TSTP Solution File: SEU328+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU328+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.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 03:05:30 EDT 2024
% Result : Theorem 24.15s 4.14s
% Output : CNFRefutation 24.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 78 ( 29 unt; 0 def)
% Number of atoms : 147 ( 68 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 127 ( 58 ~; 43 |; 11 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 107 ( 1 sgn 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f18,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f27,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f29,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f44,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f45,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f47,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f48,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f53,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f61,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f47]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f89,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f92,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f95,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f104,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f44]) ).
fof(f105,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f45]) ).
fof(f106,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f107,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f109,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f108]) ).
fof(f113,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f114,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f115,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f114]) ).
fof(f130,plain,
( ? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& empty_set != X1
& element(X1,powerset(powerset(X0))) )
=> ( union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,meet_of_subsets(sK4,sK5))
& empty_set != sK5
& element(sK5,powerset(powerset(sK4))) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
( union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,meet_of_subsets(sK4,sK5))
& empty_set != sK5
& element(sK5,powerset(powerset(sK4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f109,f130]) ).
fof(f157,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f17]) ).
fof(f158,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f162,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f164,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f200,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f104]) ).
fof(f201,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f105]) ).
fof(f202,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f203,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f61]) ).
fof(f204,plain,
element(sK5,powerset(powerset(sK4))),
inference(cnf_transformation,[],[f131]) ).
fof(f205,plain,
empty_set != sK5,
inference(cnf_transformation,[],[f131]) ).
fof(f206,plain,
union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,meet_of_subsets(sK4,sK5)),
inference(cnf_transformation,[],[f131]) ).
fof(f210,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f211,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_74,plain,
cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f157]) ).
cnf(c_75,plain,
( ~ element(X0,powerset(X1))
| subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_79,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_81,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_117,plain,
( ~ element(X0,powerset(powerset(X1)))
| union_of_subsets(X1,X0) = union(X0) ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_118,plain,
( ~ element(X0,powerset(powerset(X1)))
| meet_of_subsets(X1,X0) = set_meet(X0) ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_119,plain,
( ~ element(X0,powerset(X1))
| ~ element(X2,powerset(X1))
| subset_difference(X1,X0,X2) = set_difference(X0,X2) ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_120,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f203]) ).
cnf(c_121,negated_conjecture,
subset_complement(sK4,meet_of_subsets(sK4,sK5)) != union_of_subsets(sK4,complements_of_subsets(sK4,sK5)),
inference(cnf_transformation,[],[f206]) ).
cnf(c_122,negated_conjecture,
empty_set != sK5,
inference(cnf_transformation,[],[f205]) ).
cnf(c_123,negated_conjecture,
element(sK5,powerset(powerset(sK4))),
inference(cnf_transformation,[],[f204]) ).
cnf(c_127,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_128,plain,
( ~ element(X0,powerset(powerset(X1)))
| subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0))
| X0 = empty_set ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_217,plain,
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_127]) ).
cnf(c_218,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(renaming,[status(thm)],[c_217]) ).
cnf(c_296,plain,
( X0 != X1
| X0 != X2
| element(X1,powerset(X2)) ),
inference(resolution_lifted,[status(thm)],[c_120,c_218]) ).
cnf(c_297,plain,
element(X0,powerset(X0)),
inference(unflattening,[status(thm)],[c_296]) ).
cnf(c_910,plain,
meet_of_subsets(sK4,sK5) = set_meet(sK5),
inference(superposition,[status(thm)],[c_123,c_118]) ).
cnf(c_929,plain,
union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,set_meet(sK5)),
inference(demodulation,[status(thm)],[c_121,c_910]) ).
cnf(c_1017,plain,
( ~ element(X0,powerset(powerset(X1)))
| union_of_subsets(X1,complements_of_subsets(X1,X0)) = union(complements_of_subsets(X1,X0)) ),
inference(superposition,[status(thm)],[c_81,c_117]) ).
cnf(c_1056,plain,
( ~ element(X0,powerset(powerset(X1)))
| subset_complement(X1,meet_of_subsets(X1,X0)) = set_difference(X1,meet_of_subsets(X1,X0)) ),
inference(superposition,[status(thm)],[c_79,c_75]) ).
cnf(c_1231,plain,
( ~ element(X0,powerset(X1))
| subset_difference(X1,X1,X0) = set_difference(X1,X0) ),
inference(superposition,[status(thm)],[c_297,c_119]) ).
cnf(c_1321,plain,
( subset_difference(sK4,cast_to_subset(sK4),meet_of_subsets(sK4,sK5)) = union_of_subsets(sK4,complements_of_subsets(sK4,sK5))
| empty_set = sK5 ),
inference(superposition,[status(thm)],[c_123,c_128]) ).
cnf(c_1323,plain,
subset_difference(sK4,cast_to_subset(sK4),meet_of_subsets(sK4,sK5)) = union_of_subsets(sK4,complements_of_subsets(sK4,sK5)),
inference(global_subsumption_just,[status(thm)],[c_1321,c_122,c_1321]) ).
