TSTP Solution File: SEU137+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU137+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 17:03:58 EDT 2023
% Result : Theorem 3.27s 1.18s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 5 unt; 0 def)
% Number of atoms : 239 ( 39 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 301 ( 110 ~; 125 |; 53 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 120 ( 1 sgn; 85 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f19,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,set_difference(X1,X0)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,set_difference(X1,X0)) = X1 ),
inference(negated_conjecture,[],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f33,plain,
? [X0,X1] :
( set_union2(X0,set_difference(X1,X0)) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f38]) ).
fof(f40,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(f41,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f39,f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f44,f45]) ).
fof(f54,plain,
( ? [X0,X1] :
( set_union2(X0,set_difference(X1,X0)) != X1
& subset(X0,X1) )
=> ( sK6 != set_union2(sK5,set_difference(sK6,sK5))
& subset(sK5,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
( sK6 != set_union2(sK5,set_difference(sK6,sK5))
& subset(sK5,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f33,f54]) ).
fof(f61,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f63,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f64,plain,
! [X2,X0,X1] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f65,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f82,plain,
subset(sK5,sK6),
inference(cnf_transformation,[],[f55]) ).
fof(f83,plain,
sK6 != set_union2(sK5,set_difference(sK6,sK5)),
inference(cnf_transformation,[],[f55]) ).
fof(f91,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f67]) ).
fof(f93,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f65]) ).
cnf(c_51,plain,
( ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_52,plain,
( ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_53,plain,
( set_union2(X0,X1) = X2
| in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_57,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_63,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_75,negated_conjecture,
set_union2(sK5,set_difference(sK6,sK5)) != sK6,
inference(cnf_transformation,[],[f83]) ).
cnf(c_76,negated_conjecture,
subset(sK5,sK6),
inference(cnf_transformation,[],[f82]) ).
cnf(c_346,plain,
( X0 != sK5
| X1 != sK6
| ~ in(X2,X0)
| in(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_57,c_76]) ).
cnf(c_347,plain,
( ~ in(X0,sK5)
| in(X0,sK6) ),
inference(unflattening,[status(thm)],[c_346]) ).
cnf(c_1244,plain,
( ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),set_difference(sK6,sK5))
| ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),sK6)
| set_union2(sK5,set_difference(sK6,sK5)) = sK6 ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1255,plain,
( ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),sK6)
| ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),sK5)
| set_union2(sK5,set_difference(sK6,sK5)) = sK6 ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_1310,plain,
( set_union2(sK5,set_difference(sK6,sK5)) = sK6
| in(sK0(sK5,set_difference(sK6,sK5),sK6),set_difference(sK6,sK5))
| in(sK0(sK5,set_difference(sK6,sK5),sK6),sK6)
| in(sK0(sK5,set_difference(sK6,sK5),sK6),sK5) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_1471,plain,
( ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),set_difference(sK6,sK5))
| in(sK0(sK5,set_difference(sK6,sK5),sK6),sK6) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_1897,plain,
( ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),sK6)
| in(sK0(sK5,set_difference(sK6,sK5),sK6),set_difference(sK6,X0))
| in(sK0(sK5,set_difference(sK6,sK5),sK6),X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_3158,plain,
( ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),sK5)
| in(sK0(sK5,set_difference(sK6,sK5),sK6),sK6) ),
inference(instantiation,[status(thm)],[c_347]) ).
cnf(c_8823,plain,
( ~ in(sK0(sK5,set_difference(sK6,sK5),sK6),sK6)
| in(sK0(sK5,set_difference(sK6,sK5),sK6),set_difference(sK6,sK5))
| in(sK0(sK5,set_difference(sK6,sK5),sK6),sK5) ),
inference(instantiation,[status(thm)],[c_1897]) ).
cnf(c_11387,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8823,c_3158,c_1471,c_1310,c_1255,c_1244,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU137+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n031.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 : Wed Aug 23 19:33:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.27/1.18 % SZS status Started for theBenchmark.p
% 3.27/1.18 % SZS status Theorem for theBenchmark.p
% 3.27/1.18
% 3.27/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.27/1.18
% 3.27/1.18 ------ iProver source info
% 3.27/1.18
% 3.27/1.18 git: date: 2023-05-31 18:12:56 +0000
% 3.27/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.27/1.18 git: non_committed_changes: false
% 3.27/1.18 git: last_make_outside_of_git: false
% 3.27/1.18
% 3.27/1.18 ------ Parsing...
% 3.27/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.27/1.18
% 3.27/1.18 ------ 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
% 3.27/1.18
% 3.27/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.27/1.18
% 3.27/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.27/1.18 ------ Proving...
% 3.27/1.18 ------ Problem Properties
% 3.27/1.18
% 3.27/1.18
% 3.27/1.18 clauses 30
% 3.27/1.18 conjectures 1
% 3.27/1.18 EPR 8
% 3.27/1.18 Horn 23
% 3.27/1.18 unary 9
% 3.27/1.18 binary 10
% 3.27/1.18 lits 64
% 3.27/1.18 lits eq 16
% 3.27/1.18 fd_pure 0
% 3.27/1.18 fd_pseudo 0
% 3.27/1.18 fd_cond 1
% 3.27/1.18 fd_pseudo_cond 9
% 3.27/1.18 AC symbols 0
% 3.27/1.18
% 3.27/1.18 ------ Schedule dynamic 5 is on
% 3.27/1.18
% 3.27/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.27/1.18
% 3.27/1.18
% 3.27/1.18 ------
% 3.27/1.18 Current options:
% 3.27/1.18 ------
% 3.27/1.18
% 3.27/1.18
% 3.27/1.18
% 3.27/1.18
% 3.27/1.18 ------ Proving...
% 3.27/1.18
% 3.27/1.18
% 3.27/1.18 % SZS status Theorem for theBenchmark.p
% 3.27/1.18
% 3.27/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.27/1.18
% 3.27/1.18
%------------------------------------------------------------------------------