TSTP Solution File: SET008+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET008+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 02:59:13 EDT 2024
% Result : Theorem 0.45s 1.15s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 20 unt; 0 def)
% Number of atoms : 135 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 63 ~; 51 |; 23 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 0-2 aty)
% Number of variables : 119 ( 14 sgn 66 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f10,conjecture,
! [X0,X1] : empty_set = intersection(difference(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] : empty_set = intersection(difference(X0,X1),X1),
inference(negated_conjecture,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0,X1] : empty_set != intersection(difference(X0,X1),X1),
inference(ennf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f18]) ).
fof(f20,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,[],[f12]) ).
fof(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f23,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])],[f21,f22]) ).
fof(f28,plain,
( ? [X0,X1] : empty_set != intersection(difference(X0,X1),X1)
=> empty_set != intersection(difference(sK2,sK3),sK3) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
empty_set != intersection(difference(sK2,sK3),sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f28]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f49,plain,
empty_set != intersection(difference(sK2,sK3),sK3),
inference(cnf_transformation,[],[f29]) ).
cnf(c_50,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_53,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_55,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f36]) ).
cnf(c_56,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_59,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f40]) ).
cnf(c_60,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_61,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_62,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_66,negated_conjecture,
intersection(difference(sK2,sK3),sK3) != empty_set,
inference(cnf_transformation,[],[f49]) ).
cnf(c_145,plain,
intersection(sK3,difference(sK2,sK3)) != empty_set,
inference(demodulation,[status(thm)],[c_66,c_59]) ).
cnf(c_545,plain,
subset(empty_set,X0),
inference(superposition,[status(thm)],[c_61,c_55]) ).
cnf(c_550,plain,
( member(sK0(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_61,c_50]) ).
cnf(c_608,plain,
( ~ subset(X0,X1)
| member(sK0(X0,X2),X1)
| subset(X0,X2) ),
inference(superposition,[status(thm)],[c_61,c_62]) ).
cnf(c_636,plain,
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(superposition,[status(thm)],[c_545,c_56]) ).
cnf(c_657,plain,
subset(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_550,c_60]) ).
cnf(c_683,plain,
subset(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_59,c_657]) ).
cnf(c_1011,plain,
( ~ member(sK0(X0,X1),X2)
| ~ subset(X0,difference(X3,X2))
| subset(X0,X1) ),
inference(superposition,[status(thm)],[c_608,c_53]) ).
cnf(c_2141,plain,
( ~ subset(intersection(X0,X1),difference(X2,X1))
| subset(intersection(X0,X1),X3) ),
inference(superposition,[status(thm)],[c_550,c_1011]) ).
cnf(c_2322,plain,
subset(intersection(difference(X0,X1),X1),X2),
inference(superposition,[status(thm)],[c_683,c_2141]) ).
cnf(c_2355,plain,
subset(intersection(X0,difference(X1,X0)),X2),
inference(demodulation,[status(thm)],[c_2322,c_59]) ).
cnf(c_2365,plain,
intersection(X0,difference(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_2355,c_636]) ).
cnf(c_2377,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_145,c_2365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET008+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.12 % Command : run_iprover %s %d THM
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 2 20:35:14 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 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
% 0.45/1.15 % SZS status Started for theBenchmark.p
% 0.45/1.15 % SZS status Theorem for theBenchmark.p
% 0.45/1.15
% 0.45/1.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.15
% 0.45/1.15 ------ iProver source info
% 0.45/1.15
% 0.45/1.15 git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.15 git: non_committed_changes: false
% 0.45/1.15
% 0.45/1.15 ------ Parsing...
% 0.45/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.45/1.15
% 0.45/1.15 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.45/1.15
% 0.45/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.15
% 0.45/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.15 ------ Proving...
% 0.45/1.15 ------ Problem Properties
% 0.45/1.15
% 0.45/1.15
% 0.45/1.15 clauses 16
% 0.45/1.15 conjectures 0
% 0.45/1.15 EPR 4
% 0.45/1.15 Horn 13
% 0.45/1.15 unary 4
% 0.45/1.15 binary 6
% 0.45/1.15 lits 34
% 0.45/1.15 lits eq 5
% 0.45/1.15 fd_pure 0
% 0.45/1.15 fd_pseudo 0
% 0.45/1.15 fd_cond 0
% 0.45/1.15 fd_pseudo_cond 3
% 0.45/1.15 AC symbols 0
% 0.45/1.15
% 0.45/1.15 ------ Schedule dynamic 5 is on
% 0.45/1.15
% 0.45/1.15 ------ no conjectures: strip conj schedule
% 0.45/1.15
% 0.45/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.45/1.15
% 0.45/1.15
% 0.45/1.15 ------
% 0.45/1.15 Current options:
% 0.45/1.15 ------
% 0.45/1.15
% 0.45/1.15
% 0.45/1.15
% 0.45/1.15
% 0.45/1.15 ------ Proving...
% 0.45/1.15
% 0.45/1.15
% 0.45/1.15 % SZS status Theorem for theBenchmark.p
% 0.45/1.15
% 0.45/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.15
% 0.45/1.15
%------------------------------------------------------------------------------