TSTP Solution File: SEU154+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU154+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 03:04:43 EDT 2024
% Result : Theorem 4.21s 1.17s
% Output : CNFRefutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 14 unt; 0 def)
% Number of atoms : 267 ( 75 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 327 ( 131 ~; 133 |; 49 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 134 ( 1 sgn 89 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,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(f7,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f19,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f24,plain,
? [X0,X1] :
( ~ disjoint(singleton(X0),X1)
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f33,f34]) ).
fof(f36,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,[],[f6]) ).
fof(f37,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,[],[f36]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) )
| in(sK2(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) )
| in(sK2(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,[sK2])],[f38,f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f42,plain,
( ? [X0,X1] :
( ~ disjoint(singleton(X0),X1)
& ~ in(X0,X1) )
=> ( ~ disjoint(singleton(sK3),sK4)
& ~ in(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
( ~ disjoint(singleton(sK3),sK4)
& ~ in(sK3,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f24,f42]) ).
fof(f53,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f64,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f65,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f67,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f41]) ).
fof(f70,plain,
~ in(sK3,sK4),
inference(cnf_transformation,[],[f43]) ).
fof(f71,plain,
~ disjoint(singleton(sK3),sK4),
inference(cnf_transformation,[],[f43]) ).
fof(f76,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f79,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f54]) ).
fof(f80,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f79]) ).
fof(f81,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f53]) ).
cnf(c_56,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f80]) ).
cnf(c_57,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_61,plain,
( ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X2)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_62,plain,
( set_intersection2(X0,X1) = X2
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_63,plain,
( set_intersection2(X0,X1) = X2
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_67,plain,
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_71,negated_conjecture,
~ disjoint(singleton(sK3),sK4),
inference(cnf_transformation,[],[f71]) ).
cnf(c_72,negated_conjecture,
~ in(sK3,sK4),
inference(cnf_transformation,[],[f70]) ).
cnf(c_77,plain,
subset(empty_set,X0),
inference(cnf_transformation,[],[f76]) ).
cnf(c_491,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_492,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_980,plain,
( set_intersection2(singleton(sK3),sK4) != empty_set
| disjoint(singleton(sK3),sK4) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_985,plain,
( sK3 != X0
| sK4 != X1
| ~ in(X0,X1)
| in(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_492]) ).
cnf(c_1008,plain,
( ~ in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3))
| ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| ~ in(sK2(singleton(sK3),sK4,empty_set),sK4)
| set_intersection2(singleton(sK3),sK4) = empty_set ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1009,plain,
( set_intersection2(singleton(sK3),sK4) = empty_set
| in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| in(sK2(singleton(sK3),sK4,empty_set),sK4) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_1010,plain,
( set_intersection2(singleton(sK3),sK4) = empty_set
| in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3))
| in(sK2(singleton(sK3),sK4,empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_1015,plain,
( ~ in(sK4,singleton(X0))
| sK4 = X0 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_1058,plain,
( ~ in(sK4,singleton(sK4))
| sK4 = sK4 ),
inference(instantiation,[status(thm)],[c_1015]) ).
cnf(c_1081,plain,
( ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| ~ subset(empty_set,X0)
| in(sK2(singleton(sK3),sK4,empty_set),X0) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_1108,plain,
( sK3 != sK2(singleton(sK3),sK4,empty_set)
| sK4 != sK4
| ~ in(sK2(singleton(sK3),sK4,empty_set),sK4)
| in(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_985]) ).
cnf(c_1193,plain,
in(sK4,singleton(sK4)),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_1196,plain,
( sK2(singleton(sK3),sK4,empty_set) != X0
| sK3 != X0
| sK3 = sK2(singleton(sK3),sK4,empty_set) ),
inference(instantiation,[status(thm)],[c_491]) ).
cnf(c_1198,plain,
in(sK3,singleton(sK3)),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_1289,plain,
( ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| ~ subset(empty_set,sK4)
| in(sK2(singleton(sK3),sK4,empty_set),sK4) ),
inference(instantiation,[status(thm)],[c_1081]) ).
cnf(c_1456,plain,
( ~ in(sK3,singleton(X0))
| sK3 = X0 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_1566,plain,
( sK2(singleton(sK3),sK4,empty_set) != sK3
| sK3 != sK3
| sK3 = sK2(singleton(sK3),sK4,empty_set) ),
inference(instantiation,[status(thm)],[c_1196]) ).
cnf(c_1663,plain,
subset(empty_set,sK4),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_1716,plain,
( ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| ~ subset(empty_set,singleton(sK3))
| in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3)) ),
inference(instantiation,[status(thm)],[c_1081]) ).
cnf(c_2088,plain,
( ~ in(sK3,singleton(sK3))
| sK3 = sK3 ),
inference(instantiation,[status(thm)],[c_1456]) ).
cnf(c_3289,plain,
( ~ in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3))
| sK2(singleton(sK3),sK4,empty_set) = sK3 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_3525,plain,
subset(empty_set,singleton(sK3)),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_4143,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3525,c_3289,c_2088,c_1716,c_1663,c_1566,c_1289,c_1198,c_1193,c_1108,c_1058,c_1008,c_1009,c_1010,c_980,c_71,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU154+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 17:54:13 EDT 2024
% 0.14/0.35 % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.21/1.17 % SZS status Started for theBenchmark.p
% 4.21/1.17 % SZS status Theorem for theBenchmark.p
% 4.21/1.17
% 4.21/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.21/1.17
% 4.21/1.17 ------ iProver source info
% 4.21/1.17
% 4.21/1.17 git: date: 2024-05-02 19:28:25 +0000
% 4.21/1.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.21/1.17 git: non_committed_changes: false
% 4.21/1.17
% 4.21/1.17 ------ Parsing...
% 4.21/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.21/1.17
% 4.21/1.17 ------ 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
% 4.21/1.17
% 4.21/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.21/1.17
% 4.21/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.21/1.17 ------ Proving...
% 4.21/1.17 ------ Problem Properties
% 4.21/1.17
% 4.21/1.17
% 4.21/1.17 clauses 27
% 4.21/1.17 conjectures 2
% 4.21/1.17 EPR 10
% 4.21/1.17 Horn 23
% 4.21/1.17 unary 10
% 4.21/1.17 binary 9
% 4.21/1.17 lits 53
% 4.21/1.17 lits eq 13
% 4.21/1.17 fd_pure 0
% 4.21/1.17 fd_pseudo 0
% 4.21/1.17 fd_cond 0
% 4.21/1.17 fd_pseudo_cond 6
% 4.21/1.17 AC symbols 0
% 4.21/1.17
% 4.21/1.17 ------ Input Options Time Limit: Unbounded
% 4.21/1.17
% 4.21/1.17
% 4.21/1.17 ------
% 4.21/1.17 Current options:
% 4.21/1.17 ------
% 4.21/1.17
% 4.21/1.17
% 4.21/1.17
% 4.21/1.17
% 4.21/1.17 ------ Proving...
% 4.21/1.17
% 4.21/1.17
% 4.21/1.17 % SZS status Theorem for theBenchmark.p
% 4.21/1.17
% 4.21/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.21/1.17
% 4.21/1.18
%------------------------------------------------------------------------------