cnf(c_1325,plain,
subset_difference(sK4,sK4,meet_of_subsets(sK4,sK5)) = union_of_subsets(sK4,complements_of_subsets(sK4,sK5)),
inference(demodulation,[status(thm)],[c_1323,c_74]) ).
cnf(c_1326,plain,
union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) = subset_difference(sK4,sK4,set_meet(sK5)),
inference(light_normalisation,[status(thm)],[c_1325,c_910]) ).
cnf(c_2231,plain,
( ~ element(sK5,powerset(powerset(sK4)))
| element(set_meet(sK5),powerset(sK4)) ),
inference(superposition,[status(thm)],[c_910,c_79]) ).
cnf(c_2233,plain,
element(set_meet(sK5),powerset(sK4)),
inference(global_subsumption_just,[status(thm)],[c_2231,c_123,c_2231]) ).
cnf(c_3647,plain,
union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) = union(complements_of_subsets(sK4,sK5)),
inference(superposition,[status(thm)],[c_123,c_1017]) ).
cnf(c_3679,plain,
subset_difference(sK4,sK4,set_meet(sK5)) = union(complements_of_subsets(sK4,sK5)),
inference(demodulation,[status(thm)],[c_1326,c_3647]) ).
cnf(c_3680,plain,
subset_complement(sK4,set_meet(sK5)) != union(complements_of_subsets(sK4,sK5)),
inference(demodulation,[status(thm)],[c_929,c_3647]) ).
cnf(c_4133,plain,
subset_complement(sK4,meet_of_subsets(sK4,sK5)) = set_difference(sK4,meet_of_subsets(sK4,sK5)),
inference(superposition,[status(thm)],[c_123,c_1056]) ).
cnf(c_4138,plain,
subset_complement(sK4,set_meet(sK5)) = set_difference(sK4,set_meet(sK5)),
inference(light_normalisation,[status(thm)],[c_4133,c_910]) ).
cnf(c_11042,plain,
subset_difference(sK4,sK4,set_meet(sK5)) = set_difference(sK4,set_meet(sK5)),
inference(superposition,[status(thm)],[c_2233,c_1231]) ).
cnf(c_11058,plain,
set_difference(sK4,set_meet(sK5)) = union(complements_of_subsets(sK4,sK5)),
inference(light_normalisation,[status(thm)],[c_11042,c_3679]) ).
cnf(c_11080,plain,
subset_complement(sK4,set_meet(sK5)) = union(complements_of_subsets(sK4,sK5)),
inference(demodulation,[status(thm)],[c_4138,c_11058]) ).
cnf(c_11082,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11080,c_3680]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU328+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 17:37:25 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.15/4.14 % SZS status Started for theBenchmark.p
% 24.15/4.14 % SZS status Theorem for theBenchmark.p
% 24.15/4.14
% 24.15/4.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.15/4.14
% 24.15/4.14 ------ iProver source info
% 24.15/4.14
% 24.15/4.14 git: date: 2024-05-02 19:28:25 +0000
% 24.15/4.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 24.15/4.14 git: non_committed_changes: false
% 24.15/4.14
% 24.15/4.14 ------ Parsing...
% 24.15/4.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 24.15/4.14
% 24.15/4.14 ------ Preprocessing... sf_s rm: 41 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 6 0s sf_e pe_s pe_e
% 24.15/4.14
% 24.15/4.14 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e
% 24.15/4.14
% 24.15/4.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.15/4.14 ------ Proving...
% 24.15/4.14 ------ Problem Properties
% 24.15/4.14
% 24.15/4.14
% 24.15/4.14 clauses 37
% 24.15/4.14 conjectures 3
% 24.15/4.14 EPR 10
% 24.15/4.14 Horn 34
% 24.15/4.14 unary 14
% 24.15/4.14 binary 16
% 24.15/4.14 lits 67
% 24.15/4.14 lits eq 15
% 24.15/4.14 fd_pure 0
% 24.15/4.14 fd_pseudo 0
% 24.15/4.14 fd_cond 2
% 24.15/4.14 fd_pseudo_cond 1
% 24.15/4.14 AC symbols 0
% 24.15/4.14
% 24.15/4.14 ------ Input Options Time Limit: Unbounded
% 24.15/4.14
% 24.15/4.14
% 24.15/4.14 ------
% 24.15/4.14 Current options:
% 24.15/4.14 ------
% 24.15/4.14
% 24.15/4.14
% 24.15/4.14
% 24.15/4.14
% 24.15/4.14 ------ Proving...
% 24.15/4.14
% 24.15/4.14
% 24.15/4.14 % SZS status Theorem for theBenchmark.p
% 24.15/4.14
% 24.15/4.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.15/4.14
% 24.15/4.15
%------------------------------------------------------------------------------