TSTP Solution File: SEU132+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU132+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 17:03:55 EDT 2023
% Result : Theorem 0.46s 1.14s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 182 ( 16 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 223 ( 90 ~; 86 |; 37 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 111 ( 2 sgn; 74 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f10,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(negated_conjecture,[],[f10]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ~ subset(set_difference(X0,X2),set_difference(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f24,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,[],[f19]) ).
fof(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f25,f26]) ).
fof(f28,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,[],[f3]) ).
fof(f29,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,[],[f28]) ).
fof(f30,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,[],[f29]) ).
fof(f31,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(f32,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])],[f30,f31]) ).
fof(f37,plain,
( ? [X0,X1,X2] :
( ~ subset(set_difference(X0,X2),set_difference(X1,X2))
& subset(X0,X1) )
=> ( ~ subset(set_difference(sK4,sK6),set_difference(sK5,sK6))
& subset(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( ~ subset(set_difference(sK4,sK6),set_difference(sK5,sK6))
& subset(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f20,f37]) ).
fof(f40,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f53,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f38]) ).
fof(f54,plain,
~ subset(set_difference(sK4,sK6),set_difference(sK5,sK6)),
inference(cnf_transformation,[],[f38]) ).
fof(f60,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f45]) ).
fof(f61,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f44]) ).
fof(f62,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f43]) ).
cnf(c_50,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_51,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_52,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_56,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_57,plain,
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_58,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_63,negated_conjecture,
~ subset(set_difference(sK4,sK6),set_difference(sK5,sK6)),
inference(cnf_transformation,[],[f54]) ).
cnf(c_64,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f53]) ).
cnf(c_187,plain,
( set_difference(sK4,sK6) != X0
| set_difference(sK5,sK6) != X1
| in(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_51,c_63]) ).
cnf(c_188,plain,
in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),set_difference(sK4,sK6)),
inference(unflattening,[status(thm)],[c_187]) ).
cnf(c_192,plain,
( set_difference(sK4,sK6) != X0
| set_difference(sK5,sK6) != X1
| ~ in(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_50,c_63]) ).
cnf(c_193,plain,
~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),set_difference(sK5,sK6)),
inference(unflattening,[status(thm)],[c_192]) ).
cnf(c_500,plain,
in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),set_difference(sK4,sK6)),
inference(resolution,[status(thm)],[c_51,c_63]) ).
cnf(c_516,plain,
~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK6),
inference(resolution,[status(thm)],[c_57,c_500]) ).
cnf(c_547,plain,
( ~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),set_difference(sK4,sK6))
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK4) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_699,plain,
( ~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK4)
| ~ subset(sK4,X0)
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_822,plain,
( ~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),X0)
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),set_difference(X0,X1))
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),X1) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_1540,plain,
( ~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK4)
| ~ subset(sK4,sK5)
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK5) ),
inference(instantiation,[status(thm)],[c_699]) ).
cnf(c_2061,plain,
( ~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK5)
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),set_difference(sK5,X0))
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),X0) ),
inference(instantiation,[status(thm)],[c_822]) ).
cnf(c_4518,plain,
( ~ in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK5)
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),set_difference(sK5,sK6))
| in(sK0(set_difference(sK4,sK6),set_difference(sK5,sK6)),sK6) ),
inference(instantiation,[status(thm)],[c_2061]) ).
cnf(c_4519,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4518,c_1540,c_547,c_516,c_193,c_188,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU132+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 23 13:06:40 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.46/1.14 % SZS status Started for theBenchmark.p
% 0.46/1.14 % SZS status Theorem for theBenchmark.p
% 0.46/1.14
% 0.46/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.46/1.14
% 0.46/1.14 ------ iProver source info
% 0.46/1.14
% 0.46/1.14 git: date: 2023-05-31 18:12:56 +0000
% 0.46/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.46/1.14 git: non_committed_changes: false
% 0.46/1.14 git: last_make_outside_of_git: false
% 0.46/1.14
% 0.46/1.14 ------ Parsing...
% 0.46/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.46/1.14 ------ Proving...
% 0.46/1.14 ------ Problem Properties
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 clauses 21
% 0.46/1.14 conjectures 2
% 0.46/1.14 EPR 10
% 0.46/1.14 Horn 16
% 0.46/1.14 unary 8
% 0.46/1.14 binary 7
% 0.46/1.14 lits 41
% 0.46/1.14 lits eq 7
% 0.46/1.14 fd_pure 0
% 0.46/1.14 fd_pseudo 0
% 0.46/1.14 fd_cond 1
% 0.46/1.14 fd_pseudo_cond 4
% 0.46/1.14 AC symbols 0
% 0.46/1.14
% 0.46/1.14 ------ Input Options Time Limit: Unbounded
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 ------
% 0.46/1.14 Current options:
% 0.46/1.14 ------
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 ------ Proving...
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 % SZS status Theorem for theBenchmark.p
% 0.46/1.14
% 0.46/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.15
% 0.46/1.15
%------------------------------------------------------------------------------