TSTP Solution File: SET984+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 03:02:10 EDT 2024
% Result : Theorem 7.29s 1.63s
% Output : CNFRefutation 7.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 24 unt; 0 def)
% Number of atoms : 161 ( 122 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 138 ( 42 ~; 71 |; 19 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 9 sgn 62 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
<=> ( empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| empty_set = cartesian_product2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| empty_set = cartesian_product2(X0,X1) ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1)
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1)
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( ? [X0,X1,X2,X3] :
( ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1)
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> ( ( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) )
& empty_set != cartesian_product2(sK2,sK3)
& subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) )
& empty_set != cartesian_product2(sK2,sK3)
& subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f19,f27]) ).
fof(f29,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X0 ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
empty_set != cartesian_product2(sK2,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f43,plain,
( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) ),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f12]) ).
fof(f45,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0] : empty_set = cartesian_product2(X0,empty_set),
inference(equality_resolution,[],[f37]) ).
fof(f47,plain,
! [X1] : empty_set = cartesian_product2(empty_set,X1),
inference(equality_resolution,[],[f36]) ).
cnf(c_49,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f29]) ).
cnf(c_55,plain,
cartesian_product2(X0,empty_set) = empty_set,
inference(cnf_transformation,[],[f46]) ).
cnf(c_56,plain,
cartesian_product2(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f47]) ).
cnf(c_58,plain,
set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
inference(cnf_transformation,[],[f38]) ).
cnf(c_59,plain,
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X0 = empty_set
| X1 = X3
| X1 = empty_set ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_60,plain,
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X0 = X2
| X0 = empty_set
| X1 = empty_set ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_61,negated_conjecture,
( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_62,negated_conjecture,
cartesian_product2(sK2,sK3) != empty_set,
inference(cnf_transformation,[],[f42]) ).
cnf(c_63,negated_conjecture,
subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_64,plain,
subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f44]) ).
cnf(c_65,plain,
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_405,plain,
set_intersection2(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) = cartesian_product2(sK2,sK3),
inference(superposition,[status(thm)],[c_63,c_65]) ).
cnf(c_582,plain,
cartesian_product2(set_intersection2(sK2,sK4),set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3),
inference(superposition,[status(thm)],[c_58,c_405]) ).
cnf(c_1320,plain,
subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_49,c_64]) ).
cnf(c_3159,plain,
( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
| set_intersection2(sK3,sK5) = X1
| set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK2,sK4) = empty_set ),
inference(superposition,[status(thm)],[c_582,c_59]) ).
cnf(c_3285,plain,
( set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK3,sK5) = sK3
| set_intersection2(sK2,sK4) = empty_set ),
inference(equality_resolution,[status(thm)],[c_3159]) ).
cnf(c_3839,plain,
( cartesian_product2(empty_set,set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3)
| set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK3,sK5) = sK3 ),
inference(superposition,[status(thm)],[c_3285,c_582]) ).
cnf(c_3982,plain,
( set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK3,sK5) = sK3
| cartesian_product2(sK2,sK3) = empty_set ),
inference(superposition,[status(thm)],[c_3839,c_56]) ).
cnf(c_6341,plain,
( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
| set_intersection2(sK3,sK5) = X1
| set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK2,sK4) = empty_set ),
inference(superposition,[status(thm)],[c_582,c_59]) ).
cnf(c_6364,plain,
( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
| set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK2,sK4) = X0
| set_intersection2(sK2,sK4) = empty_set ),
inference(superposition,[status(thm)],[c_582,c_60]) ).
cnf(c_6414,plain,
( set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK3,sK5) = sK3
| set_intersection2(sK2,sK4) = empty_set ),
inference(equality_resolution,[status(thm)],[c_6341]) ).
cnf(c_6426,plain,
( set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK2,sK4) = empty_set
| set_intersection2(sK2,sK4) = sK2 ),
inference(equality_resolution,[status(thm)],[c_6364]) ).
cnf(c_6891,plain,
( set_intersection2(sK3,sK5) = sK3
| set_intersection2(sK3,sK5) = empty_set ),
inference(global_subsumption_just,[status(thm)],[c_6414,c_62,c_3982]) ).
