TSTP Solution File: SET800+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 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 15:09:54 EDT 2023
% Result : Theorem 2.87s 1.14s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 13 unt; 0 def)
% Number of atoms : 216 ( 8 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 230 ( 69 ~; 51 |; 82 &)
% ( 7 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 175 ( 11 sgn; 102 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f15,axiom,
! [X5,X3,X7] :
( lower_bound(X7,X5,X3)
<=> ! [X2] :
( member(X2,X3)
=> apply(X5,X7,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_bound) ).
fof(f21,axiom,
! [X0,X2,X5,X3] :
( greatest_lower_bound(X0,X2,X5,X3)
<=> ( ! [X7] :
( ( lower_bound(X7,X5,X2)
& member(X7,X3) )
=> apply(X5,X7,X0) )
& lower_bound(X0,X5,X2)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest_lower_bound) ).
fof(f22,conjecture,
! [X5,X3] :
( order(X5,X3)
=> ! [X8,X9] :
( ( subset(X8,X9)
& subset(X9,X3)
& subset(X8,X3) )
=> ! [X10,X11] :
( ( greatest_lower_bound(X11,X9,X5,X3)
& greatest_lower_bound(X10,X8,X5,X3) )
=> apply(X5,X11,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV12) ).
fof(f23,negated_conjecture,
~ ! [X5,X3] :
( order(X5,X3)
=> ! [X8,X9] :
( ( subset(X8,X9)
& subset(X9,X3)
& subset(X8,X3) )
=> ! [X10,X11] :
( ( greatest_lower_bound(X11,X9,X5,X3)
& greatest_lower_bound(X10,X8,X5,X3) )
=> apply(X5,X11,X10) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f36,plain,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ),
inference(rectify,[],[f15]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( ( lower_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f43,plain,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4,X5] :
( ( greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
=> apply(X0,X5,X4) ) ) ),
inference(rectify,[],[f23]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
=> ( ! [X4] :
( ( lower_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f50,plain,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( apply(X2,X4,X0)
| ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3) )
& lower_bound(X0,X2,X1)
& member(X0,X1) )
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f44]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( apply(X2,X4,X0)
| ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3) )
& lower_bound(X0,X2,X1)
& member(X0,X1) )
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X5,X4)
& greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f54,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X5,X4)
& greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f56,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f56,f57]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( lower_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) )
| ~ lower_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( lower_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ! [X4] :
( apply(X0,X2,X4)
| ~ member(X4,X1) )
| ~ lower_bound(X2,X0,X1) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) )
=> ( ~ apply(X0,X2,sK3(X0,X1,X2))
& member(sK3(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( lower_bound(X2,X0,X1)
| ( ~ apply(X0,X2,sK3(X0,X1,X2))
& member(sK3(X0,X1,X2),X1) ) )
& ( ! [X4] :
( apply(X0,X2,X4)
| ~ member(X4,X1) )
| ~ lower_bound(X2,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f78,f79]) ).
fof(f81,plain,
( ? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X5,X4)
& greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) )
=> ( ? [X3,X2] :
( ? [X5,X4] :
( ~ apply(sK4,X5,X4)
& greatest_lower_bound(X5,X3,sK4,sK5)
& greatest_lower_bound(X4,X2,sK4,sK5) )
& subset(X2,X3)
& subset(X3,sK5)
& subset(X2,sK5) )
& order(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( ? [X3,X2] :
( ? [X5,X4] :
( ~ apply(sK4,X5,X4)
& greatest_lower_bound(X5,X3,sK4,sK5)
& greatest_lower_bound(X4,X2,sK4,sK5) )
& subset(X2,X3)
& subset(X3,sK5)
& subset(X2,sK5) )
=> ( ? [X5,X4] :
( ~ apply(sK4,X5,X4)
& greatest_lower_bound(X5,sK7,sK4,sK5)
& greatest_lower_bound(X4,sK6,sK4,sK5) )
& subset(sK6,sK7)
& subset(sK7,sK5)
& subset(sK6,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( ? [X5,X4] :
( ~ apply(sK4,X5,X4)
& greatest_lower_bound(X5,sK7,sK4,sK5)
& greatest_lower_bound(X4,sK6,sK4,sK5) )
=> ( ~ apply(sK4,sK9,sK8)
& greatest_lower_bound(sK9,sK7,sK4,sK5)
& greatest_lower_bound(sK8,sK6,sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ~ apply(sK4,sK9,sK8)
& greatest_lower_bound(sK9,sK7,sK4,sK5)
& greatest_lower_bound(sK8,sK6,sK4,sK5)
& subset(sK6,sK7)
& subset(sK7,sK5)
& subset(sK6,sK5)
& order(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9])],[f54,f83,f82,f81]) ).
fof(f85,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f114,plain,
! [X2,X0,X1,X4] :
( apply(X0,X2,X4)
| ~ member(X4,X1)
| ~ lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( lower_bound(X0,X2,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f123,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f84]) ).
