
% Number of atoms : 247 ( 21 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 315 ( 124 ~; 116 |; 61 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 154 ( 3 sgn; 110 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f9,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f10,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
inference(negated_conjecture,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
? [X0,X1] :
( ~ disjoint(union(X0),X1)
& ! [X2] :
( disjoint(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f20,f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK1(X0,X1),X3) )
| ~ in(sK1(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK1(X0,X1),X4) )
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK1(X0,X1),X4) )
=> ( in(sK2(X0,X1),X0)
& in(sK1(X0,X1),sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK3(X0,X5),X0)
& in(X5,sK3(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK1(X0,X1),X3) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK2(X0,X1),X0)
& in(sK1(X0,X1),sK2(X0,X1)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK3(X0,X5),X0)
& in(X5,sK3(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f24,f27,f26,f25]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK6(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f16,f33]) ).
fof(f35,plain,
( ? [X0,X1] :
( ~ disjoint(union(X0),X1)
& ! [X2] :
( disjoint(X2,X1)
| ~ in(X2,X0) ) )
=> ( ~ disjoint(union(sK7),sK8)
& ! [X2] :
( disjoint(X2,sK8)
| ~ in(X2,sK7) ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
( ~ disjoint(union(sK7),sK8)
& ! [X2] :
( disjoint(X2,sK8)
| ~ in(X2,sK7) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f17,f35]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1,X5] :
( in(X5,sK3(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X0,X1,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f55,plain,
! [X0,X1] :
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X2] :
( disjoint(X2,sK8)
| ~ in(X2,sK7) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
~ disjoint(union(sK7),sK8),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f41]) ).
fof(f60,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f40]) ).
fof(f61,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f39]) ).
fof(f63,plain,
! [X0,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f46]) ).
fof(f64,plain,
! [X0,X5] :
( in(X5,sK3(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f45]) ).
cnf(c_54,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_55,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_56,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_61,plain,
( ~ in(X0,union(X1))
| in(sK3(X1,X0),X1) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_62,plain,
( ~ in(X0,union(X1))
| in(X0,sK3(X1,X0)) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_67,plain,
( ~ in(X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_68,plain,
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_69,negated_conjecture,
~ disjoint(union(sK7),sK8),
inference(cnf_transformation,[],[f58]) ).
cnf(c_70,negated_conjecture,
( ~ in(X0,sK7)
| disjoint(X0,sK8) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_927,plain,
( in(sK6(union(sK7),sK8),set_intersection2(union(sK7),sK8))
| disjoint(union(sK7),sK8) ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_938,plain,
( ~ in(sK6(union(sK7),sK8),set_intersection2(union(sK7),sK8))
| in(sK6(union(sK7),sK8),union(sK7)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_939,plain,
( ~ in(sK6(union(sK7),sK8),set_intersection2(union(sK7),sK8))
| in(sK6(union(sK7),sK8),sK8) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_1152,plain,
( ~ in(sK6(union(sK7),sK8),union(sK7))
| in(sK6(union(sK7),sK8),sK3(sK7,sK6(union(sK7),sK8))) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_1153,plain,
( ~ in(sK6(union(sK7),sK8),union(sK7))
| in(sK3(sK7,sK6(union(sK7),sK8)),sK7) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1240,plain,
( ~ in(sK6(union(sK7),sK8),X0)
| ~ in(sK6(union(sK7),sK8),sK8)
| in(sK6(union(sK7),sK8),set_intersection2(X0,sK8)) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_2813,plain,
( ~ in(sK3(sK7,sK6(union(sK7),sK8)),sK7)
| disjoint(sK3(sK7,sK6(union(sK7),sK8)),sK8) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_3216,plain,
( ~ in(sK6(union(sK7),sK8),sK3(sK7,sK6(union(sK7),sK8)))
| ~ in(sK6(union(sK7),sK8),sK8)
| in(sK6(union(sK7),sK8),set_intersection2(sK3(sK7,sK6(union(sK7),sK8)),sK8)) ),
inference(instantiation,[status(thm)],[c_1240]) ).
cnf(c_13627,plain,
( ~ in(sK6(union(sK7),sK8),set_intersection2(sK3(sK7,sK6(union(sK7),sK8)),sK8))
| ~ disjoint(sK3(sK7,sK6(union(sK7),sK8)),sK8) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_13630,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13627,c_3216,c_2813,c_1152,c_1153,c_938,c_939,c_927,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % 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 09:57:56 EDT 2023
% 0.14/0.34 % 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
% 0.49/1.21 % SZS status Started for theBenchmark.p
% 0.49/1.21 % SZS status Theorem for theBenchmark.p
% 0.49/1.21
% 0.49/1.21 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.49/1.21
% 0.49/1.21 ------ iProver source info
% 0.49/1.21
% 0.49/1.21 git: date: 2023-05-31 18:12:56 +0000
% 0.49/1.21 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.49/1.21 git: non_committed_changes: false
% 0.49/1.21 git: last_make_outside_of_git: false
% 0.49/1.21
% 0.49/1.21 ------ Parsing...
% 0.49/1.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.49/1.21
% 0.49/1.21 ------ 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
% 0.49/1.21
% 0.49/1.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.49/1.21
% 0.49/1.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.49/1.21 ------ Proving...
% 0.49/1.21 ------ Problem Properties
% 0.49/1.21
% 0.49/1.21
% 0.49/1.21 clauses 21
% 0.49/1.21 conjectures 2
% 0.49/1.21 EPR 4
% 0.49/1.21 Horn 16
% 0.49/1.21 unary 4
% 0.49/1.21 binary 9
% 0.49/1.21 lits 48
% 0.49/1.21 lits eq 9
% 0.49/1.21 fd_pure 0
% 0.49/1.21 fd_pseudo 0
% 0.49/1.21 fd_cond 0
% 0.49/1.21 fd_pseudo_cond 6
% 0.49/1.21 AC symbols 0
% 0.49/1.21
% 0.49/1.21 ------ Schedule dynamic 5 is on
% 0.49/1.21
% 0.49/1.21 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 0.49/1.21 ------
% 0.49/1.21 Current options:
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% 0.49/1.21 ------ Proving...
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% 0.49/1.21 % SZS status Theorem for theBenchmark.p
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% 0.49/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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