TSTP Solution File: SEU138+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU138+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n032.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 17:03:59 EDT 2023
% Result : Theorem 3.57s 1.03s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 7 unt; 0 def)
% Number of atoms : 244 ( 40 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 315 ( 123 ~; 135 |; 50 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 133 ( 4 sgn; 94 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f6,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(f17,conjecture,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(negated_conjecture,[],[f17]) ).
fof(f27,plain,
? [X0,X1] : set_intersection2(X0,X1) != set_difference(X0,set_difference(X0,X1)),
inference(ennf_transformation,[],[f18]) ).
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(nnf_transformation,[],[f5]) ).
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) ) ) )
& ( ! [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,[],[f37]) ).
fof(f39,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,[],[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(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(f41,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[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,[],[f6]) ).
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(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(f46,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f44,f45]) ).
fof(f51,plain,
( ? [X0,X1] : set_intersection2(X0,X1) != set_difference(X0,set_difference(X0,X1))
=> set_intersection2(sK5,sK6) != set_difference(sK5,set_difference(sK5,sK6)) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
set_intersection2(sK5,sK6) != set_difference(sK5,set_difference(sK5,sK6)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f27,f51]) ).
fof(f61,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f63,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f70,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f71,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f72,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f80,plain,
set_intersection2(sK5,sK6) != set_difference(sK5,set_difference(sK5,sK6)),
inference(cnf_transformation,[],[f52]) ).
fof(f87,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f63]) ).
fof(f88,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f62]) ).
fof(f89,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f61]) ).
fof(f90,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f69]) ).
fof(f91,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f68]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_61,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_62,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_63,plain,
( ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(X0,X1,X2),X2)
| set_difference(X0,X1) = X2
| in(sK2(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_64,plain,
( ~ in(sK2(X0,X1,X2),X1)
| set_difference(X0,X1) = X2
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f71]) ).
cnf(c_65,plain,
( set_difference(X0,X1) = X2
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f70]) ).
cnf(c_66,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_67,plain,
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_76,negated_conjecture,
set_difference(sK5,set_difference(sK5,sK6)) != set_intersection2(sK5,sK6),
inference(cnf_transformation,[],[f80]) ).
cnf(c_691,plain,
( set_difference(sK5,set_difference(sK5,sK6)) = set_intersection2(sK5,sK6)
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6))
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK5) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_692,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_difference(sK5,sK6))
| set_difference(sK5,set_difference(sK5,sK6)) = set_intersection2(sK5,sK6)
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_693,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6))
| ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK5)
| set_difference(sK5,set_difference(sK5,sK6)) = set_intersection2(sK5,sK6)
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_difference(sK5,sK6)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_733,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6))
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK5) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_734,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6))
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_767,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK5)
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_difference(sK5,X0))
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),X0) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_772,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),X0)
| ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK5)
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,X0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_830,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_difference(X0,sK6))
| ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_1278,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK5)
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_difference(sK5,sK6))
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_767]) ).
cnf(c_1559,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_difference(sK5,sK6))
| ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_830]) ).
cnf(c_1610,plain,
( ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK5)
| ~ in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),sK6)
| in(sK2(sK5,set_difference(sK5,sK6),set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6)) ),
inference(instantiation,[status(thm)],[c_772]) ).
cnf(c_1611,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1610,c_1559,c_1278,c_733,c_734,c_691,c_692,c_693,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU138+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Wed Aug 23 15:19:56 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.57/1.03 % SZS status Started for theBenchmark.p
% 3.57/1.03 % SZS status Theorem for theBenchmark.p
% 3.57/1.03
% 3.57/1.03 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.57/1.03
% 3.57/1.03 ------ iProver source info
% 3.57/1.03
% 3.57/1.03 git: date: 2023-05-31 18:12:56 +0000
% 3.57/1.03 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.57/1.03 git: non_committed_changes: false
% 3.57/1.03 git: last_make_outside_of_git: false
% 3.57/1.03
% 3.57/1.03 ------ Parsing...
% 3.57/1.03 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.57/1.03
% 3.57/1.03 ------ 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
% 3.57/1.03
% 3.57/1.03 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.57/1.03
% 3.57/1.03 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.57/1.03 ------ Proving...
% 3.57/1.03 ------ Problem Properties
% 3.57/1.03
% 3.57/1.03
% 3.57/1.03 clauses 30
% 3.57/1.03 conjectures 1
% 3.57/1.03 EPR 10
% 3.57/1.03 Horn 23
% 3.57/1.03 unary 10
% 3.57/1.03 binary 9
% 3.57/1.03 lits 63
% 3.57/1.03 lits eq 15
% 3.57/1.03 fd_pure 0
% 3.57/1.03 fd_pseudo 0
% 3.57/1.03 fd_cond 1
% 3.57/1.03 fd_pseudo_cond 8
% 3.57/1.03 AC symbols 0
% 3.57/1.03
% 3.57/1.03 ------ Input Options Time Limit: Unbounded
% 3.57/1.03
% 3.57/1.03
% 3.57/1.03 ------
% 3.57/1.03 Current options:
% 3.57/1.03 ------
% 3.57/1.03
% 3.57/1.03
% 3.57/1.03
% 3.57/1.03
% 3.57/1.03 ------ Proving...
% 3.57/1.03
% 3.57/1.03
% 3.57/1.03 % SZS status Theorem for theBenchmark.p
% 3.57/1.03
% 3.57/1.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.57/1.03
% 3.57/1.03
%------------------------------------------------------------------------------