fof(f124,plain,
greatest_lower_bound(sK8,sK6,sK4,sK5),
inference(cnf_transformation,[],[f84]) ).
fof(f125,plain,
greatest_lower_bound(sK9,sK7,sK4,sK5),
inference(cnf_transformation,[],[f84]) ).
fof(f126,plain,
~ apply(sK4,sK9,sK8),
inference(cnf_transformation,[],[f84]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_80,plain,
( ~ lower_bound(X0,X1,X2)
| ~ member(X3,X2)
| apply(X1,X0,X3) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_82,plain,
( ~ greatest_lower_bound(X0,X1,X2,X3)
| lower_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_83,plain,
( ~ greatest_lower_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_84,negated_conjecture,
~ apply(sK4,sK9,sK8),
inference(cnf_transformation,[],[f126]) ).
cnf(c_85,negated_conjecture,
greatest_lower_bound(sK9,sK7,sK4,sK5),
inference(cnf_transformation,[],[f125]) ).
cnf(c_86,negated_conjecture,
greatest_lower_bound(sK8,sK6,sK4,sK5),
inference(cnf_transformation,[],[f124]) ).
cnf(c_87,negated_conjecture,
subset(sK6,sK7),
inference(cnf_transformation,[],[f123]) ).
cnf(c_136,plain,
( member(X0,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_137,plain,
( ~ greatest_lower_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(renaming,[status(thm)],[c_136]) ).
cnf(c_168,plain,
( ~ greatest_lower_bound(X0,X1,X2,X3)
| lower_bound(X0,X2,X1) ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
cnf(c_623,plain,
( X0 != sK9
| X1 != sK7
| X2 != sK4
| X3 != sK5
| lower_bound(X0,X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_168,c_85]) ).
cnf(c_624,plain,
lower_bound(sK9,sK4,sK7),
inference(unflattening,[status(thm)],[c_623]) ).
cnf(c_640,plain,
( X0 != sK8
| X1 != sK6
| X2 != sK4
| X3 != sK5
| member(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_137,c_86]) ).
cnf(c_641,plain,
member(sK8,sK6),
inference(unflattening,[status(thm)],[c_640]) ).
cnf(c_2005,plain,
( ~ subset(sK6,X0)
| member(sK8,X0) ),
inference(superposition,[status(thm)],[c_641,c_51]) ).
cnf(c_2114,plain,
member(sK8,sK7),
inference(superposition,[status(thm)],[c_87,c_2005]) ).
cnf(c_2565,plain,
( ~ member(X0,sK7)
| apply(sK4,sK9,X0) ),
inference(superposition,[status(thm)],[c_624,c_80]) ).
cnf(c_2720,plain,
~ member(sK8,sK7),
inference(superposition,[status(thm)],[c_2565,c_84]) ).
cnf(c_2723,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2720,c_2114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 09:43:48 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.87/1.14 % SZS status Started for theBenchmark.p
% 2.87/1.14 % SZS status Theorem for theBenchmark.p
% 2.87/1.14
% 2.87/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.87/1.14
% 2.87/1.14 ------ iProver source info
% 2.87/1.14
% 2.87/1.14 git: date: 2023-05-31 18:12:56 +0000
% 2.87/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.87/1.14 git: non_committed_changes: false
% 2.87/1.14 git: last_make_outside_of_git: false
% 2.87/1.14
% 2.87/1.14 ------ Parsing...
% 2.87/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.87/1.14
% 2.87/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e
% 2.87/1.14
% 2.87/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.87/1.14
% 2.87/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.87/1.14 ------ Proving...
% 2.87/1.14 ------ Problem Properties
% 2.87/1.14
% 2.87/1.14
% 2.87/1.14 clauses 42
% 2.87/1.14 conjectures 4
% 2.87/1.14 EPR 16
% 2.87/1.14 Horn 36
% 2.87/1.14 unary 12
% 2.87/1.14 binary 18
% 2.87/1.14 lits 89
% 2.87/1.14 lits eq 4
% 2.87/1.14 fd_pure 0
% 2.87/1.14 fd_pseudo 0
% 2.87/1.14 fd_cond 0
% 2.87/1.14 fd_pseudo_cond 3
% 2.87/1.14 AC symbols 0
% 2.87/1.14
% 2.87/1.14 ------ Schedule dynamic 5 is on
% 2.87/1.14
% 2.87/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.87/1.14
% 2.87/1.14
% 2.87/1.14 ------
% 2.87/1.14 Current options:
% 2.87/1.14 ------
% 2.87/1.14
% 2.87/1.14
% 2.87/1.14
% 2.87/1.14
% 2.87/1.14 ------ Proving...
% 2.87/1.14
% 2.87/1.14
% 2.87/1.14 % SZS status Theorem for theBenchmark.p
% 2.87/1.14
% 2.87/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.87/1.14
% 2.87/1.14
%------------------------------------------------------------------------------