TSTP Solution File: SEU245+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU245+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 17:05:09 EDT 2023
% Result : Theorem 2.78s 1.14s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 189 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 225 ( 84 ~; 87 |; 44 &)
% ( 4 <=>; 5 =>; 0 <=; 1 <~>)
% 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 3 sgn; 60 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f25,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(negated_conjecture,[],[f25]) ).
fof(f27,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(f42,plain,
! [X0] :
( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<~> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& relation(X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f56,plain,
? [X0,X1,X2] :
( ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1)) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| in(X0,relation_restriction(X2,X1)) )
& relation(X2) ),
inference(nnf_transformation,[],[f43]) ).
fof(f57,plain,
? [X0,X1,X2] :
( ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1)) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| in(X0,relation_restriction(X2,X1)) )
& relation(X2) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
( ? [X0,X1,X2] :
( ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1)) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| in(X0,relation_restriction(X2,X1)) )
& relation(X2) )
=> ( ( ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,sK8)
| ~ in(sK6,relation_restriction(sK8,sK7)) )
& ( ( in(sK6,cartesian_product2(sK7,sK7))
& in(sK6,sK8) )
| in(sK6,relation_restriction(sK8,sK7)) )
& relation(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( ( ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,sK8)
| ~ in(sK6,relation_restriction(sK8,sK7)) )
& ( ( in(sK6,cartesian_product2(sK7,sK7))
& in(sK6,sK8) )
| in(sK6,relation_restriction(sK8,sK7)) )
& relation(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f57,f58]) ).
fof(f60,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,[],[f27]) ).
fof(f61,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,[],[f60]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(sK9(X0,X1,X2),X1)
& in(sK9(X0,X1,X2),X0) )
| in(sK9(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(sK9(X0,X1,X2),X1)
& in(sK9(X0,X1,X2),X0) )
| in(sK9(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,[sK9])],[f62,f63]) ).
fof(f83,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f89,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f90,plain,
relation(sK8),
inference(cnf_transformation,[],[f59]) ).
fof(f91,plain,
( in(sK6,sK8)
| in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f92,plain,
( in(sK6,cartesian_product2(sK7,sK7))
| in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f93,plain,
( ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,sK8)
| ~ in(sK6,relation_restriction(sK8,sK7)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f94,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f95,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f96,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f100,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f96]) ).
fof(f101,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f95]) ).
fof(f102,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f94]) ).
cnf(c_65,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f83]) ).
cnf(c_71,plain,
( ~ relation(X0)
| set_intersection2(X0,cartesian_product2(X1,X1)) = relation_restriction(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_72,negated_conjecture,
( ~ in(sK6,relation_restriction(sK8,sK7))
| ~ in(sK6,cartesian_product2(sK7,sK7))
| ~ in(sK6,sK8) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_73,negated_conjecture,
( in(sK6,relation_restriction(sK8,sK7))
| in(sK6,cartesian_product2(sK7,sK7)) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_74,negated_conjecture,
( in(sK6,relation_restriction(sK8,sK7))
| in(sK6,sK8) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_75,negated_conjecture,
relation(sK8),
inference(cnf_transformation,[],[f90]) ).
cnf(c_79,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f100]) ).
cnf(c_80,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_81,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_885,plain,
set_intersection2(sK8,cartesian_product2(X0,X0)) = relation_restriction(sK8,X0),
inference(superposition,[status(thm)],[c_75,c_71]) ).
cnf(c_967,plain,
( ~ in(X0,relation_restriction(sK8,X1))
| in(X0,sK8) ),
inference(superposition,[status(thm)],[c_885,c_81]) ).
cnf(c_968,plain,
( ~ in(X0,relation_restriction(sK8,X1))
| in(X0,cartesian_product2(X1,X1)) ),
inference(superposition,[status(thm)],[c_885,c_80]) ).
cnf(c_983,plain,
in(sK6,sK8),
inference(backward_subsumption_resolution,[status(thm)],[c_74,c_967]) ).
cnf(c_984,plain,
( ~ in(sK6,relation_restriction(sK8,sK7))
| ~ in(sK6,cartesian_product2(sK7,sK7)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_72,c_967]) ).
cnf(c_1018,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ),
inference(superposition,[status(thm)],[c_65,c_79]) ).
cnf(c_1340,plain,
in(sK6,cartesian_product2(sK7,sK7)),
inference(backward_subsumption_resolution,[status(thm)],[c_73,c_968]) ).
cnf(c_1341,plain,
~ in(sK6,relation_restriction(sK8,sK7)),
inference(backward_subsumption_resolution,[status(thm)],[c_984,c_968]) ).
cnf(c_2078,plain,
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,sK8)
| in(X0,relation_restriction(sK8,X1)) ),
inference(superposition,[status(thm)],[c_885,c_1018]) ).
cnf(c_2386,plain,
( ~ in(sK6,sK8)
| in(sK6,relation_restriction(sK8,sK7)) ),
inference(superposition,[status(thm)],[c_1340,c_2078]) ).
cnf(c_2401,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2386,c_1341,c_983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU245+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 01:10:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.78/1.14 % SZS status Started for theBenchmark.p
% 2.78/1.14 % SZS status Theorem for theBenchmark.p
% 2.78/1.14
% 2.78/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.78/1.14
% 2.78/1.14 ------ iProver source info
% 2.78/1.14
% 2.78/1.14 git: date: 2023-05-31 18:12:56 +0000
% 2.78/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.78/1.14 git: non_committed_changes: false
% 2.78/1.14 git: last_make_outside_of_git: false
% 2.78/1.14
% 2.78/1.14 ------ Parsing...
% 2.78/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.78/1.14
% 2.78/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 2.78/1.14
% 2.78/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.78/1.14
% 2.78/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.78/1.14 ------ Proving...
% 2.78/1.14 ------ Problem Properties
% 2.78/1.14
% 2.78/1.14
% 2.78/1.14 clauses 27
% 2.78/1.14 conjectures 4
% 2.78/1.14 EPR 12
% 2.78/1.14 Horn 22
% 2.78/1.14 unary 11
% 2.78/1.14 binary 10
% 2.78/1.14 lits 50
% 2.78/1.14 lits eq 9
% 2.78/1.14 fd_pure 0
% 2.78/1.14 fd_pseudo 0
% 2.78/1.14 fd_cond 1
% 2.78/1.14 fd_pseudo_cond 4
% 2.78/1.14 AC symbols 0
% 2.78/1.14
% 2.78/1.14 ------ Schedule dynamic 5 is on
% 2.78/1.14
% 2.78/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.78/1.14
% 2.78/1.14
% 2.78/1.14 ------
% 2.78/1.14 Current options:
% 2.78/1.14 ------
% 2.78/1.14
% 2.78/1.14
% 2.78/1.14
% 2.78/1.14
% 2.78/1.14 ------ Proving...
% 2.78/1.14
% 2.78/1.14
% 2.78/1.14 % SZS status Theorem for theBenchmark.p
% 2.78/1.14
% 2.78/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.78/1.14
% 2.78/1.14
%------------------------------------------------------------------------------