cnf(c_6892,plain,
( set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK3,sK5) = sK3 ),
inference(renaming,[status(thm)],[c_6891]) ).
cnf(c_6895,plain,
( set_intersection2(sK3,sK5) = empty_set
| subset(sK3,sK5) ),
inference(superposition,[status(thm)],[c_6892,c_1320]) ).
cnf(c_6944,plain,
( set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK2,sK4) = empty_set
| subset(sK2,sK4) ),
inference(superposition,[status(thm)],[c_6426,c_1320]) ).
cnf(c_6963,plain,
( cartesian_product2(sK2,set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3)
| set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK2,sK4) = empty_set ),
inference(superposition,[status(thm)],[c_6426,c_582]) ).
cnf(c_6974,plain,
( set_intersection2(sK3,sK5) = empty_set
| set_intersection2(sK2,sK4) = empty_set ),
inference(global_subsumption_just,[status(thm)],[c_6963,c_61,c_6895,c_6944]) ).
cnf(c_6978,plain,
( set_intersection2(sK3,sK5) = empty_set
| subset(empty_set,sK4) ),
inference(superposition,[status(thm)],[c_6974,c_1320]) ).
cnf(c_6998,plain,
( cartesian_product2(empty_set,set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3)
| set_intersection2(sK3,sK5) = empty_set ),
inference(superposition,[status(thm)],[c_6974,c_582]) ).
cnf(c_7259,plain,
( set_intersection2(sK3,sK5) = empty_set
| cartesian_product2(sK2,sK3) = empty_set ),
inference(superposition,[status(thm)],[c_6998,c_56]) ).
cnf(c_7357,plain,
set_intersection2(sK3,sK5) = empty_set,
inference(global_subsumption_just,[status(thm)],[c_6978,c_62,c_7259]) ).
cnf(c_7382,plain,
cartesian_product2(set_intersection2(sK2,sK4),empty_set) = cartesian_product2(sK2,sK3),
inference(superposition,[status(thm)],[c_7357,c_582]) ).
cnf(c_7481,plain,
cartesian_product2(sK2,sK3) = empty_set,
inference(superposition,[status(thm)],[c_7382,c_55]) ).
cnf(c_7506,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7481,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.11 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n026.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 : Thu May 2 20:43:06 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 7.29/1.63 % SZS status Started for theBenchmark.p
% 7.29/1.63 % SZS status Theorem for theBenchmark.p
% 7.29/1.63
% 7.29/1.63 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.29/1.63
% 7.29/1.63 ------ iProver source info
% 7.29/1.63
% 7.29/1.63 git: date: 2024-05-02 19:28:25 +0000
% 7.29/1.63 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.29/1.63 git: non_committed_changes: false
% 7.29/1.63
% 7.29/1.63 ------ Parsing...
% 7.29/1.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.29/1.63
% 7.29/1.63 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 7.29/1.63
% 7.29/1.63 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.29/1.63
% 7.29/1.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.29/1.63 ------ Proving...
% 7.29/1.63 ------ Problem Properties
% 7.29/1.63
% 7.29/1.63
% 7.29/1.63 clauses 17
% 7.29/1.63 conjectures 3
% 7.29/1.63 EPR 5
% 7.29/1.63 Horn 14
% 7.29/1.63 unary 12
% 7.29/1.63 binary 2
% 7.29/1.63 lits 27
% 7.29/1.63 lits eq 18
% 7.29/1.63 fd_pure 0
% 7.29/1.63 fd_pseudo 0
% 7.29/1.63 fd_cond 1
% 7.29/1.63 fd_pseudo_cond 2
% 7.29/1.63 AC symbols 0
% 7.29/1.63
% 7.29/1.63 ------ Input Options Time Limit: Unbounded
% 7.29/1.63
% 7.29/1.63
% 7.29/1.63 ------
% 7.29/1.63 Current options:
% 7.29/1.63 ------
% 7.29/1.63
% 7.29/1.63
% 7.29/1.63
% 7.29/1.63
% 7.29/1.63 ------ Proving...
% 7.29/1.63
% 7.29/1.63
% 7.29/1.63 % SZS status Theorem for theBenchmark.p
% 7.29/1.63
% 7.29/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.29/1.63
% 7.29/1.63
%------------------------------------------------------------------------------